ChemWiki - User contributions [en]

User:Tc1812

2015-03-27T11:57:31Z

Tc1812: /* Transition Structures of Chair and Boat Conformation */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ' 'Chair' ' and ' 'Boat' ' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''' 'Chair' '''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

'''IRC(Intrinsic Reaction Coordinate)'''

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 Reaction pathway from IRC
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC, the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry. The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway. The direction of path Two approaches were tries. The first approach is that last point on the IRC was optimised at HF/3-21G theory. The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure, geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition Structure of Diels Alder Reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.41,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AM1 was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene is symmetry while the LUMO of ethene is anti-symmetry with respective to the plane. In contrast ,the LUMO of butadiene is symmetry and the HOMO of butadiene is anti-symmetry with respective to plane.
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-31G*
|-
| HF/6-31G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which is relevant transition structure. The animation from table 11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on former one.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene). Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å, which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped. In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ' ' endo ' ' and ' ' exo ' '. Each transition structure will result in different stereoisomers. These names are due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed . If they are on the same side, the product is endo . If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure was optimised at HF/3-21G level of theory and 6-31G* level of theory, respectively, from the guess transition structure.' ' Endo ' ' transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory, respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction. HOMO, LUMO of transition structures are represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition Structure of Endo and Exo Reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

'''Activation Energy of ' 'exo' ' and ' 'endo' ' product'''

{| class="wikitable" border="1"
|+ Table 13 energy of Endo and Exo Reaction
|-
| ||Cyclohexadiene/Hartrees|| Maleic Anhydride/Hartrees ||Endo Transition Structure/Hartrees || Exo Transition Structure/Hartrees ||Activation Energy of Endo/Hartrees ||Activation Energy of Exo/Hartrees ||Activation Energy of Endo(kcal/Mol) ||Activation Energy of Exo (kcal/Mol)
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G*||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result, which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however, secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster. Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system. Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software . In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation. As for the section about Diels Alder reaction, the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:55:59Z

Tc1812: /* Regioselectivity of the Diels Alder Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

'''IRC(Intrinsic Reaction Coordinate)'''

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 Reaction pathway from IRC
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC, the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry. The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway. The direction of path Two approaches were tries. The first approach is that last point on the IRC was optimised at HF/3-21G theory. The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure, geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition Structure of Diels Alder Reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.41,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AM1 was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene is symmetry while the LUMO of ethene is anti-symmetry with respective to the plane. In contrast ,the LUMO of butadiene is symmetry and the HOMO of butadiene is anti-symmetry with respective to plane.
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-31G*
|-
| HF/6-31G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which is relevant transition structure. The animation from table 11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on former one.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene). Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å, which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped. In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ' ' endo ' ' and ' ' exo ' '. Each transition structure will result in different stereoisomers. These names are due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed . If they are on the same side, the product is endo . If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure was optimised at HF/3-21G level of theory and 6-31G* level of theory, respectively, from the guess transition structure.' ' Endo ' ' transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory, respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction. HOMO, LUMO of transition structures are represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition Structure of Endo and Exo Reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

'''Activation Energy of ' 'exo' ' and ' 'endo' ' product'''

{| class="wikitable" border="1"
|+ Table 13 energy of Endo and Exo Reaction
|-
| ||Cyclohexadiene/Hartrees|| Maleic Anhydride/Hartrees ||Endo Transition Structure/Hartrees || Exo Transition Structure/Hartrees ||Activation Energy of Endo/Hartrees ||Activation Energy of Exo/Hartrees ||Activation Energy of Endo(kcal/Mol) ||Activation Energy of Exo (kcal/Mol)
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G*||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result, which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however, secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster. Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system. Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software . In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation. As for the section about Diels Alder reaction, the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:53:35Z

Tc1812: /* Regioselectivity of the Diels Alder Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

'''IRC(Intrinsic Reaction Coordinate)'''

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 Reaction pathway from IRC
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC, the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry. The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway. The direction of path Two approaches were tries. The first approach is that last point on the IRC was optimised at HF/3-21G theory. The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure, geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition Structure of Diels Alder Reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.41,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AM1 was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene is symmetry while the LUMO of ethene is anti-symmetry with respective to the plane. In contrast ,the LUMO of butadiene is symmetry and the HOMO of butadiene is anti-symmetry with respective to plane.
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-31G*
|-
| HF/6-31G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which is relevant transition structure. The animation from table 11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on former one.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene). Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å, which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped. In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ' ' endo ' ' and ' ' exo ' '. Each transition structure will result in different stereoisomers. These names are due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed . If they are on the same side, the product is endo . If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure was optimised at HF/3-21G level of theory and 6-31G* level of theory, respectively, from the guess transition structure.' ' Endo ' ' transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory, respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction. HOMO,LUMO of transition structures are represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition Structure of Endo and Exo Reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

'''Activation Energy of ' 'exo' ' and ' 'endo' ' product'''

{| class="wikitable" border="1"
|+ Table 13 energy of Endo and Exo Reaction
|-
| ||Cyclohexadiene/Hartrees|| Maleic Anhydride/Hartrees ||Endo Transition Structure/Hartrees || Exo Transition Structure/Hartrees ||Activation Energy of Endo/Hartrees ||Activation Energy of Exo/Hartrees ||Activation Energy of Endo(kcal/Mol) ||Activation Energy of Exo (kcal/Mol)
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G*||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result, which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however, secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster. Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system. Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software . In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation. As for the section about Diels Alder reaction, the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:52:52Z

Tc1812: /* Transition State for Prototype Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

'''IRC(Intrinsic Reaction Coordinate)'''

