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Rep:Xizi

2018-01-31T11:35:44Z

Xy3513: /* Single point energy and IRC calculation */

==Introduction==
===Transition State===
Transition state on a 1D potential energy surface is the highest point. But a 2D PES is in 3D-6 dimensions (degrees of freedom). It has lots of local minimas and maximas. Reactants and products corrsponding to local minimas, stationary point, with dV/dq=0 for all q and d2V/dq2>0 for all q, q is the geometric parameter. Intrinsic reaction coordinate, the lowest energy pathway linking two minima, is the path that would be followed by a molecule in going from one minimum to another when it just get enough energy to overcome the activation barrier, pass through the transition state, and reach the other minimum. A transition it is located on the maxima of the reaction path, which corresponding to reaction corrdinate, but minima of all other demesions, defined by dV/dq=0 and d2V/dq2>0 when q= reaction coordinate but d2V/dq2<0 for all other q.
The geometric parameter corresponding to the reaction coordinate is usually a composite of several parameters like bond lengths, angles and dihedrals. This will result in that sometimes trasntion state can be maxima on more than one reaction coordinate, which could be called a hilltop. Because two reaction path will lead to the same transition state, like the first exercise in the extension work. (1)
===Born–Oppenheimer Approximation===
When talking about the geometric coordiante, it is defined by nuclear coordinates the parameter. Which is to say, a potential energy surface is a plot of the energy of a collection of nuclei and electrons against the geometric coordinates of the nuclei. The reason is in the BO approximation which say nuclei could be assumed stationary with respect to electrons. So Schrcodinger equation for a molecule could be separated into an electronic and a nuclear equation. Two solved and added together to get the total internal energy.
===Computational method===
Computational method finds potential energy by computing Haltonian <Ψ|H|Ψ>=E, direction vectors, r=ax+by+cz=(1,3)Σci|i> in 3D space. <br>
LCAO gives |Ψ>=(1,N)Σci|Φ> in N dimension. Then E=(c1,...)(<Φ1|H|Φ1>...)(c1,...) and |Φ1>=aexp(-ar2) <br>
There are two methods used in this computational lab, semi-empirical paramazation method 6 (PM6) and density functional method Becke-3-LYP (B3lYP) with basis set 631G. <br>
PM6 is under Hartree–Fock formalism, but make many approximations and obtain some parameters from empirical data which allows some electron correlations. <br>
631g is a basis set of basis functions represent the electronic wave function in the Hartree–Fock method or DFT in order to turn the partial differential equations of the model into algebraic equations for computer. Molecular orbitals could then be expressed as linear combinations of the basis functions. <br>
Becke-3-LYP: a hybrid functional uses a mixing scheme of 3 parameters <br>
EXC = 0.2*EX(HF) + 0.8*EX(LSDA) + 0.72*DEX(B88) + 0.81*EC(LYP) + 0.19*EC(VWN) <br>
===Geometry Optimization===
Geometry optimization is the process of starting with an input structure and finding a stationary point on the PES. The stationary point found will normally be the one closest to the input structure. If calculating TS, analytical first and section derivative should as algorithms to be used.
===Frequency calculation and zero point energy===
Calculating vibrational spectrum (normal-mode vibrations) is often needed to check if the geometry is the desired one. The algorithm for this works by calculating an accurate
Hessian (force constant matrix) and diagonalizing it to give a matrix with the direction vectors,ř, of the normal modes, and a diagonal matrix with the force
constants,k, of these modes. Mass weighted force constants give the normal-mode vibration frequencies, v=h/2πc* (k/m)1/2. A transition state has one imaginary vibration, corresponding to motion along the reaction coordinate. K values calculated for transition state is all positive except one on reaction coordinate. <br>
The equations used for computing thermochemical data in Gaussian are equivalent to those in thermodynamics. One of the most important approximations to be aware of throughout this analysis is that all the equations assume non-interacting particles and therefore apply only to an ideal gas. This added up contribution of translation, electronic, vibrational and rotational motion. <br>
Sum of electronic and thermal free energies = ɛ0 + Gcorr

==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 14; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 8; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 9; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_REAL_TS_WITH_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).
===Calculation output by PM6===
optimized reactant: [[Media:YXZ_EXP1_DIENE_MINIPM6.LOG]] [[Media:YXZ EXP1 DIENE MINIPM6.LOG]]

optimized product: [[Media:YXZ_EXP_PRODUCT.LOG]]

otimized/frequency calculated transition state:[[Media:YXZ_EXP1_REAL_TS_WITH_MO.LOG]]

IRC to confirm the transition state: [[Media:YXZ_EXP2_IRC2.LOG]]

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
====Single point energy and IRC calculation====
{| class="wikitable" style="border: none; background: none;"
|+|Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}

IRC Calculation
[[File:YXZ EXP2 ENDO IRCPIC.png|800px|thumb|left|IRC of endo TS]]
[[File:YXZ EXP2 EXO IRCPIC.png|800px|thumb|left|IRC of exo TS]]

====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>Endo TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
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===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Kinetic product and thermodynamic product are ones have smallest activation energy and largest reaction ernergy. In this case, both are endo product, numerical calculation will be shown soon.
However, Diesl Alder reaction could be reversed by taking in and releasing energy. Also interesting are the fastest formed product and the most stable product. <br>
The fastest formed product. <br>
The Arrhenius Equation states that reaction rate constant is related to Ea by k=Ae−Ea/RT. A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lowest free energy of TS and one is higher rate of collision. <br> So thermodynamic control involves raising temperature.
The most stable product, having less chance of going reversible reaction to products or other dissociation reaction. One has lowest free energy of product and lowest rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. It is also the fastest and most stable product. <br>

====Secondary orbital interation====

Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

===Calculation output by B3LYP 621g.d.p===
Optimized endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_TS_631_WITH_MO3.log]]

Optimized exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_TS631_MOLATEST.log]]

Energy calulation exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_ENERGY4WITHMO.log]]

Energy calculation endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_ENERGY2.log]]

IRC endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_IRC4.log.log]]

IRC exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_IRC4.log]]

B3LYP optimized dioxole (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIXOLE631.LOG]]

B3LYP optimized cyclohexadiene (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIENE631.LOG]]

B3LYP optimized endo product (frequency calculation is done in the same file): [[Media:EXP2_ENDO_MINI631_FREQUENCY_CHECK.LOG]]

B3LYP optimized exo product (frequency calculation is done in the same file): [[Media:EXP2_EXO_621_MINI.LOG]]

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; </script>
<uploadedFileContents>YXZ_EXP3_DAENDO_TS1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXP3_CHELE_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output by PM6===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

==Further work==
1. Ring opening of a cyclobutene <br>
Reaction proceeds with conrotation. This reaction involves forming of Möbius aromatic transition state involving one antarafacial four-electron component. Pi bond of double bond overlap with sp3 C-C anti bond followed by the rotation of sigma bond of double and rotation of sp3 bonding of C-C. To form a monocyclic array of molecular orbitals which has odd number of out-of-phase overlaps, Mobius aromatic TS, forming HOMO of butadiene, rotation is restricted to conrotation. Diene formed then have different phases of p orbitals on terminal. <br>
2. Photochemical reaction <br>
Reaction proceeds with disrotation. When such a diene absorbs light of right frequency, an electron will be exiced from HOMO to LUMO. Now this diene has new HOMO and LUMO of ψ3 and ψ4 of ground state. In this case, To form Möbius aromatic transition state, sigma bond will choose disrotation to form the new bond p orbitals of different phase at ends. And now the transition state is better understood by a conical intersection in 2D PES accompanied by a change of symmetry. <br>
3.Opening of the cyclopropyl cation <br>
Reaction proceeds with dis-rotation. It forms a Huckel aromatic TS of 2 electrons and form a product of allylic cation which has same phases on terminal p orbital and stabilized by conical form. HOMO of OTs- helps stabilizing form of TS and leaves just after that. <br>
4. Opening of the cyclopropyl cation with hetero-atoms <br>
Conrotation needed to form Möbius aromatic transition state and gives a product with different phases at ends and has HOMO of C2v and pi cloud localized. <br>

==Conclusion==
In this work, different calculations are studied. Optimization to find the right structure. Frequency to check if it is correct. IRC to visualize free energy surface on intrinsic coordinate. Energy to compare different molecules on one potential surface. <br>
Important information can be extracted by using Gaussview like visualization of MO to study the FMO theory and symmetry of reaction. Thermochemistry data like Gibbs free enrgy, zero point energy and enthalpy an so on. Visualization of vibration modes can give the reaction coordinate. <br>
For pericyclic reactions, symmetry rules, Hammond's postulate, bond forming and rotation have been studied and there is still something to be explored like other thermal pericyclic reactions and light-induced pericyclic reactions.

==Reference==
1. file://icnas4.cc.ic.ac.uk/xy3513/9789048138609-c2.pdf

Rep:Xizi

2018-01-31T11:34:31Z

Xy3513: /* Further work */

==Introduction==
===Transition State===
Transition state on a 1D potential energy surface is the highest point. But a 2D PES is in 3D-6 dimensions (degrees of freedom). It has lots of local minimas and maximas. Reactants and products corrsponding to local minimas, stationary point, with dV/dq=0 for all q and d2V/dq2>0 for all q, q is the geometric parameter. Intrinsic reaction coordinate, the lowest energy pathway linking two minima, is the path that would be followed by a molecule in going from one minimum to another when it just get enough energy to overcome the activation barrier, pass through the transition state, and reach the other minimum. A transition it is located on the maxima of the reaction path, which corresponding to reaction corrdinate, but minima of all other demesions, defined by dV/dq=0 and d2V/dq2>0 when q= reaction coordinate but d2V/dq2<0 for all other q.
The geometric parameter corresponding to the reaction coordinate is usually a composite of several parameters like bond lengths, angles and dihedrals. This will result in that sometimes trasntion state can be maxima on more than one reaction coordinate, which could be called a hilltop. Because two reaction path will lead to the same transition state, like the first exercise in the extension work. (1)
===Born–Oppenheimer Approximation===
When talking about the geometric coordiante, it is defined by nuclear coordinates the parameter. Which is to say, a potential energy surface is a plot of the energy of a collection of nuclei and electrons against the geometric coordinates of the nuclei. The reason is in the BO approximation which say nuclei could be assumed stationary with respect to electrons. So Schrcodinger equation for a molecule could be separated into an electronic and a nuclear equation. Two solved and added together to get the total internal energy.
===Computational method===
Computational method finds potential energy by computing Haltonian <Ψ|H|Ψ>=E, direction vectors, r=ax+by+cz=(1,3)Σci|i> in 3D space. <br>
LCAO gives |Ψ>=(1,N)Σci|Φ> in N dimension. Then E=(c1,...)(<Φ1|H|Φ1>...)(c1,...) and |Φ1>=aexp(-ar2) <br>
There are two methods used in this computational lab, semi-empirical paramazation method 6 (PM6) and density functional method Becke-3-LYP (B3lYP) with basis set 631G. <br>
PM6 is under Hartree–Fock formalism, but make many approximations and obtain some parameters from empirical data which allows some electron correlations. <br>
631g is a basis set of basis functions represent the electronic wave function in the Hartree–Fock method or DFT in order to turn the partial differential equations of the model into algebraic equations for computer. Molecular orbitals could then be expressed as linear combinations of the basis functions. <br>
Becke-3-LYP: a hybrid functional uses a mixing scheme of 3 parameters <br>
EXC = 0.2*EX(HF) + 0.8*EX(LSDA) + 0.72*DEX(B88) + 0.81*EC(LYP) + 0.19*EC(VWN) <br>
===Geometry Optimization===
Geometry optimization is the process of starting with an input structure and finding a stationary point on the PES. The stationary point found will normally be the one closest to the input structure. If calculating TS, analytical first and section derivative should as algorithms to be used.
===Frequency calculation and zero point energy===
Calculating vibrational spectrum (normal-mode vibrations) is often needed to check if the geometry is the desired one. The algorithm for this works by calculating an accurate
Hessian (force constant matrix) and diagonalizing it to give a matrix with the direction vectors,ř, of the normal modes, and a diagonal matrix with the force
constants,k, of these modes. Mass weighted force constants give the normal-mode vibration frequencies, v=h/2πc* (k/m)1/2. A transition state has one imaginary vibration, corresponding to motion along the reaction coordinate. K values calculated for transition state is all positive except one on reaction coordinate. <br>
The equations used for computing thermochemical data in Gaussian are equivalent to those in thermodynamics. One of the most important approximations to be aware of throughout this analysis is that all the equations assume non-interacting particles and therefore apply only to an ideal gas. This added up contribution of translation, electronic, vibrational and rotational motion. <br>
Sum of electronic and thermal free energies = ɛ0 + Gcorr