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 Reaction pathway from IRC
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC, the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry. The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway. The direction of path Two approaches were tries. The first approach is that last point on the IRC was optimised at HF/3-21G theory. The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure, geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition Structure of Diels Alder Reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.41,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AM1 was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene is symmetry while the LUMO of ethene is anti-symmetry with respective to the plane. In contrast ,the LUMO of butadiene is symmetry and the HOMO of butadiene is anti-symmetry with respective to plane.
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-31G*
|-
| HF/6-31G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which is relevant transition structure. The animation from table 11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on former one.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene). Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å, which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped. In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ' ' endo ' ' and ' ' exo ' '. Each transition structure will result in different stereoisomers. These names are due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed . If they are on the same side, the product is endo . If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure was optimised at HF/3-21G level of theory and 6-31G* level of theory, respectively, from the guess transition structure.' ' Endo ' ' transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory, respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction. HOMO,LUMO of transition structures are represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition Structure of Endo and Exo Reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

'''Activation Energy of ' 'exo' ' and ' 'endo' ' product'''

{| class="wikitable" border="1"
|+ Table 13 energy of Endo and Exo Reaction
|-
| ||Cyclohexadiene/Hartrees|| Maleic Anhydride/Hartrees ||Endo Transition Structure/Hartrees || Exo Transition Structure/Hartrees ||Activation Energy of Endo/Hartrees ||Activation Energy of Exo/Hartrees ||Activation Energy of Endo(kcal/Mol) ||Activation Energy of Exo (kcal/Mol)
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result, which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however, secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster. Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system. Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software . In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation. As for the section about Diels Alder reaction, the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:52:37Z

Tc1812: /* Transition State for Prototype Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

'''IRC(Intrinsic Reaction Coordinate)'''

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 Reaction pathway from IRC
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC, the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry. The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway. The direction of path Two approaches were tries. The first approach is that last point on the IRC was optimised at HF/3-21G theory. The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure, geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition Structure of Diels Alder Reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.41,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AM1 was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene is symmetry while the LUMO of ethene is anti-symmetry with respective to the plane. In contrast ,the LUMO of butadiene is symmetry and the HOMO of butadiene is anti-symmetry with respective to plane.
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-31G*
|-
| HF/6-31G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which is relevant transition structure. The animation from table 11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on former one.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene). Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å, which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped. In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ' ' endo ' ' and ' ' exo ' '. Each transition structure will result in different stereoisomers. These names are due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed . If they are on the same side, the product is endo . If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure was optimised at HF/3-21G level of theory and 6-31G* level of theory, respectively, from the guess transition structure.' ' Endo ' ' transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory, respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction. HOMO,LUMO of transition structures are represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition Structure of Endo and Exo Reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

'''Activation Energy of ' 'exo' ' and ' 'endo' ' product'''

{| class="wikitable" border="1"
|+ Table 13 energy of Endo and Exo Reaction
|-
| ||Cyclohexadiene/Hartrees|| Maleic Anhydride/Hartrees ||Endo Transition Structure/Hartrees || Exo Transition Structure/Hartrees ||Activation Energy of Endo/Hartrees ||Activation Energy of Exo/Hartrees ||Activation Energy of Endo(kcal/Mol) ||Activation Energy of Exo (kcal/Mol)
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result, which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however, secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster. Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system. Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software . In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation. As for the section about Diels Alder reaction, the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:49:49Z

Tc1812: /* Regioselectivity of the Diels Alder Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

'''IRC(Intrinsic Reaction Coordinate)'''

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 Reaction pathway from IRC
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC, the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry. The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway. The direction of path Two approaches were tries. The first approach is that last point on the IRC was optimised at HF/3-21G theory. The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure, geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition Structure of Diels Alder Reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.41,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AM1 was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane. In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-31G*
|-
| HF/6-31G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which is relevant transition structure. The animation from table 11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on former one.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene). Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å, which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped. In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ' ' endo ' ' and ' ' exo ' '. Each transition structure will result in different stereoisomers. These names are due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed . If they are on the same side, the product is endo . If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure was optimised at HF/3-21G level of theory and 6-31G* level of theory, respectively, from the guess transition structure.' ' Endo ' ' transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory, respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction. HOMO,LUMO of transition structures are represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition Structure of Endo and Exo Reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

'''Activation Energy of ' 'exo' ' and ' 'endo' ' product'''

{| class="wikitable" border="1"
|+ Table 13 energy of Endo and Exo Reaction
|-
| ||Cyclohexadiene/Hartrees|| Maleic Anhydride/Hartrees ||Endo Transition Structure/Hartrees || Exo Transition Structure/Hartrees ||Activation Energy of Endo/Hartrees ||Activation Energy of Exo/Hartrees ||Activation Energy of Endo(kcal/Mol) ||Activation Energy of Exo (kcal/Mol)
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result, which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however, secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster. Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system. Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software . In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation. As for the section about Diels Alder reaction, the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:46:15Z

Tc1812: /* Regioselectivity of the Diels Alder Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

'''IRC(Intrinsic Reaction Coordinate)'''

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 Reaction pathway from IRC
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC, the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry. The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway. The direction of path Two approaches were tries. The first approach is that last point on the IRC was optimised at HF/3-21G theory. The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure, geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition Structure of Diels Alder Reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.41,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AM1 was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane. In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-31G*
|-
| HF/6-31G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which is relevant transition structure. The animation from table 11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on former one.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene). Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å, which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped. In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ' ' endo ' ' and ' ' exo ' '. Each transition structure will result in different stereoisomers. These names are due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed . If they are on the same side, the product is endo . If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure was optimised at HF/3-21G level of theory and 6-31G* level of theory, respectively, from the guess transition structure.' ' Endo ' ' transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory, respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction. HOMO,LUMO of transition structures are represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition Structure of Endo and Exo Reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

'''Activation Energy of ' 'exo' ' and ' 'endo' ' product'''

{| class="wikitable" border="1"
|+ Table 13 energy of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result, which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however, secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster. Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system. Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software . In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation. As for the section about Diels Alder reaction, the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:45:27Z

Tc1812: /* Conclusion */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

'''IRC(Intrinsic Reaction Coordinate)'''

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 Reaction pathway from IRC
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC, the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry. The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway. The direction of path Two approaches were tries. The first approach is that last point on the IRC was optimised at HF/3-21G theory. The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure, geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition Structure of Diels Alder Reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.41,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AM1 was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane. In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-31G*
|-
| HF/6-31G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which is relevant transition structure. The animation from table 11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on former one.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene). Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å, which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped. In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ' ' endo ' ' and ' ' exo ' '. Each transition structure will result in different stereoisomers. These names are due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed . If they are on the same side, the product is endo . If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure was optimised at HF/3-21G level of theory and 6-31G* level of theory, respectively, from the guess transition structure.' ' Endo ' ' transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory, respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction. HOMO,LUMO of transition structures are represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

'''Activation Energy of ' 'exo' ' and ' 'endo' ' product'''

{| class="wikitable" border="1"
|+ Table 13 energy of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result, which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however, secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster. Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system. Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software . In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation. As for the section about Diels Alder reaction, the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:44:34Z

Tc1812: /* Regioselectivity of the Diels Alder Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

'''IRC(Intrinsic Reaction Coordinate)'''

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 Reaction pathway from IRC
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC, the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry. The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway. The direction of path Two approaches were tries. The first approach is that last point on the IRC was optimised at HF/3-21G theory. The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure, geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition Structure of Diels Alder Reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.41,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AM1 was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane. In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-31G*
|-
| HF/6-31G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which is relevant transition structure. The animation from table 11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on former one.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene). Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å, which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped. In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ' ' endo ' ' and ' ' exo ' '. Each transition structure will result in different stereoisomers. These names are due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed . If they are on the same side, the product is endo . If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure was optimised at HF/3-21G level of theory and 6-31G* level of theory, respectively, from the guess transition structure.' ' Endo ' ' transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory, respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction. HOMO,LUMO of transition structures are represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

'''Activation Energy of ' 'exo' ' and ' 'endo' ' product'''

{| class="wikitable" border="1"
|+ Table 13 energy of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result, which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however, secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster. Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system. Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:41:39Z

Tc1812: /* Regioselectivity of the Diels Alder Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

'''IRC(Intrinsic Reaction Coordinate)'''

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 Reaction pathway from IRC
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC, the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry. The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway. The direction of path Two approaches were tries. The first approach is that last point on the IRC was optimised at HF/3-21G theory. The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure, geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition Structure of Diels Alder Reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.41,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AM1 was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane. In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-31G*
|-
| HF/6-31G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which is relevant transition structure. The animation from table 11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on former one.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene). Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å, which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped. In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ' ' endo ' ' and ' ' exo ' '. Each transition structure will result in different stereoisomers. These names are due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed . If they are on the same side, the product is endo . If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure was optimised at HF/3-21G level of theory and 6-31G* level of theory, respectively, from the guess transition structure.' ' Endo ' ' transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory, respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction. HOMO,LUMO of transition structures are represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:38:59Z

Tc1812: /* Transition State for Prototype Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

'''IRC(Intrinsic Reaction Coordinate)'''

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 Reaction pathway from IRC
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC, the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry. The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway. The direction of path Two approaches were tries. The first approach is that last point on the IRC was optimised at HF/3-21G theory. The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure, geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition Structure of Diels Alder Reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.41,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AM1 was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane. In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-31G*
|-
| HF/6-31G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which is relevant transition structure. The animation from table 11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on former one.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene). Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å, which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:37:05Z

Tc1812: /* Transition structure of Diels Alder reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

'''IRC(Intrinsic Reaction Coordinate)'''

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 Reaction pathway from IRC
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC, the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry. The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway. The direction of path Two approaches were tries. The first approach is that last point on the IRC was optimised at HF/3-21G theory. The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure, geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition Structure of Diels Alder Reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.41,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AM1 was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane. In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which is relevant transition structure. The animation from table 11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on former one.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene). Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å, which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:29:58Z

Tc1812: /* Transition Structures of Chair and Boat Conformation */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

'''IRC(Intrinsic Reaction Coordinate)'''

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 Reaction pathway from IRC
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC, the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry. The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway. The direction of path Two approaches were tries. The first approach is that last point on the IRC was optimised at HF/3-21G theory. The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure, geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:27:12Z

Tc1812: /* Transition Structures of Chair and Boat Conformation */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure 2.
[[File:Transition_state_Chair.png|thumb|center|Figure 2. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure were optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table 4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o,as shown below.

{| class="wikitable" border="1"
|+ Table 5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table 6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest.It can be thought that the initial structure(transition structure) in the input file deter the direction of pathway.The direction of path Two approaches were tries . The first approach is that last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,geometry with wrong minimum energy will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same. It seems that the more steps is,The more subtle the process is.

'''Summary of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of ' 'chair ' ' transition structure is lower, in comparison with that of ' 'boat ' ' transition structure. Therefore, kinetic product is formed if the reaction proceeds via ' 'chair' ' transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table 7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| HF/3-21G || colspan="3" style="text-align: center;"| B3LYP/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table 8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:16:16Z

Tc1812: /* Optimization of Reactants and Products */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 1. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list, hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp = 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table .4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table .5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table .6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:15:22Z

Tc1812: /* Optimization of Reactants and Products */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1 The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2 The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K , because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3 Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table .4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table .5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table .6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:06:14Z

Tc1812: /* Transition Structure of Cope Rearrangement */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table .4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table .5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table .6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:05:11Z

Tc1812: /* Introduction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry. It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest, illustrated by energy surface diagram or reaction profiles. Furthermore, transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction. One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound .Therefore ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table .4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table .5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table .6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T11:02:28Z

Tc1812: /* Reference */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table .4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table .5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table .6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1. P. Atkins,J.D.Paula,2010,Atkins' Physical Chemistry, 9th Edn,Oxford press,Oxford

2. B.W. Gung,Z.Zhou,R.A.Fouch,''J.Am.Chem.Soc.'',1995,'''117''',pp 1783-1788

3. H. Sayin. Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4. J. Clayden,N. Greeves, S.Warren, Organic Chemistry,2rd Edn,Oxford Press,Oxford