==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 14; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 8; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 9; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_REAL_TS_WITH_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).
===Calculation output by PM6===
optimized reactant: [[Media:YXZ_EXP1_DIENE_MINIPM6.LOG]] [[Media:YXZ EXP1 DIENE MINIPM6.LOG]]

optimized product: [[Media:YXZ_EXP_PRODUCT.LOG]]

otimized/frequency calculated transition state:[[Media:YXZ_EXP1_REAL_TS_WITH_MO.LOG]]

IRC to confirm the transition state: [[Media:YXZ_EXP2_IRC2.LOG]]

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|-
|}
====Single point energy and IRC calculation====
{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|<jmol>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|<jmol>
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<color>white</color>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}

IRC Calculation
[[File:YXZ EXP2 ENDO IRCPIC.png|800px|thumb|left|IRC of endo TS]]
[[File:YXZ EXP2 EXO IRCPIC.png|800px|thumb|left|IRC of exo TS]]

====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
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<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
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===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Kinetic product and thermodynamic product are ones have smallest activation energy and largest reaction ernergy. In this case, both are endo product, numerical calculation will be shown soon.
However, Diesl Alder reaction could be reversed by taking in and releasing energy. Also interesting are the fastest formed product and the most stable product. <br>
The fastest formed product. <br>
The Arrhenius Equation states that reaction rate constant is related to Ea by k=Ae−Ea/RT. A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lowest free energy of TS and one is higher rate of collision. <br> So thermodynamic control involves raising temperature.
The most stable product, having less chance of going reversible reaction to products or other dissociation reaction. One has lowest free energy of product and lowest rate of collision to go back to product. <br>
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Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. It is also the fastest and most stable product. <br>

====Secondary orbital interation====

Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

===Calculation output by B3LYP 621g.d.p===
Optimized endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_TS_631_WITH_MO3.log]]

Optimized exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_TS631_MOLATEST.log]]

Energy calulation exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_ENERGY4WITHMO.log]]

Energy calculation endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_ENERGY2.log]]

IRC endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_IRC4.log.log]]

IRC exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_IRC4.log]]

B3LYP optimized dioxole (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIXOLE631.LOG]]

B3LYP optimized cyclohexadiene (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIENE631.LOG]]

B3LYP optimized endo product (frequency calculation is done in the same file): [[Media:EXP2_ENDO_MINI631_FREQUENCY_CHECK.LOG]]

B3LYP optimized exo product (frequency calculation is done in the same file): [[Media:EXP2_EXO_621_MINI.LOG]]

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
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<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 30; </script>
<uploadedFileContents>YXZ_EXP3_DAENDO_TS1.LOG</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
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|<jmol>
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<color>white</color>
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<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
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|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output by PM6===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

==Further work==
1. Ring opening of a cyclobutene <br>
Reaction proceeds with conrotation. This reaction involves forming of Möbius aromatic transition state involving one antarafacial four-electron component. Pi bond of double bond overlap with sp3 C-C anti bond followed by the rotation of sigma bond of double and rotation of sp3 bonding of C-C. To form a monocyclic array of molecular orbitals which has odd number of out-of-phase overlaps, Mobius aromatic TS, forming HOMO of butadiene, rotation is restricted to conrotation. Diene formed then have different phases of p orbitals on terminal. <br>
2. Photochemical reaction <br>
Reaction proceeds with disrotation. When such a diene absorbs light of right frequency, an electron will be exiced from HOMO to LUMO. Now this diene has new HOMO and LUMO of ψ3 and ψ4 of ground state. In this case, To form Möbius aromatic transition state, sigma bond will choose disrotation to form the new bond p orbitals of different phase at ends. And now the transition state is better understood by a conical intersection in 2D PES accompanied by a change of symmetry. <br>
3.Opening of the cyclopropyl cation <br>
Reaction proceeds with dis-rotation. It forms a Huckel aromatic TS of 2 electrons and form a product of allylic cation which has same phases on terminal p orbital and stabilized by conical form. HOMO of OTs- helps stabilizing form of TS and leaves just after that. <br>
4. Opening of the cyclopropyl cation with hetero-atoms <br>
Conrotation needed to form Möbius aromatic transition state and gives a product with different phases at ends and has HOMO of C2v and pi cloud localized. <br>

==Conclusion==
In this work, different calculations are studied. Optimization to find the right structure. Frequency to check if it is correct. IRC to visualize free energy surface on intrinsic coordinate. Energy to compare different molecules on one potential surface. <br>
Important information can be extracted by using Gaussview like visualization of MO to study the FMO theory and symmetry of reaction. Thermochemistry data like Gibbs free enrgy, zero point energy and enthalpy an so on. Visualization of vibration modes can give the reaction coordinate. <br>
For pericyclic reactions, symmetry rules, Hammond's postulate, bond forming and rotation have been studied and there is still something to be explored like other thermal pericyclic reactions and light-induced pericyclic reactions.

==Reference==
1. file://icnas4.cc.ic.ac.uk/xy3513/9789048138609-c2.pdf

Rep:Xizi

2018-01-31T10:08:02Z

Xy3513: /* Introduction */

==Introduction==
===Transition State===
Transition state on a 1D potential energy surface is the highest point. But a 2D PES is in 3D-6 dimensions (degrees of freedom). It has lots of local minimas and maximas. Reactants and products corrsponding to local minimas, stationary point, with dV/dq=0 for all q and d2V/dq2>0 for all q, q is the geometric parameter. Intrinsic reaction coordinate, the lowest energy pathway linking two minima, is the path that would be followed by a molecule in going from one minimum to another when it just get enough energy to overcome the activation barrier, pass through the transition state, and reach the other minimum. A transition it is located on the maxima of the reaction path, which corresponding to reaction corrdinate, but minima of all other demesions, defined by dV/dq=0 and d2V/dq2>0 when q= reaction coordinate but d2V/dq2<0 for all other q.
The geometric parameter corresponding to the reaction coordinate is usually a composite of several parameters like bond lengths, angles and dihedrals. This will result in that sometimes trasntion state can be maxima on more than one reaction coordinate, which could be called a hilltop. Because two reaction path will lead to the same transition state, like the first exercise in the extension work. (1)
===Born–Oppenheimer Approximation===
When talking about the geometric coordiante, it is defined by nuclear coordinates the parameter. Which is to say, a potential energy surface is a plot of the energy of a collection of nuclei and electrons against the geometric coordinates of the nuclei. The reason is in the BO approximation which say nuclei could be assumed stationary with respect to electrons. So Schrcodinger equation for a molecule could be separated into an electronic and a nuclear equation. Two solved and added together to get the total internal energy.
===Computational method===
Computational method finds potential energy by computing Haltonian <Ψ|H|Ψ>=E, direction vectors, r=ax+by+cz=(1,3)Σci|i> in 3D space. <br>
LCAO gives |Ψ>=(1,N)Σci|Φ> in N dimension. Then E=(c1,...)(<Φ1|H|Φ1>...)(c1,...) and |Φ1>=aexp(-ar2) <br>
There are two methods used in this computational lab, semi-empirical paramazation method 6 (PM6) and density functional method Becke-3-LYP (B3lYP) with basis set 631G. <br>
PM6 is under Hartree–Fock formalism, but make many approximations and obtain some parameters from empirical data which allows some electron correlations. <br>
631g is a basis set of basis functions represent the electronic wave function in the Hartree–Fock method or DFT in order to turn the partial differential equations of the model into algebraic equations for computer. Molecular orbitals could then be expressed as linear combinations of the basis functions. <br>
Becke-3-LYP: a hybrid functional uses a mixing scheme of 3 parameters <br>
EXC = 0.2*EX(HF) + 0.8*EX(LSDA) + 0.72*DEX(B88) + 0.81*EC(LYP) + 0.19*EC(VWN) <br>
===Geometry Optimization===
Geometry optimization is the process of starting with an input structure and finding a stationary point on the PES. The stationary point found will normally be the one closest to the input structure. If calculating TS, analytical first and section derivative should as algorithms to be used.
===Frequency calculation and zero point energy===
Calculating vibrational spectrum (normal-mode vibrations) is often needed to check if the geometry is the desired one. The algorithm for this works by calculating an accurate
Hessian (force constant matrix) and diagonalizing it to give a matrix with the direction vectors,ř, of the normal modes, and a diagonal matrix with the force
constants,k, of these modes. Mass weighted force constants give the normal-mode vibration frequencies, v=h/2πc* (k/m)1/2. A transition state has one imaginary vibration, corresponding to motion along the reaction coordinate. K values calculated for transition state is all positive except one on reaction coordinate. <br>
The equations used for computing thermochemical data in Gaussian are equivalent to those in thermodynamics. One of the most important approximations to be aware of throughout this analysis is that all the equations assume non-interacting particles and therefore apply only to an ideal gas. This added up contribution of translation, electronic, vibrational and rotational motion. <br>
Sum of electronic and thermal free energies = ɛ0 + Gcorr

==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 14; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 8; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 9; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_REAL_TS_WITH_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).
===Calculation output by PM6===
optimized reactant: [[Media:YXZ_EXP1_DIENE_MINIPM6.LOG]] [[Media:YXZ EXP1 DIENE MINIPM6.LOG]]

optimized product: [[Media:YXZ_EXP_PRODUCT.LOG]]

otimized/frequency calculated transition state:[[Media:YXZ_EXP1_REAL_TS_WITH_MO.LOG]]

IRC to confirm the transition state: [[Media:YXZ_EXP2_IRC2.LOG]]

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
====Single point energy and IRC calculation====
{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}

IRC Calculation
[[File:YXZ EXP2 ENDO IRCPIC.png|800px|thumb|left|IRC of endo TS]]
[[File:YXZ EXP2 EXO IRCPIC.png|800px|thumb|left|IRC of exo TS]]

====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>Endo TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Kinetic product and thermodynamic product are ones have smallest activation energy and largest reaction ernergy. In this case, both are endo product, numerical calculation will be shown soon.
However, Diesl Alder reaction could be reversed by taking in and releasing energy. Also interesting are the fastest formed product and the most stable product. <br>
The fastest formed product. <br>
The Arrhenius Equation states that reaction rate constant is related to Ea by k=Ae−Ea/RT. A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lowest free energy of TS and one is higher rate of collision. <br> So thermodynamic control involves raising temperature.
The most stable product, having less chance of going reversible reaction to products or other dissociation reaction. One has lowest free energy of product and lowest rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. It is also the fastest and most stable product. <br>

====Secondary orbital interation====

Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

===Calculation output by B3LYP 621g.d.p===
Optimized endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_TS_631_WITH_MO3.log]]

Optimized exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_TS631_MOLATEST.log]]

Energy calulation exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_ENERGY4WITHMO.log]]

Energy calculation endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_ENERGY2.log]]

IRC endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_IRC4.log.log]]

IRC exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_IRC4.log]]

B3LYP optimized dioxole (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIXOLE631.LOG]]

B3LYP optimized cyclohexadiene (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIENE631.LOG]]

B3LYP optimized endo product (frequency calculation is done in the same file): [[Media:EXP2_ENDO_MINI631_FREQUENCY_CHECK.LOG]]

B3LYP optimized exo product (frequency calculation is done in the same file): [[Media:EXP2_EXO_621_MINI.LOG]]

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; </script>
<uploadedFileContents>YXZ_EXP3_DAENDO_TS1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXP3_CHELE_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output by PM6===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

==Further work==
==Conclusion==
In this work, different calculations are studied. Optimization to find the right structure. Frequency to check if it is correct. IRC to visualize free energy surface on intrinsic coordinate. Energy to compare different molecules on one potential surface. <br>
Important information can be extracted by using Gaussview like visualization of MO to study the FMO theory and symmetry of reaction. Thermochemistry data like Gibbs free enrgy, zero point energy and enthalpy an so on. Visualization of vibration modes can give the reaction coordinate. <br>
For pericyclic reactions, symmetry rules, Hammond's postulate, bond forming and rotation have been studied and there is still something to be explored like other thermal pericyclic reactions and light-induced pericyclic reactions.