5. Astle,W.H. Beyer,1984. CRC Handbook of Chemistry and Physics, 65th Edn, Inc. CRC Press, Boca Raton, FL

6. M.F.Ruiz-Lopez,X.Asseld,J.l.Garcia,J.A.Mayoral,L. Salvatella,''J.Am.Chem.Soc.'',1993,'''115''',pp 8780-8787

User:Tc1812

2015-03-27T10:57:10Z

Tc1812: /* Regioselectivity of the Diels Alder Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table .4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table .5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table .6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, Inc.CRC Press, Boca Raton, FL

User:Tc1812

2015-03-27T10:55:40Z

Tc1812: /* Reference */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table .4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table .5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table .6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, Inc.CRC Press, Boca Raton, FL

User:Tc1812

2015-03-27T10:53:28Z

Tc1812: /* Regioselectivity of the Diels Alder Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table .4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table .5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table .6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.6

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T10:53:07Z

Tc1812: /* Conclusion */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table .4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table .5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table .6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian software .In the first section, the activation energy to ' 'chair or boat' ' transition state will be calculated and the value are involved in the expected range. However, the geometry with minimum energy from IRC was not found due to time limitation.As for the section about Diels Alder reaction. the result from 6-31G* level theory proves that endo product is preferred. However, the 3-21G method is unable to prove. Further effort are needed to figure out this problem.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T10:42:58Z

Tc1812: /* Regioselectivity of the Diels Alder Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table .4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table .5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table .6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||Transition Structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||Transition Structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Table 13 Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T10:42:20Z

Tc1812:

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table .4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table .5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table .6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Exo transition structure were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively, from the guess transition structure. Endo transition structure was optimised by QST2 method at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation. The geometry corresponding to four orbital are all antisymmetrical,which proves reaction condition of Diels Alder reaction.
HOMO,LUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Table 12 Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable , which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G*. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain because the -(C=O)-O-(C=O)- has more steric interaction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T10:23:53Z

Tc1812: /* Transition State for Prototype Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table .4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table .5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table .6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9 Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10 Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11 Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T10:21:46Z

Tc1812: /* Transition Structures of Chair and Boat Conformation */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table .4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table .5 Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table .6 The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9.Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10. Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11. Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T10:19:44Z

Tc1812: /* Regioselectivity of the Diels Alder Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9.Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10. Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11. Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. Exo and Endo Transition Structure|450px]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T10:19:05Z

Tc1812: /* Regioselectivity of the Diels Alder Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9.Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10. Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11. Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. ' 'exo'' and ' 'endo' ' transition |450px]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T10:18:24Z

Tc1812: /* Regioselectivity of the Diels Alder Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9.Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10. Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11. Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groups on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathway of Diels-Alder reaction and activation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures were optimised at HF/3-21G level of theory and 6-31G* level of theory,respectively. The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. The_structure_of_exo_endo|450px]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T10:17:13Z

Tc1812: /* Regioselectivity of the Diels Alder Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9.Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10. Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11. Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG|thumb|center|Figure 2. The_structure_of_exo_endo|250px]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T10:15:45Z

Tc1812: h

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9.Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table 10. Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Table 11. Transition Structure illustrated by IRC and HF/6-13G
|-
| HF/6-13G* || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04 cm-1) is given, which illustrates this structure is a transition structure.The animation from table.11 is relevant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous, which represents a interaction fragment with πp electrons with the fragment with πq electrons. The Woodward-Hoffman Rule is based on fromer.4 According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length, as the bond is partial formed. Furthermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T10:00:02Z

Tc1812: /* Transition structure of Diels Alder reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Transition State in Prototype Reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition Structure illlustrated by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:57:14Z

Tc1812: /* Optimization of Reactants and Products */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from HF/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9.Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table. Transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:55:16Z

Tc1812: /* Transition State for the Prototype Reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9.Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table. Transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:50:53Z

Tc1812: /* Transition Structure of Cope Rearrangement */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|450px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for the Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9.Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table. Transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:50:38Z

Tc1812: /* Transition Structure of Cope Rearrangement */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|300px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for the Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9.Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table. Transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:49:58Z

Tc1812: /* Transition Structure of Cope Rearrangement */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.|150px]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for the Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9.Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table. Transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:45:49Z

Tc1812: /* Transition state for the prototype reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition State for the Prototype Reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.s-trans butadiene can not take place diels alder reaction because the terminal carbon of diene can not be close enough to react with ethene.
Prototype reaction as a branch of diels Alder reaction must obey the rule which HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . The HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9.Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table. Transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:30:42Z

Tc1812: /* Transition state for the prototype reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition state for the prototype reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.
Prototype reaction as a branch of diels Alder reaction must obey the rule.The Diels-Alder reaction as a HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . the HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Table 9.Orbtial of Cis-butadiene and Ethene
|-
| The type of orbital ||[Cis-butadiene || Ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table. Transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:29:45Z

Tc1812: /* Transition state for the prototype reaction */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition state for the prototype reaction====
The Diels Alder reaction is one type of percyclic reaction. The Characteristics of this reaction is concerted and stereospecific. In the first exercise, the reaction between the cis-butadiene and ethene were investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.
Prototype reaction as a branch of diels Alder reaction must obey the rule.The Diels-Alder reaction as a HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . the HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Orbtial of Cis-butadiene and ethene
|-
| The type of orbital ||[cis-butadiene || ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table. Transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:24:25Z

Tc1812: /* Transition Structures of Chair and Boat Conformation */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ' 'always' ' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic Energy/hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree ||Electronic Energy/Hartree || Sum of Electronic and Zero-point Energies/Hartree || Sum of Electronic and Thermal Energies/Hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of Activation Energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition state for the prototype reaction====
The Diels Alder reaction is one type of percyclic reaction.The Characteristics of this reaction is concerted and stereospecific.In the first exercise,the reaction between the cis-butadiene and ethylene will be investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.
Prototype reaction as a branch of diels Alder reaction must obey the rule.The Diels-Alder reaction as a HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . the HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Orbtial of Cis-butadiene and ethene
|-
| The type of orbital ||[cis-butadiene || ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table.The transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:22:07Z