==Reference==
1. file://icnas4.cc.ic.ac.uk/xy3513/9789048138609-c2.pdf

Rep:Xizi

2018-01-31T03:14:53Z

Xy3513: /* Further work */

==Introduction==
===Transition State===
Transition state on a 1D potential energy surface is the highest point. But a 2D PES is in 3D-6 dimensions (degrees of freedom). It has lots of local minimas and maximas. Reactants and products corrsponding to local minimas, stationary point, with dV/dq=0 for all q and d2V/dq2>0 for all q, q is the geometric parameter. Intrinsic reaction coordinate, the lowest energy pathway linking two minima, is the path that would be followed by a molecule in going from one minimum to another when it just get enough energy to overcome the activation barrier, pass through the transition state, and reach the other minimum. A transition it is located on the maxima of the reaction path, which corresponding to reaction corrdinate, but minima of all other demesions, defined by dV/dq=0 and d2V/dq2>0 when q= reaction coordinate but d2V/dq2<0 for all other q.
The geometric parameter corresponding to the reaction coordinate is usually a composite of several parameters like bond lengths, angles and dihedrals. This will result in that sometimes trasntion state can be maxima on more than one reaction coordinate, which could be called a hilltop. Because two reaction path will lead to the same transition state, like the first exercise in the extension work. (1)
===Born–Oppenheimer Approximation===
When talking about the geometric coordiante, it is defined by nuclear coordinates the parameter. Which is to say, a potential energy surface is a plot of the energy of a collection of nuclei and electrons against the geometric coordinates of the nuclei. The reason is in the BO approximation which say nuclei could be assumed stationary with respect to electrons. So Schrcodinger equation for a molecule could be separated into an electronic and a nuclear equation. Two solved and added together to get the total internal energy.
===Computational method===
Computational method finds potential energy by computing Haltonian <Ψ|H|Ψ>=E, direction vectors, r=ax+by+cz=(1,3)Σci|i> in 3D space. <br>
LCAO gives |Ψ>=(1,N)Σci|Φ> in N dimension. Then E=(c1,...)(<Φ1|H|Φ1>...)(c1,...) and |Φ1>=aexp(-ar2) <br>
There are two methods used in this computational lab, semi-empirical paramazation method 6 (PM6) and density functional method Becke-3-LYP (B3lYP) with basis set 631G. <br>
PM6 is under Hartree–Fock formalism, but make many approximations and obtain some parameters from empirical data which allows some electron correlations. <br>
631g is a basis set of basis functions represent the electronic wave function in the Hartree–Fock method or DFT in order to turn the partial differential equations of the model into algebraic equations for computer. Molecular orbitals could then be expressed as linear combinations of the basis functions. <br>
Becke-3-LYP: a hybrid functional uses a mixing scheme of 3 parameters <br>
EXC = 0.2*EX(HF) + 0.8*EX(LSDA) + 0.72*DEX(B88) + 0.81*EC(LYP) + 0.19*EC(VWN) <br>
===Geometry Optimization===
Geometry optimization is the process of starting with an input structure and finding a stationary point on the PES. The stationary point found will normally be the one closest to the input structure. If calculating TS, analytical first and section derivative should as algorithms to be used.
===Frequency calculation and zero energy===
Calculating vibrational spectrum (normal-mode vibrations) is often needed to check if the geometry is the desired one. The algorithm for this works by calculating an accurate
Hessian (force constant matrix) and diagonalizing it to give a matrix with the direction vectors,ř, of the normal modes, and a diagonal matrix with the force
constants,k, of these modes. Mass weighted force constants give the normal-mode vibration frequencies, v=h/2πc* (k/m)1/2. A transition state has one imaginary vibration, corresponding to motion along the reaction coordinate. K values calculated for transition state is all positive except one on reaction coordinate.

==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 14; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 8; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 9; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_REAL_TS_WITH_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).
===Calculation output by PM6===
optimized reactant: [[Media:YXZ_EXP1_DIENE_MINIPM6.LOG]] [[Media:YXZ EXP1 DIENE MINIPM6.LOG]]

optimized product: [[Media:YXZ_EXP_PRODUCT.LOG]]

otimized/frequency calculated transition state:[[Media:YXZ_EXP1_REAL_TS_WITH_MO.LOG]]

IRC to confirm the transition state: [[Media:YXZ_EXP2_IRC2.LOG]]

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
====Single point energy and IRC calculation====
{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
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<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}

IRC Calculation
[[File:YXZ EXP2 ENDO IRCPIC.png|800px|thumb|left|IRC of endo TS]]
[[File:YXZ EXP2 EXO IRCPIC.png|800px|thumb|left|IRC of exo TS]]

====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>Endo TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
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===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Kinetic product and thermodynamic product are ones have smallest activation energy and largest reaction ernergy. In this case, both are endo product, numerical calculation will be shown soon.
However, Diesl Alder reaction could be reversed by taking in and releasing energy. Also interesting are the fastest formed product and the most stable product. <br>
The fastest formed product. <br>
The Arrhenius Equation states that reaction rate constant is related to Ea by k=Ae−Ea/RT. A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lowest free energy of TS and one is higher rate of collision. <br> So thermodynamic control involves raising temperature.
The most stable product, having less chance of going reversible reaction to products or other dissociation reaction. One has lowest free energy of product and lowest rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. It is also the fastest and most stable product. <br>

====Secondary orbital interation====

Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

===Calculation output by B3LYP 621g.d.p===
Optimized endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_TS_631_WITH_MO3.log]]

Optimized exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_TS631_MOLATEST.log]]

Energy calulation exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_ENERGY4WITHMO.log]]

Energy calculation endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_ENERGY2.log]]

IRC endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_IRC4.log.log]]

IRC exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_IRC4.log]]

B3LYP optimized dioxole (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIXOLE631.LOG]]

B3LYP optimized cyclohexadiene (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIENE631.LOG]]

B3LYP optimized endo product (frequency calculation is done in the same file): [[Media:EXP2_ENDO_MINI631_FREQUENCY_CHECK.LOG]]

B3LYP optimized exo product (frequency calculation is done in the same file): [[Media:EXP2_EXO_621_MINI.LOG]]

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; </script>
<uploadedFileContents>YXZ_EXP3_DAENDO_TS1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXP3_CHELE_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output by PM6===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

==Further work==
==Conclusion==
In this work, different calculations are studied. Optimization to find the right structure. Frequency to check if it is correct. IRC to visualize free energy surface on intrinsic coordinate. Energy to compare different molecules on one potential surface. <br>
Important information can be extracted by using Gaussview like visualization of MO to study the FMO theory and symmetry of reaction. Thermochemistry data like Gibbs free enrgy, zero point energy and enthalpy an so on. Visualization of vibration modes can give the reaction coordinate. <br>
For pericyclic reactions, symmetry rules, Hammond's postulate, bond forming and rotation have been studied and there is still something to be explored like other thermal pericyclic reactions and light-induced pericyclic reactions.

==Reference==
1. file://icnas4.cc.ic.ac.uk/xy3513/9789048138609-c2.pdf

Rep:Xizi

2018-01-31T02:57:36Z

Xy3513: /* Calculation output by PM6 */

==Introduction==
===Transition State===
Transition state on a 1D potential energy surface is the highest point. But a 2D PES is in 3D-6 dimensions (degrees of freedom). It has lots of local minimas and maximas. Reactants and products corrsponding to local minimas, stationary point, with dV/dq=0 for all q and d2V/dq2>0 for all q, q is the geometric parameter. Intrinsic reaction coordinate, the lowest energy pathway linking two minima, is the path that would be followed by a molecule in going from one minimum to another when it just get enough energy to overcome the activation barrier, pass through the transition state, and reach the other minimum. A transition it is located on the maxima of the reaction path, which corresponding to reaction corrdinate, but minima of all other demesions, defined by dV/dq=0 and d2V/dq2>0 when q= reaction coordinate but d2V/dq2<0 for all other q.
The geometric parameter corresponding to the reaction coordinate is usually a composite of several parameters like bond lengths, angles and dihedrals. This will result in that sometimes trasntion state can be maxima on more than one reaction coordinate, which could be called a hilltop. Because two reaction path will lead to the same transition state, like the first exercise in the extension work. (1)
===Born–Oppenheimer Approximation===
When talking about the geometric coordiante, it is defined by nuclear coordinates the parameter. Which is to say, a potential energy surface is a plot of the energy of a collection of nuclei and electrons against the geometric coordinates of the nuclei. The reason is in the BO approximation which say nuclei could be assumed stationary with respect to electrons. So Schrcodinger equation for a molecule could be separated into an electronic and a nuclear equation. Two solved and added together to get the total internal energy.
===Computational method===
Computational method finds potential energy by computing Haltonian <Ψ|H|Ψ>=E, direction vectors, r=ax+by+cz=(1,3)Σci|i> in 3D space. <br>
LCAO gives |Ψ>=(1,N)Σci|Φ> in N dimension. Then E=(c1,...)(<Φ1|H|Φ1>...)(c1,...) and |Φ1>=aexp(-ar2) <br>
There are two methods used in this computational lab, semi-empirical paramazation method 6 (PM6) and density functional method Becke-3-LYP (B3lYP) with basis set 631G. <br>
PM6 is under Hartree–Fock formalism, but make many approximations and obtain some parameters from empirical data which allows some electron correlations. <br>
631g is a basis set of basis functions represent the electronic wave function in the Hartree–Fock method or DFT in order to turn the partial differential equations of the model into algebraic equations for computer. Molecular orbitals could then be expressed as linear combinations of the basis functions. <br>
Becke-3-LYP: a hybrid functional uses a mixing scheme of 3 parameters <br>
EXC = 0.2*EX(HF) + 0.8*EX(LSDA) + 0.72*DEX(B88) + 0.81*EC(LYP) + 0.19*EC(VWN) <br>
===Geometry Optimization===
Geometry optimization is the process of starting with an input structure and finding a stationary point on the PES. The stationary point found will normally be the one closest to the input structure. If calculating TS, analytical first and section derivative should as algorithms to be used.
===Frequency calculation and zero energy===
Calculating vibrational spectrum (normal-mode vibrations) is often needed to check if the geometry is the desired one. The algorithm for this works by calculating an accurate
Hessian (force constant matrix) and diagonalizing it to give a matrix with the direction vectors,ř, of the normal modes, and a diagonal matrix with the force
constants,k, of these modes. Mass weighted force constants give the normal-mode vibration frequencies, v=h/2πc* (k/m)1/2. A transition state has one imaginary vibration, corresponding to motion along the reaction coordinate. K values calculated for transition state is all positive except one on reaction coordinate.

==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 14; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_REAL_TS_WITH_MO.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<uploadedFileContents>YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).
===Calculation output by PM6===
optimized reactant: [[Media:YXZ_EXP1_DIENE_MINIPM6.LOG]] [[Media:YXZ EXP1 DIENE MINIPM6.LOG]]

optimized product: [[Media:YXZ_EXP_PRODUCT.LOG]]

otimized/frequency calculated transition state:[[Media:YXZ_EXP1_REAL_TS_WITH_MO.LOG]]

IRC to confirm the transition state: [[Media:YXZ_EXP2_IRC2.LOG]]

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
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<color>white</color>
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|<jmol>
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|-
|}
====Single point energy and IRC calculation====
{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
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<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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|<jmol>
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|<jmol>
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|<jmol>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
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|<jmol>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}

IRC Calculation
[[File:YXZ EXP2 ENDO IRCPIC.png|800px|thumb|left|IRC of endo TS]]
[[File:YXZ EXP2 EXO IRCPIC.png|800px|thumb|left|IRC of exo TS]]

====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>white</color>
<size>200</size>
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<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>Endo TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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|}

[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Kinetic product and thermodynamic product are ones have smallest activation energy and largest reaction ernergy. In this case, both are endo product, numerical calculation will be shown soon.
However, Diesl Alder reaction could be reversed by taking in and releasing energy. Also interesting are the fastest formed product and the most stable product. <br>
The fastest formed product. <br>
The Arrhenius Equation states that reaction rate constant is related to Ea by k=Ae−Ea/RT. A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lowest free energy of TS and one is higher rate of collision. <br> So thermodynamic control involves raising temperature.
The most stable product, having less chance of going reversible reaction to products or other dissociation reaction. One has lowest free energy of product and lowest rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. It is also the fastest and most stable product. <br>

====Secondary orbital interation====

Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

===Calculation output by B3LYP 621g.d.p===
Optimized endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_TS_631_WITH_MO3.log]]

Optimized exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_TS631_MOLATEST.log]]

Energy calulation exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_ENERGY4WITHMO.log]]

Energy calculation endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_ENERGY2.log]]

IRC endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_IRC4.log.log]]

IRC exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_IRC4.log]]

B3LYP optimized dioxole (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIXOLE631.LOG]]

B3LYP optimized cyclohexadiene (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIENE631.LOG]]

B3LYP optimized endo product (frequency calculation is done in the same file): [[Media:EXP2_ENDO_MINI631_FREQUENCY_CHECK.LOG]]

B3LYP optimized exo product (frequency calculation is done in the same file): [[Media:EXP2_EXO_621_MINI.LOG]]

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
|<jmol>
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<size>200</size>
<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
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|<jmol>
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<script>frame 30; </script>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
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|<jmol>
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<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
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|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output by PM6===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

==Further work==
==Reference==
1. file://icnas4.cc.ic.ac.uk/xy3513/9789048138609-c2.pdf

File:YXZ EXP PRODUCT.LOG

2018-01-31T02:57:12Z

Xy3513: Xy3513 uploaded a new version of File:YXZ EXP PRODUCT.LOG

Rep:Xizi

2018-01-31T02:55:44Z

Xy3513: /* Exercise 1: Reaction of Butadiene with Ethylene */

==Introduction==
===Transition State===
Transition state on a 1D potential energy surface is the highest point. But a 2D PES is in 3D-6 dimensions (degrees of freedom). It has lots of local minimas and maximas. Reactants and products corrsponding to local minimas, stationary point, with dV/dq=0 for all q and d2V/dq2>0 for all q, q is the geometric parameter. Intrinsic reaction coordinate, the lowest energy pathway linking two minima, is the path that would be followed by a molecule in going from one minimum to another when it just get enough energy to overcome the activation barrier, pass through the transition state, and reach the other minimum. A transition it is located on the maxima of the reaction path, which corresponding to reaction corrdinate, but minima of all other demesions, defined by dV/dq=0 and d2V/dq2>0 when q= reaction coordinate but d2V/dq2<0 for all other q.
The geometric parameter corresponding to the reaction coordinate is usually a composite of several parameters like bond lengths, angles and dihedrals. This will result in that sometimes trasntion state can be maxima on more than one reaction coordinate, which could be called a hilltop. Because two reaction path will lead to the same transition state, like the first exercise in the extension work. (1)
===Born–Oppenheimer Approximation===
When talking about the geometric coordiante, it is defined by nuclear coordinates the parameter. Which is to say, a potential energy surface is a plot of the energy of a collection of nuclei and electrons against the geometric coordinates of the nuclei. The reason is in the BO approximation which say nuclei could be assumed stationary with respect to electrons. So Schrcodinger equation for a molecule could be separated into an electronic and a nuclear equation. Two solved and added together to get the total internal energy.
===Computational method===
Computational method finds potential energy by computing Haltonian <Ψ|H|Ψ>=E, direction vectors, r=ax+by+cz=(1,3)Σci|i> in 3D space. <br>
LCAO gives |Ψ>=(1,N)Σci|Φ> in N dimension. Then E=(c1,...)(<Φ1|H|Φ1>...)(c1,...) and |Φ1>=aexp(-ar2) <br>
There are two methods used in this computational lab, semi-empirical paramazation method 6 (PM6) and density functional method Becke-3-LYP (B3lYP) with basis set 631G. <br>
PM6 is under Hartree–Fock formalism, but make many approximations and obtain some parameters from empirical data which allows some electron correlations. <br>
631g is a basis set of basis functions represent the electronic wave function in the Hartree–Fock method or DFT in order to turn the partial differential equations of the model into algebraic equations for computer. Molecular orbitals could then be expressed as linear combinations of the basis functions. <br>
Becke-3-LYP: a hybrid functional uses a mixing scheme of 3 parameters <br>
EXC = 0.2*EX(HF) + 0.8*EX(LSDA) + 0.72*DEX(B88) + 0.81*EC(LYP) + 0.19*EC(VWN) <br>
===Geometry Optimization===
Geometry optimization is the process of starting with an input structure and finding a stationary point on the PES. The stationary point found will normally be the one closest to the input structure. If calculating TS, analytical first and section derivative should as algorithms to be used.
===Frequency calculation and zero energy===
Calculating vibrational spectrum (normal-mode vibrations) is often needed to check if the geometry is the desired one. The algorithm for this works by calculating an accurate
Hessian (force constant matrix) and diagonalizing it to give a matrix with the direction vectors,ř, of the normal modes, and a diagonal matrix with the force
constants,k, of these modes. Mass weighted force constants give the normal-mode vibration frequencies, v=h/2πc* (k/m)1/2. A transition state has one imaginary vibration, corresponding to motion along the reaction coordinate. K values calculated for transition state is all positive except one on reaction coordinate.

==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
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<uploadedFileContents> YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
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<uploadedFileContents> YXZ_EXP1_REAL_TS_WITH_MO.LOG </uploadedFileContents>
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|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).
===Calculation output by PM6===
optimized reactant: [[Media:YXZ_EXP1_DIENE_MINIPM6.LOG]] [[Media:YXZ EXP1 DIENE MINIPM6.LOG]]

optimized product: [[Media:JSHENY3_EX1_OPT1_PRODUCT.LOG]]

otimized/frequency calculated transition state:[[Media:YXZ_EXP1_REAL_TS_WITH_MO.LOG]]

IRC to confirm the transition state: [[Media:YXZ_EXP2_IRC2.LOG]]

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
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|-
|}
====Single point energy and IRC calculation====
{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
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<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}

IRC Calculation
[[File:YXZ EXP2 ENDO IRCPIC.png|800px|thumb|left|IRC of endo TS]]
[[File:YXZ EXP2 EXO IRCPIC.png|800px|thumb|left|IRC of exo TS]]

====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>Endo TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
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===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Kinetic product and thermodynamic product are ones have smallest activation energy and largest reaction ernergy. In this case, both are endo product, numerical calculation will be shown soon.
However, Diesl Alder reaction could be reversed by taking in and releasing energy. Also interesting are the fastest formed product and the most stable product. <br>
The fastest formed product. <br>
The Arrhenius Equation states that reaction rate constant is related to Ea by k=Ae−Ea/RT. A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lowest free energy of TS and one is higher rate of collision. <br> So thermodynamic control involves raising temperature.
The most stable product, having less chance of going reversible reaction to products or other dissociation reaction. One has lowest free energy of product and lowest rate of collision to go back to product. <br>
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Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
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Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. It is also the fastest and most stable product. <br>

====Secondary orbital interation====

Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

===Calculation output by B3LYP 621g.d.p===
Optimized endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_TS_631_WITH_MO3.log]]

Optimized exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_TS631_MOLATEST.log]]

Energy calulation exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_ENERGY4WITHMO.log]]

Energy calculation endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_ENERGY2.log]]

IRC endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_IRC4.log.log]]

IRC exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_IRC4.log]]

B3LYP optimized dioxole (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIXOLE631.LOG]]

B3LYP optimized cyclohexadiene (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIENE631.LOG]]

B3LYP optimized endo product (frequency calculation is done in the same file): [[Media:EXP2_ENDO_MINI631_FREQUENCY_CHECK.LOG]]

B3LYP optimized exo product (frequency calculation is done in the same file): [[Media:EXP2_EXO_621_MINI.LOG]]

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; </script>
<uploadedFileContents>YXZ_EXP3_DAENDO_TS1.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXP3_CHELE_TS.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output by PM6===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

==Further work==
==Reference==
1. file://icnas4.cc.ic.ac.uk/xy3513/9789048138609-c2.pdf

File:YXZ EXP2 IRC2.LOG

2018-01-31T02:55:21Z

Xy3513:

File:YXZ EXP1 REAL TS WITH MO.LOG

2018-01-31T02:52:01Z

Xy3513:

File:YXZ EXP1 DIENE MINIPM6.LOG

2018-01-31T02:46:49Z

Xy3513:

File:DIENE MINIPM6.LOG

2018-01-31T02:46:03Z

Xy3513:

Rep:Xizi

2018-01-31T02:42:23Z

Xy3513:

==Introduction==
===Transition State===
Transition state on a 1D potential energy surface is the highest point. But a 2D PES is in 3D-6 dimensions (degrees of freedom). It has lots of local minimas and maximas. Reactants and products corrsponding to local minimas, stationary point, with dV/dq=0 for all q and d2V/dq2>0 for all q, q is the geometric parameter. Intrinsic reaction coordinate, the lowest energy pathway linking two minima, is the path that would be followed by a molecule in going from one minimum to another when it just get enough energy to overcome the activation barrier, pass through the transition state, and reach the other minimum. A transition it is located on the maxima of the reaction path, which corresponding to reaction corrdinate, but minima of all other demesions, defined by dV/dq=0 and d2V/dq2>0 when q= reaction coordinate but d2V/dq2<0 for all other q.
The geometric parameter corresponding to the reaction coordinate is usually a composite of several parameters like bond lengths, angles and dihedrals. This will result in that sometimes trasntion state can be maxima on more than one reaction coordinate, which could be called a hilltop. Because two reaction path will lead to the same transition state, like the first exercise in the extension work. (1)
===Born–Oppenheimer Approximation===
When talking about the geometric coordiante, it is defined by nuclear coordinates the parameter. Which is to say, a potential energy surface is a plot of the energy of a collection of nuclei and electrons against the geometric coordinates of the nuclei. The reason is in the BO approximation which say nuclei could be assumed stationary with respect to electrons. So Schrcodinger equation for a molecule could be separated into an electronic and a nuclear equation. Two solved and added together to get the total internal energy.
===Computational method===
Computational method finds potential energy by computing Haltonian <Ψ|H|Ψ>=E, direction vectors, r=ax+by+cz=(1,3)Σci|i> in 3D space. <br>
LCAO gives |Ψ>=(1,N)Σci|Φ> in N dimension. Then E=(c1,...)(<Φ1|H|Φ1>...)(c1,...) and |Φ1>=aexp(-ar2) <br>
There are two methods used in this computational lab, semi-empirical paramazation method 6 (PM6) and density functional method Becke-3-LYP (B3lYP) with basis set 631G. <br>
PM6 is under Hartree–Fock formalism, but make many approximations and obtain some parameters from empirical data which allows some electron correlations. <br>
631g is a basis set of basis functions represent the electronic wave function in the Hartree–Fock method or DFT in order to turn the partial differential equations of the model into algebraic equations for computer. Molecular orbitals could then be expressed as linear combinations of the basis functions. <br>
Becke-3-LYP: a hybrid functional uses a mixing scheme of 3 parameters <br>
EXC = 0.2*EX(HF) + 0.8*EX(LSDA) + 0.72*DEX(B88) + 0.81*EC(LYP) + 0.19*EC(VWN) <br>
===Geometry Optimization===
Geometry optimization is the process of starting with an input structure and finding a stationary point on the PES. The stationary point found will normally be the one closest to the input structure. If calculating TS, analytical first and section derivative should as algorithms to be used.
===Frequency calculation and zero energy===
Calculating vibrational spectrum (normal-mode vibrations) is often needed to check if the geometry is the desired one. The algorithm for this works by calculating an accurate
Hessian (force constant matrix) and diagonalizing it to give a matrix with the direction vectors,ř, of the normal modes, and a diagonal matrix with the force
constants,k, of these modes. Mass weighted force constants give the normal-mode vibration frequencies, v=h/2πc* (k/m)1/2. A transition state has one imaginary vibration, corresponding to motion along the reaction coordinate. K values calculated for transition state is all positive except one on reaction coordinate.

==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
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<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
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|<jmol>
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|<jmol>
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</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 9; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
====Single point energy and IRC calculation====
{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}

IRC Calculation
[[File:YXZ EXP2 ENDO IRCPIC.png|800px|thumb|left|IRC of endo TS]]
[[File:YXZ EXP2 EXO IRCPIC.png|800px|thumb|left|IRC of exo TS]]

====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>Endo TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Kinetic product and thermodynamic product are ones have smallest activation energy and largest reaction ernergy. In this case, both are endo product, numerical calculation will be shown soon.
However, Diesl Alder reaction could be reversed by taking in and releasing energy. Also interesting are the fastest formed product and the most stable product. <br>
The fastest formed product. <br>
The Arrhenius Equation states that reaction rate constant is related to Ea by k=Ae−Ea/RT. A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lowest free energy of TS and one is higher rate of collision. <br> So thermodynamic control involves raising temperature.
The most stable product, having less chance of going reversible reaction to products or other dissociation reaction. One has lowest free energy of product and lowest rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. It is also the fastest and most stable product. <br>

====Secondary orbital interation====

Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

===Calculation output by B3LYP 621g.d.p===
Optimized endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_TS_631_WITH_MO3.log]]

Optimized exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_TS631_MOLATEST.log]]

Energy calulation exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_ENERGY4WITHMO.log]]

Energy calculation endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_ENERGY2.log]]

IRC endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_IRC4.log.log]]

IRC exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_IRC4.log]]

B3LYP optimized dioxole (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIXOLE631.LOG]]

B3LYP optimized cyclohexadiene (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIENE631.LOG]]

B3LYP optimized endo product (frequency calculation is done in the same file): [[Media:EXP2_ENDO_MINI631_FREQUENCY_CHECK.LOG]]

B3LYP optimized exo product (frequency calculation is done in the same file): [[Media:EXP2_EXO_621_MINI.LOG]]

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; </script>
<uploadedFileContents>YXZ_EXP3_DAENDO_TS1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXP3_CHELE_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output by PM6===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

==Further work==
==Reference==
1. file://icnas4.cc.ic.ac.uk/xy3513/9789048138609-c2.pdf