Tc1812: /* Transition Structures of Chair and Boat Conformation */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''' 'Chair' ' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ' 'Chair' ' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ' 'guess' ' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å , so the coordinates were freezed . The structure was optimised at HF/3-21G level of theory. Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. However, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ''always'' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of activation energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition state for the prototype reaction====
The Diels Alder reaction is one type of percyclic reaction.The Characteristics of this reaction is concerted and stereospecific.In the first exercise,the reaction between the cis-butadiene and ethylene will be investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.
Prototype reaction as a branch of diels Alder reaction must obey the rule.The Diels-Alder reaction as a HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . the HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Orbtial of Cis-butadiene and ethene
|-
| The type of orbital ||[cis-butadiene || ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table.The transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:19:12Z

Tc1812: /* Transition Structure of Cope Rearrangement */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ' 'boat' ' and the other is ' 'chair' '. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''''Chair'' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ''Chair'' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ''guess'' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å ,so the coordinates were freezed .The structure was optimised at HF/3-21G level of theory.Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 :The Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. Howvever, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ''always'' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of activation energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition state for the prototype reaction====
The Diels Alder reaction is one type of percyclic reaction.The Characteristics of this reaction is concerted and stereospecific.In the first exercise,the reaction between the cis-butadiene and ethylene will be investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.
Prototype reaction as a branch of diels Alder reaction must obey the rule.The Diels-Alder reaction as a HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . the HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Orbtial of Cis-butadiene and ethene
|-
| The type of orbital ||[cis-butadiene || ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table.The transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:18:43Z

Tc1812: /* Transition Structures of Chair and Boat Conformation */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ''boat'' and the other is ''chair''. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''''Chair'' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ''Chair'' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ''guess'' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å ,so the coordinates were freezed .The structure was optimised at HF/3-21G level of theory.Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 :The Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. Howvever, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''' 'Boat' ' Transition Structure'''

In QST2 method, ' 'Boat' '(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the ' 'boat' ' transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ''always'' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1. Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries . The first approach is that Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.but the electronic energy is still be same.It seems that the more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for ' 'Chair' ' or ' 'Boat' ' transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of activation energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition state for the prototype reaction====
The Diels Alder reaction is one type of percyclic reaction.The Characteristics of this reaction is concerted and stereospecific.In the first exercise,the reaction between the cis-butadiene and ethylene will be investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.
Prototype reaction as a branch of diels Alder reaction must obey the rule.The Diels-Alder reaction as a HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . the HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Orbtial of Cis-butadiene and ethene
|-
| The type of orbital ||[cis-butadiene || ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table.The transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:11:57Z

Tc1812: /* Transition Structures of Chair and Boat Conformation */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ''boat'' and the other is ''chair''. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''''Chair'' Transition Structure'''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ''Chair'' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ''guess'' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å ,so the coordinates were freezed .The structure was optimised at HF/3-21G level of theory.Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 :The Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. Howvever, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature, bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''''Boat'' Transition Structure'''

In QST2 method, ''Boat''(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the boat transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. ' 'Chair' ' transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ''always'' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1.Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries .The first approach is that the Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.the increasing steps will not affect the result. The more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for chair or boat transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of activation energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition state for the prototype reaction====
The Diels Alder reaction is one type of percyclic reaction.The Characteristics of this reaction is concerted and stereospecific.In the first exercise,the reaction between the cis-butadiene and ethylene will be investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.
Prototype reaction as a branch of diels Alder reaction must obey the rule.The Diels-Alder reaction as a HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . the HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Orbtial of Cis-butadiene and ethene
|-
| The type of orbital ||[cis-butadiene || ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table.The transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:10:03Z

Tc1812: /* Transition Structures of Chair and Boat Conformation */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ''boat'' and the other is ''chair''. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

''''Chair'''' Transition Structure ''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ''Chair'' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ''guess'' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å ,so the coordinates were freezed .The structure was optimised at HF/3-21G level of theory.Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 :The Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. Howvever, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature,bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''''Boat'' Transition Structure'''

In QST2 method, ''Boat''(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the boat transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. Chair transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ''always'' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1.Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries .The first approach is that the Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.the increasing steps will not affect the result. The more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for chair or boat transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of activation energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition state for the prototype reaction====
The Diels Alder reaction is one type of percyclic reaction.The Characteristics of this reaction is concerted and stereospecific.In the first exercise,the reaction between the cis-butadiene and ethylene will be investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.
Prototype reaction as a branch of diels Alder reaction must obey the rule.The Diels-Alder reaction as a HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . the HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Orbtial of Cis-butadiene and ethene
|-
| The type of orbital ||[cis-butadiene || ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table.The transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:08:40Z

Tc1812: /* Transition Structures of Chair and Boat conformation */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ''boat'' and the other is ''chair''. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' Conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''Transition Structure of ''Chair'''''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ''Chair'' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ''guess'' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å ,so the coordinates were freezed .The structure was optimised at HF/3-21G level of theory.Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 :The Transition Structure of ''''Chair''''
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. Howvever, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature,bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''''Boat'' Transition Structure'''

In QST2 method, ''Boat''(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the boat transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. Chair transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ''always'' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1.Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries .The first approach is that the Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.the increasing steps will not affect the result. The more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for chair or boat transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of activation energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition state for the prototype reaction====
The Diels Alder reaction is one type of percyclic reaction.The Characteristics of this reaction is concerted and stereospecific.In the first exercise,the reaction between the cis-butadiene and ethylene will be investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.
Prototype reaction as a branch of diels Alder reaction must obey the rule.The Diels-Alder reaction as a HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . the HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Orbtial of Cis-butadiene and ethene
|-
| The type of orbital ||[cis-butadiene || ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table.The transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:07:36Z

Tc1812: /* Optimization of Reactants and products */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ''boat'' and the other is ''chair''. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.]]