Rep:Xizi

2018-01-31T02:41:22Z

Xy3513: /* Calculation output by PM6 */

==Introduction==
===Transition State===
Transition state on a 1D potential energy surface is the highest point. But a 2D PES is in 3D-6 dimensions (degrees of freedom). It has lots of local minimas and maximas. Reactants and products corrsponding to local minimas, stationary point, with dV/dq=0 for all q and d2V/dq2>0 for all q, q is the geometric parameter. Intrinsic reaction coordinate, the lowest energy pathway linking two minima, is the path that would be followed by a molecule in going from one minimum to another when it just get enough energy to overcome the activation barrier, pass through the transition state, and reach the other minimum. A transition it is located on the maxima of the reaction path, which corresponding to reaction corrdinate, but minima of all other demesions, defined by dV/dq=0 and d2V/dq2>0 when q= reaction coordinate but d2V/dq2<0 for all other q.
The geometric parameter corresponding to the reaction coordinate is usually a composite of several parameters like bond lengths, angles and dihedrals. This will result in that sometimes trasntion state can be maxima on more than one reaction coordinate, which could be called a hilltop. Because two reaction path will lead to the same transition state, like the first exercise in the extension work. (1)
===Born–Oppenheimer Approximation===
When talking about the geometric coordiante, it is defined by nuclear coordinates the parameter. Which is to say, a potential energy surface is a plot of the energy of a collection of nuclei and electrons against the geometric coordinates of the nuclei. The reason is in the BO approximation which say nuclei could be assumed stationary with respect to electrons. So Schrcodinger equation for a molecule could be separated into an electronic and a nuclear equation. Two solved and added together to get the total internal energy.
===Computational method===
Computational method finds potential energy by computing Haltonian <Ψ|H|Ψ>=E, direction vectors, r=ax+by+cz=(1,3)Σci|i> in 3D space. <br>
LCAO gives |Ψ>=(1,N)Σci|Φ> in N dimension. Then E=(c1,...)(<Φ1|H|Φ1>...)(c1,...) and |Φ1>=aexp(-ar2) <br>
There are two methods used in this computational lab, semi-empirical paramazation method 6 (PM6) and density functional method Becke-3-LYP (B3lYP) with basis set 631G. <br>
PM6 is under Hartree–Fock formalism, but make many approximations and obtain some parameters from empirical data which allows some electron correlations. <br>
631g is a basis set of basis functions represent the electronic wave function in the Hartree–Fock method or DFT in order to turn the partial differential equations of the model into algebraic equations for computer. Molecular orbitals could then be expressed as linear combinations of the basis functions. <br>
Becke-3-LYP: a hybrid functional uses a mixing scheme of 3 parameters <br>
EXC = 0.2*EX(HF) + 0.8*EX(LSDA) + 0.72*DEX(B88) + 0.81*EC(LYP) + 0.19*EC(VWN) <br>
===Geometry Optimization===
Geometry optimization is the process of starting with an input structure and finding a stationary point on the PES. The stationary point found will normally be the one closest to the input structure. If calculating TS, analytical first and section derivative should as algorithms to be used.
===Frequency calculation and zero energy===
Calculating vibrational spectrum (normal-mode vibrations) is often needed to check if the geometry is the desired one. The algorithm for this works by calculating an accurate
Hessian (force constant matrix) and diagonalizing it to give a matrix with the direction vectors,ř, of the normal modes, and a diagonal matrix with the force
constants,k, of these modes. Mass weighted force constants give the normal-mode vibration frequencies, v=h/2πc* (k/m)1/2. A transition state has one imaginary vibration, corresponding to motion along the reaction coordinate. K values calculated for transition state is all positive except one on reaction coordinate.

==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 14; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
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|<jmol>
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<color>white</color>
<size>150</size>
<script>frame 12; mo 8; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
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|<jmol>
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<color>white</color>
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<script>frame 12; mo 9; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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</jmol>
|-
|}
====Single point energy and IRC calculation====
{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
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<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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</jmol>

|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}

IRC Calculation
[[File:YXZ EXP2 ENDO IRCPIC.png|800px|thumb|left|IRC of endo TS]]
[[File:YXZ EXP2 EXO IRCPIC.png|800px|thumb|left|IRC of exo TS]]

====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>Endo TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
<br>
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<br>
===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Kinetic product and thermodynamic product are ones have smallest activation energy and largest reaction ernergy. In this case, both are endo product, numerical calculation will be shown soon.
However, Diesl Alder reaction could be reversed by taking in and releasing energy. Also interesting are the fastest formed product and the most stable product. <br>
The fastest formed product. <br>
The Arrhenius Equation states that reaction rate constant is related to Ea by k=Ae−Ea/RT. A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lowest free energy of TS and one is higher rate of collision. <br> So thermodynamic control involves raising temperature.
The most stable product, having less chance of going reversible reaction to products or other dissociation reaction. One has lowest free energy of product and lowest rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. It is also the fastest and most stable product. <br>

====Secondary orbital interation====

Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

===Calculation output by B3LYP 621g.d.p===
Optimized endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_TS_631_WITH_MO3.log]]

Optimized exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_TS631_MOLATEST.log]]

Energy calulation exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_ENERGY4WITHMO.log]]

Energy calculation endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_ENERGY2.log]]

IRC endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_IRC4.log.log]]

IRC exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_IRC4.log]]

B3LYP optimized dioxole (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIXOLE631.LOG]]

B3LYP optimized cyclohexadiene (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIENE631.LOG]]

B3LYP optimized endo product (frequency calculation is done in the same file): [[Media:EXP2_ENDO_MINI631_FREQUENCY_CHECK.LOG]]

B3LYP optimized exo product (frequency calculation is done in the same file): [[Media:EXP2_EXO_621_MINI.LOG]]

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; </script>
<uploadedFileContents>YXZ_EXP3_DAENDO_TS1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXP3_CHELE_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output by PM6===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

==Further work==
==Reference==
1. file://icnas4.cc.ic.ac.uk/xy3513/9789048138609-c2.pdf

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

Rep:Xizi

2018-01-31T02:38:19Z

Xy3513:

==Introduction==
===Transition State===
Transition state on a 1D potential energy surface is the highest point. But a 2D PES is in 3D-6 dimensions (degrees of freedom). It has lots of local minimas and maximas. Reactants and products corrsponding to local minimas, stationary point, with dV/dq=0 for all q and d2V/dq2>0 for all q, q is the geometric parameter. Intrinsic reaction coordinate, the lowest energy pathway linking two minima, is the path that would be followed by a molecule in going from one minimum to another when it just get enough energy to overcome the activation barrier, pass through the transition state, and reach the other minimum. A transition it is located on the maxima of the reaction path, which corresponding to reaction corrdinate, but minima of all other demesions, defined by dV/dq=0 and d2V/dq2>0 when q= reaction coordinate but d2V/dq2<0 for all other q.
The geometric parameter corresponding to the reaction coordinate is usually a composite of several parameters like bond lengths, angles and dihedrals. This will result in that sometimes trasntion state can be maxima on more than one reaction coordinate, which could be called a hilltop. Because two reaction path will lead to the same transition state, like the first exercise in the extension work. (1)
===Born–Oppenheimer Approximation===
When talking about the geometric coordiante, it is defined by nuclear coordinates the parameter. Which is to say, a potential energy surface is a plot of the energy of a collection of nuclei and electrons against the geometric coordinates of the nuclei. The reason is in the BO approximation which say nuclei could be assumed stationary with respect to electrons. So Schrcodinger equation for a molecule could be separated into an electronic and a nuclear equation. Two solved and added together to get the total internal energy.
===Computational method===
Computational method finds potential energy by computing Haltonian <Ψ|H|Ψ>=E, direction vectors, r=ax+by+cz=(1,3)Σci|i> in 3D space. <br>
LCAO gives |Ψ>=(1,N)Σci|Φ> in N dimension. Then E=(c1,...)(<Φ1|H|Φ1>...)(c1,...) and |Φ1>=aexp(-ar2) <br>
There are two methods used in this computational lab, semi-empirical paramazation method 6 (PM6) and density functional method Becke-3-LYP (B3lYP) with basis set 631G. <br>
PM6 is under Hartree–Fock formalism, but make many approximations and obtain some parameters from empirical data which allows some electron correlations. <br>
631g is a basis set of basis functions represent the electronic wave function in the Hartree–Fock method or DFT in order to turn the partial differential equations of the model into algebraic equations for computer. Molecular orbitals could then be expressed as linear combinations of the basis functions. <br>
Becke-3-LYP: a hybrid functional uses a mixing scheme of 3 parameters <br>
EXC = 0.2*EX(HF) + 0.8*EX(LSDA) + 0.72*DEX(B88) + 0.81*EC(LYP) + 0.19*EC(VWN) <br>
===Geometry Optimization===
Geometry optimization is the process of starting with an input structure and finding a stationary point on the PES. The stationary point found will normally be the one closest to the input structure. If calculating TS, analytical first and section derivative should as algorithms to be used.
===Frequency calculation and zero energy===
Calculating vibrational spectrum (normal-mode vibrations) is often needed to check if the geometry is the desired one. The algorithm for this works by calculating an accurate
Hessian (force constant matrix) and diagonalizing it to give a matrix with the direction vectors,ř, of the normal modes, and a diagonal matrix with the force
constants,k, of these modes. Mass weighted force constants give the normal-mode vibration frequencies, v=h/2πc* (k/m)1/2. A transition state has one imaginary vibration, corresponding to motion along the reaction coordinate. K values calculated for transition state is all positive except one on reaction coordinate.

==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 14; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 8; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 9; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
====Single point energy and IRC calculation====
{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}

IRC Calculation
[[File:YXZ EXP2 ENDO IRCPIC.png|800px|thumb|left|IRC of endo TS]]
[[File:YXZ EXP2 EXO IRCPIC.png|800px|thumb|left|IRC of exo TS]]

====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>Endo TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
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===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Kinetic product and thermodynamic product are ones have smallest activation energy and largest reaction ernergy. In this case, both are endo product, numerical calculation will be shown soon.
However, Diesl Alder reaction could be reversed by taking in and releasing energy. Also interesting are the fastest formed product and the most stable product. <br>
The fastest formed product. <br>
The Arrhenius Equation states that reaction rate constant is related to Ea by k=Ae−Ea/RT. A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lowest free energy of TS and one is higher rate of collision. <br> So thermodynamic control involves raising temperature.
The most stable product, having less chance of going reversible reaction to products or other dissociation reaction. One has lowest free energy of product and lowest rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. It is also the fastest and most stable product. <br>

====Secondary orbital interation====

Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

===Calculation output by B3LYP 621g.d.p===
Optimized endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_TS_631_WITH_MO3.log]]

Optimized exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_TS631_MOLATEST.log]]

Energy calulation exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_ENERGY4WITHMO.log]]

Energy calculation endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_ENERGY2.log]]

IRC endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_IRC4.log.log]]

IRC exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_IRC4.log]]

B3LYP optimized dioxole (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIXOLE631.LOG]]

B3LYP optimized cyclohexadiene (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIENE631.LOG]]

B3LYP optimized endo product (frequency calculation is done in the same file): [[Media:EXP2_ENDO_MINI631_FREQUENCY_CHECK.LOG]]

B3LYP optimized exo product (frequency calculation is done in the same file): [[Media:EXP2_EXO_621_MINI.LOG]]

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; </script>
<uploadedFileContents>YXZ_EXP3_DAENDO_TS1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXP3_CHELE_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output by PM6===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

File:YXZ EXP1 IRCPIC.png

2018-01-30T22:02:04Z

Xy3513:

Rep:Xizi

2018-01-30T21:53:43Z

Xy3513: /* Calculation output */

==Introduction==
===Method===
===Theory===
==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 14; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 8; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 9; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
====Single point energy and IRC calculation====
{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}

IRC Calculation
[[File:YXZ EXP2 ENDO IRCPIC.png|800px|thumb|left|IRC of endo TS]]
[[File:YXZ EXP2 EXO IRCPIC.png|800px|thumb|left|IRC of exo TS]]

====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>Endo TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Kinetic product and thermodynamic product are ones have smallest activation energy and largest reaction ernergy. In this case, both are endo product, numerical calculation will be shown soon.
However, Diesl Alder reaction could be reversed by taking in and releasing energy. Also interesting are the fastest formed product and the most stable product. <br>
The fastest formed product. <br>
The Arrhenius Equation states that reaction rate constant is related to Ea by k=Ae−Ea/RT. A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lowest free energy of TS and one is higher rate of collision. <br> So thermodynamic control involves raising temperature.
The most stable product, having less chance of going reversible reaction to products or other dissociation reaction. One has lowest free energy of product and lowest rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. It is also the fastest and most stable product. <br>

====Secondary orbital interation====

Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

===Calculation output by B3LYP 621g.d.p===
Optimized endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_TS_631_WITH_MO3.log]]

Optimized exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_TS631_MOLATEST.log]]

Energy calulation exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_ENERGY4WITHMO.log]]

Energy calculation endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_ENERGY2.log]]

IRC endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_IRC4.log.log]]

IRC exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_IRC4.log]]

B3LYP optimized dioxole (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIXOLE631.LOG]]

B3LYP optimized cyclohexadiene (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIENE631.LOG]]

B3LYP optimized endo product (frequency calculation is done in the same file): [[Media:EXP2_ENDO_MINI631_FREQUENCY_CHECK.LOG]]

B3LYP optimized exo product (frequency calculation is done in the same file): [[Media:EXP2_EXO_621_MINI.LOG]]

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; </script>
<uploadedFileContents>YXZ_EXP3_DAENDO_TS1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXP3_CHELE_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output by PM6===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

Rep:Xizi

2018-01-30T21:52:55Z

Xy3513: /* Calculation by B3LYP 621g.d.p */

==Introduction==
===Method===
===Theory===
==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 14; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 8; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
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|<jmol>
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<script>frame 12; mo 9; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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</jmol>
|<jmol>
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<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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|<jmol>
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<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
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|<jmol>
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|-
|}
====Single point energy and IRC calculation====
{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
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<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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|<jmol>
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|<jmol>
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|<jmol>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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</jmol>

|<jmol>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}

IRC Calculation
[[File:YXZ EXP2 ENDO IRCPIC.png|800px|thumb|left|IRC of endo TS]]
[[File:YXZ EXP2 EXO IRCPIC.png|800px|thumb|left|IRC of exo TS]]

====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>Endo TS MO of HOMO</title>
<color>white</color>
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<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
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===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Kinetic product and thermodynamic product are ones have smallest activation energy and largest reaction ernergy. In this case, both are endo product, numerical calculation will be shown soon.
However, Diesl Alder reaction could be reversed by taking in and releasing energy. Also interesting are the fastest formed product and the most stable product. <br>
The fastest formed product. <br>
The Arrhenius Equation states that reaction rate constant is related to Ea by k=Ae−Ea/RT. A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lowest free energy of TS and one is higher rate of collision. <br> So thermodynamic control involves raising temperature.
The most stable product, having less chance of going reversible reaction to products or other dissociation reaction. One has lowest free energy of product and lowest rate of collision to go back to product. <br>
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Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
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Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. It is also the fastest and most stable product. <br>

====Secondary orbital interation====

Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

===Calculation output by B3LYP 621g.d.p===
Optimized endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_TS_631_WITH_MO3.log]]

Optimized exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_TS631_MOLATEST.log]]

Energy calulation exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_ENERGY4WITHMO.log]]

Energy calculation endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_ENERGY2.log]]

IRC endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_IRC4.log.log]]

IRC exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_IRC4.log]]

B3LYP optimized dioxole (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIXOLE631.LOG]]

B3LYP optimized cyclohexadiene (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIENE631.LOG]]

B3LYP optimized endo product (frequency calculation is done in the same file): [[Media:EXP2_ENDO_MINI631_FREQUENCY_CHECK.LOG]]

B3LYP optimized exo product (frequency calculation is done in the same file): [[Media:EXP2_EXO_621_MINI.LOG]]

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; </script>
<uploadedFileContents>YXZ_EXP3_DAENDO_TS1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXP3_CHELE_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

Rep:Xizi

2018-01-30T21:44:57Z

Xy3513: /* MO and FMO */

==Introduction==
===Method===
===Theory===
==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 14; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 8; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 9; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
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<color>white</color>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
====Single point energy and IRC calculation====
{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
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|<jmol>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|<jmol>
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<color>white</color>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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</jmol>

|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}

IRC Calculation
[[File:YXZ EXP2 ENDO IRCPIC.png|800px|thumb|left|IRC of endo TS]]
[[File:YXZ EXP2 EXO IRCPIC.png|800px|thumb|left|IRC of exo TS]]

====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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!<jmol>
<jmolApplet>
<title>Endo TS MO of HOMO</title>
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<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
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===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Kinetic product and thermodynamic product are ones have smallest activation energy and largest reaction ernergy. In this case, both are endo product, numerical calculation will be shown soon.
However, Diesl Alder reaction could be reversed by taking in and releasing energy. Also interesting are the fastest formed product and the most stable product. <br>
The fastest formed product. <br>
The Arrhenius Equation states that reaction rate constant is related to Ea by k=Ae−Ea/RT. A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lowest free energy of TS and one is higher rate of collision. <br> So thermodynamic control involves raising temperature.
The most stable product, having less chance of going reversible reaction to products or other dissociation reaction. One has lowest free energy of product and lowest rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. It is also the fastest and most stable product. <br>

====Secondary orbital interation====

Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

===Calculation by B3LYP 621g.d.p===
Optimized endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_TS_631_WITH_MO3.log]]

Optimized exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_TS631_MOLATEST.log]]

Energy calulation exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_ENERGY4WITHMO.log]]

Energy calculation endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_ENERGY2.log]]

IRC endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_IRC4.log.log]]

IRC exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_IRC4.log]]

B3LYP optimized dioxole (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIXOLE631.LOG]]

B3LYP optimized cyclohexadiene (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIENE631.LOG]]

B3LYP optimized endo product (frequency calculation is done in the same file): [[Media:EXP2_ENDO_MINI631_FREQUENCY_CHECK.LOG]]

B3LYP optimized exo product (frequency calculation is done in the same file): [[Media:EXP2_EXO_621_MINI.LOG]]

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
|<jmol>
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<color>white</color>
<size>200</size>
<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; </script>
<uploadedFileContents>YXZ_EXP3_DAENDO_TS1.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<uploadedFileContents>YXZ_EXP3_CHELE_TS.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

File:YXZ EXP2 EXO IRCPIC.png

2018-01-30T21:42:47Z

Xy3513:

File:YXZ EXP2 ENDO IRCPIC.png

2018-01-30T21:39:38Z

Xy3513:

Rep:Xizi

2018-01-30T21:33:21Z

Xy3513: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

==Introduction==
===Method===
===Theory===
==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 14; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 8; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 12; mo 9; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG </uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
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<color>white</color>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
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<color>white</color>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}
====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>Endo TS MO of HOMO</title>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Kinetic product and thermodynamic product are ones have smallest activation energy and largest reaction ernergy. In this case, both are endo product, numerical calculation will be shown soon.
However, Diesl Alder reaction could be reversed by taking in and releasing energy. Also interesting are the fastest formed product and the most stable product. <br>
The fastest formed product. <br>
The Arrhenius Equation states that reaction rate constant is related to Ea by k=Ae−Ea/RT. A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lowest free energy of TS and one is higher rate of collision. <br> So thermodynamic control involves raising temperature.
The most stable product, having less chance of going reversible reaction to products or other dissociation reaction. One has lowest free energy of product and lowest rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. It is also the fastest and most stable product. <br>

====Secondary orbital interation====

Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

===Calculation by B3LYP 621g.d.p===
Optimized endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_TS_631_WITH_MO3.log]]

Optimized exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_TS631_MOLATEST.log]]

Energy calulation exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_ENERGY4WITHMO.log]]

Energy calculation endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_ENERGY2.log]]

IRC endo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_ENDO_IRC4.log.log]]

IRC exo transition state (frequency calculation is done in the same file): [[Media:YXZ_EXP2_EXO_IRC4.log]]

B3LYP optimized dioxole (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIXOLE631.LOG]]

B3LYP optimized cyclohexadiene (frequency calculation is done in the same file): [[Media:YXZ_EXP2_DIENE631.LOG]]

B3LYP optimized endo product (frequency calculation is done in the same file): [[Media:EXP2_ENDO_MINI631_FREQUENCY_CHECK.LOG]]

B3LYP optimized exo product (frequency calculation is done in the same file): [[Media:EXP2_EXO_621_MINI.LOG]]

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; </script>
<uploadedFileContents>YXZ_EXP3_DAENDO_TS1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXP3_CHELE_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

File:EXP2 EXO 621 MINI.LOG

2018-01-30T21:31:53Z

Xy3513:

File:EXP2 ENDO MINI631 FREQUENCY CHECK.LOG

2018-01-30T21:31:07Z

Xy3513:

File:YXZ EXP2 DIENE631.LOG

2018-01-30T21:29:19Z

Xy3513:

File:YXZ EXP2 DIXOLE631.LOG

2018-01-30T21:28:12Z

Xy3513:

File:YXZ EXP2 EXO IRC4.log

2018-01-30T21:26:44Z

Xy3513:

File:YXZ EXP2 ENDO IRC4.log

2018-01-30T21:26:02Z

Xy3513:

File:YXZ EXP2 ENDO ENERGY2.log

2018-01-30T21:24:08Z

Xy3513: Xy3513 uploaded a new version of File:YXZ EXP2 ENDO ENERGY2.log

File:YXZ EXP2 EXO ENERGY4WITHMO.log

2018-01-30T21:23:00Z

Xy3513: Xy3513 uploaded a new version of File:YXZ EXP2 EXO ENERGY4WITHMO.log

Rep:Xizi

2018-01-30T20:58:42Z

Xy3513: /* Exercise 3. Diels-Alder vs Cheletropic */

==Introduction==
===Method===
===Theory===
==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
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<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
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|<jmol>
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<color>white</color>
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<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG </uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
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|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
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<color>white</color>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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|-
|}

{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
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<size>150</size>
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<uploadedFileContents>YXZ_EXP2_EXO_ENERGY4WITHMO.log</uploadedFileContents>
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|<jmol>
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|<jmol>
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|<jmol>
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|<jmol>
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<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}
====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
<jmolApplet>
<title>EXO TS MO of HOMO</title>
<color>white</color>
<size>200</size>
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<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<title>Endo TS MO of HOMO</title>
<color>white</color>
<size>200</size>
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<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
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===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Diesl Alder reaction could be reversed by taking in and releasing energy. <br>
Kinetic product is the fastest formed product. <br>
k=Ae−Ea/RT A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lower free energy of TS and one is higher rate of collision. <br>
Thermodynamic product is the most stable product, having less chance of going revsible reaction to products. One has lower free enrgy of product and lower rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. <br>

====Secondary orbital interation====

(lone pair electrons of oxygen are actually not perpendicular to C-O bond like shown in the graph ) <br>
Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding sp3 orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 10; </script>
<uploadedFileContents>YXZ_EXP3_EXOPM6MINI.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; </script>
<uploadedFileContents>YXZ_EXP3_DAENDO_TS1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXP3_CHELE_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ EXTENSION TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Dimerization and isomerization====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output===
PM6 optimized endo transition state: [[Media:YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized exo transition state: [[Media: YXZ_EXP3_DAENDO_TS1.LOG]]

PM6 optimized cheletropic transition state:[[Media:YXZ_EXP3_CHELE_TS.LOG]]

PM6 optimized Second exo transition state: [[Media:YXZ EXTENSION TS.LOG]]

PM6 optimized Second endo transition state:[[Media:YXZ_EXTENSION_ENDO_TS.LOG]]

PM6 optimized endo transition state IRC: [[Media:YXZ_EXP3_ENDO_IRC.log]]

PM6 optimized exo transition state IRC:[[Media:YXZ_EXP3_EXO_IRC.log]]

PM6 optimized cheletropic transition state IRC: [[Media:YXZ_EXP3_CHELE_IRC.log]]

PM6 optimized second endo transition state IRC: [[Media:YXZ_EXTENSIONENDO_IRC.log]]

PM6 optimized second exo transition state IRC:[[Media:YXZ EXTENSIONEXO IRC.log]]

PM6 optimized endo product: [[Media:YXZ_EXP3_ENDO_PRODUCTLATEST.LOG]]

PM6 optimized exo product:[[Media: YXZ_EXP3_EXOPM6MINI.LOG]]

PM6 optimized cheletropic product:[[Media:YXZ_EXP3_CHELE_MINI2.LOG]]

PM6 optimized second endo product: [[Media:YXZ_EXTENSION_ENDO_PRODUCT.LOG]]

PM6 optimized second exo product:[[Media: YXZ_EXTENSION_PRODUCT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: YXZ_EXP3_SO2MINI2.LOG]]

PM6 optimized xylylene:[[Media: YXZ_EXP3_DIENEMINI2.LOG]]

File:YXZ EXP3 DIENEMINI2.LOG

2018-01-30T20:56:26Z

Xy3513:

File:YXZ EXP3 SO2MINI2.LOG

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Xy3513:

File:YXZ EXTENSION PRODUCT1.LOG

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Xy3513:

File:YXZ EXTENSION ENDO PRODUCT.LOG

2018-01-30T20:53:56Z

Xy3513: Xy3513 uploaded a new version of File:YXZ EXTENSION ENDO PRODUCT.LOG

File:YXZ EXP3 CHELE MINI2.LOG

2018-01-30T20:52:39Z

Xy3513:

File:YXZ EXP3 EXOPM6MINI.LOG

2018-01-30T20:51:49Z

Xy3513: Xy3513 uploaded a new version of File:YXZ EXP3 EXOPM6MINI.LOG

File:YXZ EXP3 ENDO PRODUCTLATEST.LOG

2018-01-30T20:47:17Z

Xy3513:

File:YXZ EXP3 CHELE IRC.log

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Xy3513:

File:YXZ EXP3 ENDO IRC.log

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Xy3513: Xy3513 uploaded a new version of File:YXZ EXP3 ENDO IRC.log

File:YXZ EXP3 EXO IRC.log

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Xy3513:

File:YXZ EXP3 CHELE IRC.txt

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Xy3513:

File:YXZ EXTENSIONENDO IRC.log

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Xy3513:

File:YXZ EXTENSIONEXO IRC.log

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Xy3513:

Rep:Xizi

2018-01-30T20:33:10Z

Xy3513: /* Exercise 3. Diels-Alder vs Cheletropic */

==Introduction==
===Method===
===Theory===
==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 14; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_DIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 8; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 12; mo 9; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP1_ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
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<color>white</color>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_TS_631_WITH_MO3.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
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<color>white</color>
<size>150</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>150</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_EXO_TS631_MOLATEST.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
|<jmol>
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|<jmol>
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<color>white</color>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>YXZ_EXP2_ENDO_ENERGY2.log</uploadedFileContents>
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|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}
====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
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<title>EXO TS MO of HOMO</title>
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[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
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===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Diesl Alder reaction could be reversed by taking in and releasing energy. <br>
Kinetic product is the fastest formed product. <br>
k=Ae−Ea/RT A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lower free energy of TS and one is higher rate of collision. <br>
Thermodynamic product is the most stable product, having less chance of going revsible reaction to products. One has lower free enrgy of product and lower rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. <br>

====Secondary orbital interation====

(lone pair electrons of oxygen are actually not perpendicular to C-O bond like shown in the graph ) <br>
Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding sp3 orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

==Exercise 3. Diels-Alder vs Cheletropic==
All this exercise use method PM6 <br>
===Data reprensatation===
====Optimisation of TS====
{| class="wikitable"
|+ Optimisation
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
| style="text-align: centre;" | Optimisation of TS of Second Exo
| style="text-align: centre;" | Optimisation of TS of Second Endo
|-
|-
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 30; </script>
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|<jmol>
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|<jmol>
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<color>white</color>
<size>200</size>
<script>frame 16; </script>
<uploadedFileContents>YXZ_EXTENSION_ENDO_TS.LOG</uploadedFileContents>
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</jmol>
|}

====IRC analysis====
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

====Thermochemistry data====
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

====Reaction profile====
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explanation of data and answers to questions===
====Competing reactions analyse with help of IRC====
This exercise is focused on comparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
By inspection of energy graph, the kinetic product is DA endo with least activation energy and second lowest product energy. The thermodynamic product is the cheletropic product which has lowest product energy and third lowest activation energy. The preferred reaction path should only be specified under kintic or thermodynamic control. Details in Exercise 2. <br>
IRC can give generalised idea about how stable the product is and how hard TS can be reached because it measures many steps TS needed to go to reactant and product. <br>
====Rationalization of free energy surface by FMO theory====
These five reaction paths can be firstly divided into two classes accroding to different parts of conjugated 4 pi bond. Here for simplicity only considering two dienes inside and outside the ring separately. And also the MO of two dienes treated separately. <br>
1. diene outisde ring <br>
The first three reactions used diene outside the ring or at end. These three reactions are more competing than the other two because diene outside the ring is more accessible for less steric and reorganization of structure and benzene formation from xylylene giving a larger stabilization in energy. <br>
Two DA reactions in this class uses HOMO of SO2 and cheletropic reaction uses LUMO. Then diene uses HOMO and LUMO according to the SO2. For DA endo reaction, the lowest TS of three benefited from secondary orbital interaction of one pi cloud localized on oxygen, the one not in bonding interaction. Cheletropic reaction uses pi cloud delocalzed on soft sufurhas higher TS for larger gap of its LUMO and diene`s HOMO. However it has most stable product because two strong S=O bonds remain there. All reactions form new two bonds but cheletropic reaction destory least bonds and has least steric hindrance. <br>
2. diene in ring <br>
These two DA reactions uses dienes in ring and are far less competitive for the unstable product and high activation energy. <br>
====Other competing reactions====
O-xylylene is highly reactive because it can dimerize to a dimer and isomerize via electrocylic reaction to form a benzocyclobutenes. This two reactions can also benefited from formation of benzene in product like the first three reactions. And, product of these five reactions are all more stable than the two second DA mechanism reactions for the aromatic product instead of the aromatic TS only. So the second two DA reactions can hardly be seen.
===Calculation output===
PM6 optimized endo transition state: [[Media:SHENJY3 EX3 ENDO OPT3.LOG]]

PM6 optimized exo transition state: [[Media: SHENJY3 EX3 EXO OPT3.LOG]]

PM6 optimized cheletropic transition state:[[Media:JSHENY3 EX3 CHE OPT3.LOG]]

PM6 optimized endo transition state IRC: [[Media:SHENJY3 EX3 ENDO IRC.LOG]]

PM6 optimized exo transition state IRC:[[Media:SHENJY3 M3 IRC.LOG]]

PM6 optimized cheletropic transition state IRC: [[Media:JSHENY3 EX3 CHE IRC.LOG]]

PM6 optimized endo product: [[Media:SHENJY3 EX3 ENDO OPT1.LOG]]

PM6 optimized exo product:[[Media: SHENJY3 M3 OPT1.LOG]]

PM6 optimized cheletropic product:[[Media:JSHENY3 EX3 CHE OPT1.LOG]]

PM6 optimized SO<sub>2</sub>:[[Media: JSHENY3 EX3 OPT SO2.LOG]]

PM6 optimized xylylene:[[Media: JSHENY3 EX3 OPT XYLYLENE.LOG]]

File:YXZ EXTENSION ENDO TS.LOG

2018-01-30T20:32:09Z

Xy3513:

File:YXZ EXTENSION TS.LOG

2018-01-30T20:29:34Z

Xy3513:

File:YXZ EXTENSION ENDO PRODUCT.LOG

2018-01-30T20:26:43Z

Xy3513:

Rep:Xizi

2018-01-30T16:58:48Z

Xy3513: /* Exercise 3. Diels-Alder vs Cheletropic */

==Introduction==
===Method===
===Theory===
==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat" "; frank off</script>
<uploadedFileContents>REAL TS WITH MO.LOG</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>REAL TS WITH MO.LOG </uploadedFileContents>
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|<jmol>
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<color>white</color>
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<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
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|<jmol>
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<uploadedFileContents> REAL TS WITH MO.LOG </uploadedFileContents>
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|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
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{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
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|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}
====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
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[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
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===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Diesl Alder reaction could be reversed by taking in and releasing energy. <br>
Kinetic product is the fastest formed product. <br>
k=Ae−Ea/RT A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lower free energy of TS and one is higher rate of collision. <br>
Thermodynamic product is the most stable product, having less chance of going revsible reaction to products. One has lower free enrgy of product and lower rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. <br>

====Secondary orbital interation====

(lone pair electrons of oxygen are actually not perpendicular to C-O bond like shown in the graph ) <br>
Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding sp3 orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

==Exercise 3. Diels-Alder vs Cheletropic==

===Optimisation of TS===
{| class="wikitable"
|+ Table8. optimisation to PM6
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
|-
|-
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===IRC analysis===
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

In the first trajectory, which is the formation of endo product, the IRC did the inverse calculation which calculate reaction process from products to reactants so the approach trajectory is product dissociation to reactant. All IRC and reaction trajectory are clear for how reactants approach each other and how energy changes associated with trajectory.

===Thermodynamics===
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

===Reaction profile===
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explantion of data and answrs to questions===
This exercise is focused on cmparing five possible paths: Diesl alder reaction by exo, DA by endo, cheletropic, DA by endo by second diene, DA by exo by second diene and how they they copetes.
These five reaction paths can be firstly divided into two classes:
1. diene outisde ring
The first three reactiuons used diene outside the ring or at end. These three reactions are more competing than the other two beacause diene outside the ring is more accessible for steric reason and benzen formation from xylylene giving a largr stablization in energy.

This graph is more obvious way than energy calculation. As shown on the graph, in endo/exo reaction, exo product is slightly more stable than endo product due to less steric repulsion. However, it is such a small effect in this reaction so the difference between two products are not large. Cheletropic product is much stable compare with Diles-Alder reaction product. The ring stain on cheletropic product is relieved by large S atom.

<u>Xylylene is highly unstable. Look at the IRCs for the reactions - what happens to the bonding of the 6-membered ring during the course of the reaction?</u>

Xylylene is highly reactive, it contains two cis-diene which can both react with alkene to undergo cycloaddition. In experiment 3, 3 possible reactions are shown with diene outside the ring. when 6-membered ring is forming, it becomes aromatic because both O and S contains lone pairs, which makes system more stable. Cycloaddition with diene inside the ring will be shown on the extension experiment.

Rep:Xizi

2018-01-30T16:36:04Z

Xy3513: /* Exercise 3. Diels-Alder vs Cheletropic */

==Introduction==
===Method===
===Theory===
==Exercise 1: Reaction of Butadiene with Ethylene==
===MO Constructions and Data Presenting ===
====MO and FMO anlysis====
[[File:MO of EXP1.png|thumb|center|500px|Molecular Orbital Diagram for the formation of the transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of correlations of the visualised MOs and MO diagrams in MO analysis (fig 1)
! colspan="2"| S-cis Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state
|-
| HOMO || LUMO || HOMO || LUMO || HOMO-1 || HOMO || LUMO || LUMO+1
|-
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|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:YXZ_DIENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_DIENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_HOMO.png|100px|]]
|align=center|[[File:YXZ_ETHENE_LUMO.png|100px|]]
|align=center|[[File:YXZ_TS16.png|100px|]]
|align=center|[[File:YXZ_TS17.png|100px|]]
|align=center|[[File:YXZ_TS18.png|100px|]]
|align=center|[[File:YXZ_TS19.png|100px|]]
|}

====Bond Changes in Diels Alder Reaction====
{| class="wikitable" style="border: none; background: none;"
|+|table 2: Bond Length Display
|-
! colspan="4"| carbon atom annoted
|-
|align=center|[[File:YXZ_DIENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_ETHENE_CARBON.png|400px|]]
|align=center|[[File:YXZ_TS_CARBON.png|400px|]]
|align=center|[[File:YXZ_PRODUCT_CARBON.png|400px|]]
|-
! colspan="2"| BOND LENGTH AND BOND CHANGE
|-
|align=center|[[File:YXZ_BONDLENGTH.png|400px|]]
|align=CENTER|[[File:YXZ_BONDCHANGE.png|500px|]]
|}

The vibration corresponds to the reaction path at transition state is shown below:

[[File:YXZ_VIBRATIONMOVIE.gif]]

<br>

===Explanation of Graph and Table and Answers to Questions===
====Requirements for Diels Alder Reaction====
Quantitative analysis of MO with energy will be discussed in Exercise 2.
In this [4+2] cycloaddition reaction, interactions were between the conjugated pi system of butadiene and pi bond of alkene to form an aromatic transition state with 6 pi electrons. Two new C-C bonds were generated between two species at ends of each. Molecular diagram for the formation of transition state was tried to be constructed. HOMO and LUMO of alkene and butadiene were used for formation of the transition state for their right symmetry of the bonding orbital.
By inspection of the frontier molecular orbital of the transition state in the Jmol, it could be found that all molecular orbitals constructed in the transition state are formed supra-facially. That is to say two reactants approach each other with their pi orbitals parallel head to head via sigma interactions. P orbitals of both ends of both reactants dis-rotate to form two new sigma bonds symmetrically. This is supported by Woodward–Hoffmann rules which stated that a [4+2] cycloadditon reaction is thermally allowed if ps+qs= 4n+2 or pa+qa=4n+2. 4n+2 is the number of pi electrons used, s and a notations mean that a fragment uses it molecular orbital supra-facially or antasupra-facially. For this reaction, must be 4s+2s which means this reaction only happens if two new bonds formed symmetrically with C2v plane.
Orbital overlap integrals provide a quantitative understanding about how much two orbitals/ wave functions overlap. As shown in the MO diagram, overlap integral between symmetric-symmetric (u-u) and asymmetrical-asymmetric (g-g)are non-zero. Overlap of symmetric-asymmetric interaction (u-g) is 0 because the interaction is asymmetric.
====Bond Change====
All numbers in this section saved the unit Angstrom for convenience.
The table outlines all carbon-carbon bond lengths in reactants, transition states and products and how they change. Explanation about the color in the table: red the double bond, orange the single bond, yellow the partial double bond, pale yellow the partial single bond. It is found all double bond length increases and bond order decreases. The only single bond lengthens and become a double bond. Two newly formed single bonds have decreased the length from infinity to partial single bond in the tradition state. All bond lengths changed dramatically near transition state. Typical bond length: sp3-sp3 1.54, sp2-sp2 1.34, sp2-sp3 (in product)1.50, Van der Waal radius of carbon 1.7. Two carbon with Vdw radius 1.7 have 3.4 interaction length, any length shorter than this means two atoms are in interaction like 2.11 in partial single bond in TS, of course, longer than typical C-C single bond.
====Synchronous Reaction====
At transition state, the vibration is as shown with a negative vibration frequency along the reaction coordinate. This frequency in transition state is an imaginary number but represented as a negative value. It is imaginary number from square root of -1 when solving equations for force constant, k, a negative value.

The vibration with the lowest positive frequency is along their plane. Comparing with the transition state vibration, these vibrations are orthogonal of each other, which can be described as the energy exchange only happens within one normal mode and never exchanges to another. The one with negative frequency describes the formation of two bonds synchronously (hence Diels-Alder reactions are concerted reactions).