====Optimization of Reactants and Products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''Transition Structure of ''Chair'''''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ''Chair'' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ''guess'' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å ,so the coordinates were freezed .The structure was optimised at HF/3-21G level of theory.Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 :The transition structure of chair
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. Howvever, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature,bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''''Boat'' Transition Structure'''

In QST2 method, ''Boat''(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the boat transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. Chair transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ''always'' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1.Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries .The first approach is that the Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.the increasing steps will not affect the result. The more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for chair or boat transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of activation energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition state for the prototype reaction====
The Diels Alder reaction is one type of percyclic reaction.The Characteristics of this reaction is concerted and stereospecific.In the first exercise,the reaction between the cis-butadiene and ethylene will be investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.
Prototype reaction as a branch of diels Alder reaction must obey the rule.The Diels-Alder reaction as a HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . the HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Orbtial of Cis-butadiene and ethene
|-
| The type of orbital ||[cis-butadiene || ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table.The transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL

User:Tc1812

2015-03-27T09:07:18Z

Tc1812: /* Transition Structure of Cope Rearrangement */

== Introduction ==
Computational chemistry has been an important sub-discipline within chemistry.It has been frequently used to support the theory and results. Based on the computational program and theoretical calculation, the major application of computational chemistry is to predict the thermodynamic motion of reaction , stereo-chemistry of compounds , molecular orbital calculation and transition structure.
Transition structure, also called as activated complex, is a significant conformation on the process of reaction. Obviously,potential energy of the transition state is the highest,illustrated by energy surface diagram or reaction profiles.Furthermore,transition structure/state and the energy barrier are dependent on reactivity ,regioselectivity,and mechanism. This characteristic could be well performed in term of the Cope rearrangement and the Diels Alder reaction.One measure of the progress is to deter the length of bond being made or broken .However ,this method is no longer suitable for complicated compound . Instead ,molecular orbital-based method will be adopted to estimate the transition structure.In this experiment,transition structure of Cope Rearrangement and Diels Alder reaction will be predicted by the Gaussian software respectively.1

==Result and disscussion ==
=== Transition Structure of Cope Rearrangement ===
Cope-rearrangement is one type of [3,3]sigmatropic rearrangement.The bond breaking and formation occur simultaneously. Currently, Cope-rearrangement proceed via two acceptable transition structures.One is a ''boat'' and the other is ''chair''. Both of transition structures are illustrated in Figure.1.
[[File:Transition_state_Chair.png|thumb|center|Figure 1. Transition structure of Cope Rearrangement.]]

====Optimization of Reactants and products====

The conformers of the 1,5-hexadiene was analysed by optimization at HF/3-21G level of theory. Point groups, electronic energy and relative energy(Note:1 Hartree = 627.509 Kcal/mol) corresponding to each conformer are illustrated in Table 1. Anti-periplanar structure is often regarded as the conformer with the lowest energy due to minimization of steric interaction . However , conformer gauche 3 possesses the lowest electronic energy among the conformers , resulted from the interaction of п orbital with vinyl protons. Anti 2 conformer has center of symmetry , as illustrated by point group Ci. It was then optimized with B3LYP/6-31G*. After optimization via B3LYP/6-31G*, the final structure was compared with structure from Hf/3-21G . It is noticeable that the structure from optismation B3LYP/6-31G* possesses lower electronic energy , which is more stable. It can explained by the structural geometry.The bond length does not give any support, even if the bond length slightly changed . The dihedral angle , also called as torsional angle, proves this fact.The dihedral angle (C1-C4)slightly increases , indicating carbon in position 1 and 6 away from each other.
{| class="wikitable" border="1"
|+ Table 1. The representation of different conformations
|-
| Conformer || style="text-align: center;"|Structure || Point Group || Energy/Hartrees HF/3-21G || Relative energy/Kcal/Mol
|-
| Gauche || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68772 ||3.10
|-
| Gauche2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_2.mol</uploadedFileContents>
</jmolApplet></jmol>|| C2 || -231.69167 || 0.62
|-
| Gauche3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69266 || 0.00
|-
| Gauche4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69153 || 0.71
|-
| Gauche5 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_5.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.68962 || 1.91
|-
| Gauche6 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Gauche_6.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.68916 ||2.20
|-
| Anti1 ||<jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>App_1.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69260 ||0.04
|-
| Anti2 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Tutorial_react_app2.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci || -231.69254 || 0.08
|-
| Anti3 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_3.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 || 2.25
|-
| Anti4 || <jmol><jmolApplet>
<color>black</color>
<size>200</size>
<uploadedFileContents>Anti_4.mol</uploadedFileContents>
</jmolApplet></jmol> || C1 || -231.69091 || 1.06
|}

{| class="wikitable" border="1"
|+ Table 2. The comparison of structures from different methods
|-
| colspan="3" align="center"|[[File:Structure_for_comparision.PNG]]
|-
! colspan="3" style="text-align: left;"|Figure 2. Labelled anti-periplanar structure
|-
|style="text-align: center;"|Geometry/Method||HF/3-21G|| B3LYP/6-31G*
|-
|Double bond length(C1-C2) || 1.31620 ||1.33350
|-
|Single bond/Å(C2-C3) || 1.50893 || 1.50420
|-
|Single bond/Å(C3-C4) || 1.55300 || 1.54816
|-
|Dihedral angle(C1-C2)-C3-C4)|| 114.68924 || 118.59893
|-
|Dihedral angle(C1-C2)-C3-C4)|| 180.0000 || 180.0000
|-
|Energy/Hartrees|| -231.69253 || -234.61171
|}

In end of this exercise, frequency of anti 2 conformer at 298.15 K was obtained by same method B3LYP/6-31G*. None of imaginary frequency are illustrated in vibration list,hence ,the energy of this conformer is minimized. The energy of structure at 0 K could also be estimated by typing temp= 0.01 on windows with same method B3LYP/6-31G* in order to correct the energy. According to the table 3., the sum of electronic and zero-point Energies is same at either 0 K or 298.15 K. All types of energy are sames at 0 K ,because energy only consists of zero-point energy(residual energy) and electronic energy at this situation .

{| class="wikitable" border="1"
|+ Table 3. Summary of thermal energy in 0 and 298 K
|-
|Type of energy/Hartrees || 0 K|| at 298.15 K
|-
|The sum of electronic and zero-point Energies || -234.469219 || -234.469219
|-
|The sum of electronic and thermal Energies || -234.469219 || -234.461869
|-
|The sum of electronic and thermal Enthapies || -234.469219 || -234.460925
|-
|The sum of electronic and thermal Free Energies || -234.469219 || -234.500808
|}

====Transition Structures of ''Chair'' and ''Boat'' conformation====
In this section, chair and boat transition structure are optimised by three different method .The method(a) is to calculate the force constant .The method (b) is about the application of redundant coordinate editor and the method(c) is QST2 .

'''Transition Structure of ''Chair'''''

An allyl fragment (CH2CHCH2) was optimised with HF/3-21G level of theory to generate a new transition structure.This new transition structure were copied twice and put into a new window.The intermolecular distance between two allyl fragments was adjusted to 2.2 Å. Therefore, ''Chair'' transition structure(C2h) was successfully optimized at HF/3-21G level of theory and an imaginary frequency -817. 97 cm-1 was obtained. However, this method has a limitation. If the geometry of ''guess'' transition structure is not really similar to the that of actual transition structure ,it will generate a undesired result or failure of programming. In same case, redundant coordinate editor will be used to generate a more acceptable transition structure by editing redundant coordinates.The chair structure was also run with the freezer-coordinate method,(shown in table 4.) In this method, the intermolecular distance was fixed at 2.2 Å ,so the coordinates were freezed .The structure was optimised at HF/3-21G level of theory.Later on ,the the coordinates were unfreezed and the structure was optimised again.
{| class="wikitable" border="1"
|+ Table.4 :The transition structure of chair
! Structure!!
|-
| Chair ||[[ File:Chair_ts_guess_6-31G_optimisation.gif ]]
|-
|}
After running with freezer coordinate editor,the electronic energy of chair transition structure is -817.96 cm-1,which is closer to the bond length from the method A. Howvever, the bond length increases to 2.0270 Å from 2.02025 Å. According to the literature,bond length between two allyl fragment is 2.086 Å. Therefore, redundant coordinate editor can provide more accurate result.3.

'''''Boat'' Transition Structure'''

In QST2 method, ''Boat''(C2v) transition structure is found by interpolating between reactant and product . In this method, 1,5-hexadiene(antiperiplanar 2) is as the reactant and product, respectively. Atoms in reactant and product must be numbering. Furthermore, the geometry for product and reactant must be adjusted to be closer to the boat transition structure by changing dihedral angle of C2-C3-C4-C5 to 100o.

{| class="wikitable" border="1"
|+ Table.5 :Reactants and products of QST2
|-
| Reactant|| [[ File:Reactant_QS2.PNG |150px ]] ||Product|| [[ File:Product_QS2.PNG |150px ]]||Boat transition structure ||[[ File:Boat_living_image.gif]]
|-
|}

IRC(Intrinsic Reaction Coordinate)

The IRC method allows to demonstrate the minimum pathway from a transition state to the reaction coordinate of the minimum energy. Chair transition structure was run in the forward direction because reaction coordinate is symmetrical. Default increased to 50 from 6 , in order to illustrate the process in detailed. Finally, The force constant was adjusted to ''always'' option.
{| class="wikitable" border="1"
|+ Table.6 :The transition structure of chair
|-
| IRC|[[ File:IRC.gif]]||[[ File:Capture_IRC.PNG ]]
|}
From the IRC,the conformer will undergo in gauche 2 or gauche 4 from the Appendix 1.Once the IRC finished, it did not reached a minimum geometry .The main function of IRC is to predict the trend where the slope of potential energy surface is steepest. Two approaches were tries .The first approach is that the Last point on the IRC was optimised at HF/3-21G theory.The resultant electronic energy is -231.691667 cm-1.However, if the structure is not really similar to the transition structure,wrong minimum will be obtained. As for the approach 2, number of steps was increased from 50 to 100.the increasing steps will not affect the result. The more steps is,The more subtle the process is.

'''Summation of Activation Energy'''

Following table summaries the activation energy corresponding to two different level of theory from the Gaussian. The activation energy of chair transition structure is lower, in comparison with that of boat transition structure. Therefore, kinetic product is formed if the reaction proceeds via chair transition pathway. B3LYP/6-31G* level of theory can provide more accurate value as the value is closer to the experimental value.

{|class="wikitable" border="1"
|+ Table .7 Summary of energy (in hartree) for chair or boat transition structure
| ||colspan="3" style="text-align: center;"| Hf/3-21g || colspan="3" style="text-align: center;"| b3lyp/6-31G*
|-
| ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree ||Electronic energy/hartree || Sum of electronic and zero-point energies/hartree || Sum of electronic and thermal energies/hartree
|-
| || || at 0 K || at 298.15 K || || at 0 K || at 298.15 K
|-
|Chair TS || -231.619322 || -231.466700 || -231.461341 || -234.556983 || -234.414929 || -234.409009
|-
|Boat TS || -231.60280249 || -231.450928 || -231.44299 || -234.543093 || -234.402342 || -234.396008
|-
|Reactant (anti)||-231.69235|| -231.539542 || -231.532566 || -234.61171064 || -234.469219 || -234.461869
|}

{| class="wikitable" border="1"
|+ Table .8 Summary of activation energy (in Kcal/mol)
|-
| || HF/3-21G|| HF/3-21G || B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
| || 0 K || 298.15 K || 0 K || 298.15 K || 0 K
|-
|Δ E(Chair) || 45.71 ||44.69 || 34.08 ||33.17 ||33.5± 0.5
|-
|Δ E(Boat) || 55.61 || 56.21 || 43.06 || 41.97 ||44.7±2.0
|}

=== Transition structure of Diels Alder reaction===

====Transition state for the prototype reaction====
The Diels Alder reaction is one type of percyclic reaction.The Characteristics of this reaction is concerted and stereospecific.In the first exercise,the reaction between the cis-butadiene and ethylene will be investigated by orbital interaction.4
Many dienes will have more than one conformations and the conformation can be interchanged by rotation around single bonds.1,3-butadiene will be interchanged from s-cis confromation to s-trans conformation by σ bond between the π bond.Among two conformations,only s-cis butadiene can take place.
Prototype reaction as a branch of diels Alder reaction must obey the rule.The Diels-Alder reaction as a HOMO-LUMO interaction must have the same symmetry.
In this section, semi-empirical AMi was used for optimisation of Cis-butadene and ethene,and the HOMO and LUMO orbital for both of reactants are illustrated in table . the HOMO of ethene has plane of symmetry while the LUMO of ethene is anti-symmetry with respective to the plane.In contrast ,the LUMO of butadiene has plane of symmetry and the HOMO of butadiene does not have it .
{| class="wikitable" border="1"
|+ Orbtial of Cis-butadiene and ethene
|-
| The type of orbital ||[cis-butadiene || ethene
|-
| HOMO ||[[File:HOMO.jpg|150px]] ||[[File:HOMO ethene.jpg|150px]]
|-
| LUMO ||[[File:LUMO.jpg|150px]] || [[File:LUMO ethene.jpg|150px]]
|-
|}

{| class="wikitable" border="1"
|+ Table.The transition state in prototype reaction
|-
| Orbital|| || Relative Energy
|-
| HOMO || [[File:Transition_structure_of_HOMO.PNG ‎|150px]] || -0.32393
|-
| LUMO || [[File:Transition_structure_of_LUMO.PNG|150px]] ||0.02315
|-
|}

{| class="wikitable" border="1"
|+ Transition structure illlustrate by IRC and HF/6-13G
|-
| HF/6-13G || IRC
|-
|[[File:Prototype_raction.gif]] ||[[File:IRC_prototype_reaction.gif]]
|-
|}
An imaginary frequency (-956.04cm-1) is given,which illustrates this structure is a transition structure or saddle point.The animation from table is relavant to the reaction pathway.It illustrates that the formation of the two bonds is synchronous,which represents a interaction fragment with πp electrons with the fragment with πq electrons,which is referred to Woodward-Hoffman Rule.According to the transition structure of prototype reaction,antisymmetric HOMO is generated from the orbital overlap of LUMO(ethene) and HOMO(cis-butadiene).Also, HOMO of ethene and LUMO(cis-butadiene) overlaps to form symmetric LUMO.
According to the reference, C-C(sp3) bond length is 1.54 Å and C-C(sp2) is 1.47 Å. The van der waals radius of carbon is about 1.7 Å. The partial bond length found from the transition structure is about 2.28 Å which is much longer C-C(sp3) bond length,as the bond is partial formed.Furhermore, bond length corresponding to the C=C bond and C-C is closer to 1.40 Å,which demonstrates that electrons are delocalised in the transition state.

===Regioselectivity of the Diels Alder Reaction===
The Diels Alder reaction will take place when the HOMO and LUMO are maximum overlapped.In most times,Diels-Alder reaction that between cyclohexdiene and maleic anhydride,there are two different possible transition states ,which are named the ''endo'' and ''exo''.Each transition structure will result in different stereoisomers.These names is due to the relationship in position between the carbonyl groupS on the maleic anhydride and the double bond formed .If they are on the same side, the product is endo .If they are opposite to each other,the product is exo. The HOMO-LUMO interaction can illustrate the reaction pathwayof Diels-Alder reaction and acitivation energy will be computed to confirm the kinetic product and thermodynamic product . Both of transition structures are optimised at HF/3-21G level of theory and 6-31G level of theory.The reaction path is performed by animation.HOMO,lUMO of transition structures were represented as follows.

[[File:The_structure_of_exo_endo.PNG]]

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
|Exo ||HOMO||[[File:Exo 6-31G HOMO.jpg|150px ]] ||LUMO || [[File:Exo 6-31G LUMO.jpg|150px ]] |150px ||transition structure ||[[File:Exo_6-31G_try.gif]]
|-
|Endo||HOMO|| [[File:Endo-HUMO-improve.PNG|150px ]] ||LUMO ||[[ File:Endo LUMO.jpg|150px ]] ||transition structure || [[File:Endo improve try.gif|500px ]]
|}

The activation energy of ''exo'' and ''endo'' product

{| class="wikitable" border="1"
|+ Transition structure of Endo and Exo reaction
|-
| ||Cyclohexadiene||[[ Maleic anhydride ||Endo transition structure || Exo transition structure ||Activation energy of Endo ||Activation energy of Exo ||Activation energy of Endo(kcal) ||Activation energy of Exo
|-
|3-21G||-230.53967121 || -375.10351347 || -605.61036817|| -605.61036821 || 0.03281651 || 0.032811647 || 20.592655 ||20.5895743
|-
|6-31G||-233.41587925||-379.28953540 ||-612.68339678 ||-612.68339673 || 0.02201787 || 0.02201792 || 13.816412 ||13.917648
|-
|}
In comparison with exo structure, The endo product is less stable ,which prefers in irreversible Diels-Alder-Reaction.Therefore, it is the kinetic product of the reaction,which can be proved by the activation energy of endo transition structure from the 6-31G. The result computing from 3-21G level of theory gives a undesired result,which will be discussed in the future. It also can be explained by frontier molecular theory .Exo-product is the thermodynamics product,however,secondary orbital interaction(bond interaction between the carbonyl group of maleic anhydride with π bond at the back of cyclohexadiene) result in lower energy barrier of endo-transition state.Therefore,the reaction towards endo product can proceed faster.Furthermore,Exo transition structure is more strain beacause the -(C=O)-O-(C=O)- has more steric ineraction with the remainder of system.Overall,this computational analysis is under ideal system and the solvent effect is neglected.

==Conclusion==
All of sections were successfully run by the Guassian online .In the first part of experiment, the activation energy about ''chair or boat'' will be calculated and the value are involved in the expected range.In the section about the diels alder reaction, The result from 6-13G level theory proves that endo product is preferred.However, the 3-21G method is unable to prove,it will be investigated in the future.As all of the programming are assumed in the ideal system.The reaction in aqueous environment will be investigated in the future work.

==Reference==
1.P.Atlins,J.D.Paula,2010,Atkins' Physical Chemistry,9th Edn,Oxford press,Oxford

2.B.W.Gung,Z.Zhou,R.A.Fouch,''J.An.Chem.Soc'',1995,'''117''',pp 1783-1788

3.H.Sayin.Quantum Chemical Studies and Kinetics of Gas Reaction,2006,Aubrun,Alabama

4.J.Clayden,N.Greeves,S.Warren,Organic Chemistry,2rd Edn,Oxford Press,Oxford

5.Astle,W.H. Beyer, Eds. CRC Handbook of Chemistry and Physics,1984 65th Edn, CRC Press, Inc. Boca Raton, FL