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO construction and data presentation===
====MO and FMO====
MO diagrams of transition states were approximated quantitatively by IRC and single point energy calculation which were demonstrated as well.
[[File:MO of endo TS.png|thumb|left|500px|Molecular Orbital Diagram for endo transition state.]]
[[File:MO of exo TS.png|thumb|right|500px| Molecular Orbital Diagram for exo transition state.]]

{| class="wikitable" style="border: none; background: none;"
|+|Visualisation of Frontier Molecular Orbital of Transition State
! colspan="4"| Endo-transition state !! colspan="4"| Exo-transition state
|-
| HOMO-1 || HOMO || LUMO || LUMO+1 || HOMO-1 || HOMO || LUMO || LUMO+1
|-
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|-
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{| class="wikitable" style="border: none; background: none;"
|+|Single Point Energy Calculation of Reactants: Display of MO and Energy
! colspan="4"| reactants to form exo-product !! colspan="4"| reactants to form endo-product
|-
| MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole || MO 40:HOMO of cyclohexadiene || MO 41:HOMO of dioxole || MO 42:LUMO of cyclohexadiene || MO 43:LUMO of dioxole
|-
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|<jmol>
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|-
! colspan="4"|[[File:YXZ_EXP2_EXO_ENERGYLEVEL.png |400px|thumb|left|ENERGY OF MO 40-43]]!!colspan="4"|[[File:YXZ_EXP2_ENDO_ENERGYLEVEL.png|400px|thumb|left|ENERGY OF MO 40-43]]
|-
|}
====Reaction Thermodynamics====
{| class="wikitable"
|+|thermochemistry data from Gaussian calculation
! !!1,3-cyclohexadiene!! 1,3-dioxole!! endo-transition state!! endo-product!! exo-transition state!! exo-product
|-
!style="text-align: left;"| Sum of electronic and thermal energies at 298k (Hartree/Particle)
| -233.303306 || -267.044172 || -500.306014 || -500.395004 || -500.303864 || -500.394008
|-
|}

====Secondary Orbital Interactions====
{| class="wikitable"
!<jmol>
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<title>EXO TS MO of HOMO</title>
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<title>Endo TS MO of HOMO</title>
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[[File:MO of secon orbital.png|200px|left|orbital interactions in exo and endo approach]]
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<br>
===Explanation of data and answers to questions===
====MO analysis====
By using single point energy calculation, energies of MOs could be compared under same potential energy surfaces. In the Energy Calculation of reactants, diene and dienophile called for simplicty, (displacement of C-C set larger than 2xVdw radius: >3.5 A) it was found that MOs of their frontier orbitals for bonding are arranged low to high: HOMO of diene, HOMO of dienophile, LUMO of diene, LUMO of dienophile with energy gap 3:4:4 approximately. This is beacuse diene has conjugated pi bond thus smaller HOMO-LUMO energy gap(consistent with calcualtion: 3+4<4+4). Electron donating groups (heteroatoms) in dienophile raised energies of MOs thus its HOMO and LUMO all higher than diene and normal dienophile. <br>
For the FMO in transition state, by doing the Electron Calculation and setting C-C displace ment just at 2xVdw radius, reactants MOs began to overlap. Reactants MOs under calculation were not pure one reactant, sometimes orbitals small in size of another reactant and its enrgy is between two pure MOs of reactants. Finally when setting C-C displacement to distance in transition state in exo transition state, the energy gap between HOMO-1, HOMO, LUMO, LUMO+1 are 4:10:3. <br>
It could be concluded that this is an inverse demand DA reaction for EDG in dienophile. When orbitals began to interact, filled orbitals(bonding orbitals in reactants) energy raise and unfilled orbitals(anti bonding orbitals in reactant) energy lowered because electrons began to appear in the overlapped region. When forming the transition state, new bonding orbitals energies reached a maximum and began to lower to a minimum, new anti-bonding orbital energy lowered to a minimum and began to raise to the highest. In endo-transition sate, because of its lower Gibbs energy, energy gaps between frontier orbitals should be larger, in other words, bonding orbitals lower in energy than exo-TS and anti-bonding higher because interaction of this extent is enough for it to form new bonds and damp energy to form a product. Other energies of stabilization are from secondary orbitals in endo-TS

==== Reaction Thermodynamics====

Diesl Alder reaction could be reversed by taking in and releasing energy. <br>
Kinetic product is the fastest formed product. <br>
k=Ae−Ea/RT A is frequency factor constant or also known as pre-exponential factor or Arrhenius factor. It indicates the rate of collision and the fraction of collisions with the proper orientation for the reaction to occur.
There are two ways to achieve the fastest reaction path. One is the lower free energy of TS and one is higher rate of collision. <br>
Thermodynamic product is the most stable product, having less chance of going revsible reaction to products. One has lower free enrgy of product and lower rate of collision to go back to product. <br>
<br>
Free energy information could be extracted from Thermochemistry data in output file from Gaussview. and gradient of free energy could be estimate by the vibration frequency in the TS. Gradient from IRC provides gradient in the intrinsic reaction coordinate so not always working right. <br>
Sum energy of reactants: -233.303306+(-267.044172)=-500.347478 Hartree <br>
1 Hartree = 2625.50 KJ/mol <br>
The reaction barrier of a reaction is the energy difference between the transition state and the reactants. <br>
For the endo reaction: -500.347478-(-500.306014)=0.041464 Hartree = 108.8636841 KJ/mol <br>
For the exo reaction: -500.347478-(-500.303864)=0.043614 Hartree = 114.5085066 KJ/mol <br>
The reaction energy of a reaction is the energy difference between the product and the reactants. <br>
For the endo reaction: -500.347478-(-500.395004)=-0.047526 Hartree = -124.7794581 KJ/mol <br>
For the exo reaction: -500.347478-(-500.394008)=-0.046530 Hartree = -122.1644612 KJ/mol <br>
Endo product has both lower activation energy and reaction energy because of secondary orbital interaction. <br>
<br>
Collision rate of both directions to get to TS could be understood by the inverse of frequency of vibration the forming bond in TS. Frequency equals square root of k/m. K is the gradient of potential energy. In TS, k from reactants is negative so frequency calculated by Gauss is imaginary. Thus gradient of free energy around TS could also provides an idea about the collision rate but gradient from IRC provides gradient in the intrinsic reaction corrdinate so not always working right. <br>
In this case exo-TS has negative frequency of -530 which is larger than -523 of endo-TS which means the collision rate or dissociation rate to achieve exo-TS is higher. This is because it has less steric to prevent bond forming. However, the difference is small which may be outweighed by free energy. Negative frequency is from negative k because bonds do not exist in TS, it is an imaginary vibration of bond. <br>
It is concluded that endo product is both kinetic and thermodynamic product, not like reaction of simple dienophile. <br>

====Secondary orbital interation====

(lone pair electrons of oxygen are actually not perpendicular to C-O bond like shown in the graph ) <br>
Secondary orbital interactions arises in TS when oxygen in dienophile can donate one pair of electrons in its nonbonding sp3 orbital of the correct orrientation into diene's LUMO. This is consistent with bonding interaction of HOMOs of dienophile with diene`s LUMO. This further lowers energy of LUMO of diene and HOMO of TS and helps bonding breaking of HOMO of diene. This is possilble when TS adopt a more steric arrangement in the endo way. However, this stabilization of TS energy outweighs the steric hindrance destabilization in endo TS. <br>

==Exercise 3. Diels-Alder vs Cheletropic==

===Optimisation of TS===
{| class="wikitable"
|+ Table8. optimisation to PM6
| style="text-align: centre;" | Optimisation of TS of EXO
| style="text-align: centre;" | Optimisation of TS of Endo
| style="text-align: centre;" | Optimisation of TS of cheletropic
|-
|-
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===IRC analysis===
{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:YXZ_EXP3_ENDO_IRCMOVIE.gif]]
|[[File:YXZ EXP3 ENDO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:YXZ EXP3 EXO IRCMOVIE.gif]]
|[[File:YXZ EXP3 EXO IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:YXZ EXP3 CHELE IRCMOVIE.gif]]
|[[File:YXZ EXP3 CHELE IRCGRAPH.png]]
|-
| style="text-align: centre;" | Approach trajectory of exo product using second diene
| style="text-align: centre;" | Second diene exo product IRC
|-

|[[File:YXZ EXTENSION EXO IRCMOVIE1.gif]]
|[[File:YXZ EXTENSION EXO IRCPIC.png]]
|-
| style="text-align: centre;" | Approach trajectory of endo product using second diene
| style="text-align: centre;" | Second diene endo product IRC
|-
|[[File:YXZ EXTENSION ENDO IRCMOVIE.gif]]
|[[File:YXZ EXTENSION ENDO IRCPIC.png]]
|-
|}

In the first trajectory, which is the formation of endo product, the IRC did the inverse calculation which calculate reaction process from products to reactants so the approach trajectory is product dissociation to reactant. All IRC and reaction trajectory are clear for how reactants approach each other and how energy changes associated with trajectory.

===Thermodynamics===
{| class="wikitable"
|+ Sum of electronic and thermal energies of reactants, TS, and products by Calculation PM6 at 298K
! style="background: #0D4F8B; color: yellow;" | Components
! style="background: #0D4F8B; color: yellow;" | Energy/Hatress
! style="background: #0D4F8B; color: yellow;" | Energy/kJmol<sup>-1</sup>
|-
|SO2
| style="text-align: center;" |-0.091033
| style="text-align: center;" |-239.0071415
|-
|Xylylene
| style="text-align: center;" |0.21851
| style="text-align: center;" |573.698005
|-
|Reactants energy
| style="text-align: center;" |0.127008
| style="text-align: center;" |333.459504
|-
|ExoTS
| style="text-align: center;" |0.138518

| style="text-align: center;" |363.679009

|-
|EndoTS
| style="text-align: center;" |0.136783

| style="text-align: center;" |359.1237665

|-
|Cheletropic TS
| style="text-align: center;" |0.146

| style="text-align: center;" |383.323
|-
|Exo TS from second butadiene
| style="text-align: center;" |0.151054
| style="text-align: center;" |396.592277

|-
|Endo TS from second butadiene
| style="text-align: center;" |0.148031
| style="text-align: center;" |388.6553905
|-
|Exo product
| style="text-align: center;" |0.066032
| style="text-align: center;" |173.367016
|-
|Endo Product
| style="text-align: center;" |0.067003
| style="text-align: center;" |175.9163765
|-
|Cheletropic product
| style="text-align: center;" |0.043585
| style="text-align: center;" |114.4324175
|-
|Exo product from second butadiene
| style="text-align: center;" |0.112672
| style="text-align: center;" |295.820336
|-
|Endo product from second butadiene
| style="text-align: center;" |0.10999
| style="text-align: center;" |288.778745
|-
|}
{| class="wikitable"
|+ Activation energy and reaction energy(KJ/mol) of five reaction paths at 298K
! style="background: #0D4F8B; color: yellow;" |
! style="background: #0D4F8B; color: yellow;" | Exo
! style="background: #0D4F8B; color: yellow;" | Endo
! style="background: #0D4F8B; color: yellow;" | Cheletropic
! style="background: #0D4F8B; color: yellow;" | Exo from second butadiene
! style="background: #0D4F8B; color: yellow;" | Endo from second butadiene
|-
|Activation energy
| style="text-align: center;" |30.219505
| style="text-align: center;" |25.6642625
| style="text-align: center;" |49.863496
| style="text-align: center;" |63.132773
| style="text-align: center;" |55.1958865
|-
|Reaction energy
| style="text-align: center;" |-160.092488
| style="text-align: center;" |-157.5431275
| style="text-align: center;" |-219.0270865
| style="text-align: center;" |-37.639168
| style="text-align: center;" |-44.680759
|}

===Reaction profile===
[[File:Graph2.png|500px|thumb|left|Reaction Energy Profile]]

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===Explantion of data and answrs to questions===

This graph is more obvious way than energy calculation. As shown on the graph, in endo/exo reaction, exo product is slightly more stable than endo product due to less steric repulsion. However, it is such a small effect in this reaction so the difference between two products are not large. Cheletropic product is much stable compare with Diles-Alder reaction product. The ring stain on cheletropic product is relieved by large S atom.

<u>Xylylene is highly unstable. Look at the IRCs for the reactions - what happens to the bonding of the 6-membered ring during the course of the reaction?</u>

Xylylene is highly reactive, it contains two cis-diene which can both react with alkene to undergo cycloaddition. In experiment 3, 3 possible reactions are shown with diene outside the ring. when 6-membered ring is forming, it becomes aromatic because both O and S contains lone pairs, which makes system more stable. Cycloaddition with diene inside the ring will be shown on the extension experiment.

File:YXZ EXTENSION EXO IRCPIC.png

2018-01-30T16:31:36Z

Xy3513: