ChemWiki - User contributions [en]

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T13:29:00Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations the AM1 semi-empirical molecular orbital was used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.71158
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.31661
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.15130
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the the van der Waals radii of the terminal carbon atoms are within each other to allow for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs2''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the carbon atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
| -0.34273
| -215.06616
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
| -0.04045
| -25.38274
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
| -0.34505
| -216.52198
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
| -0.03571
| -22.40835
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

{| align="center"
|- align="center"
|
|[[Image:Secondary_overlap.gif|thumb|350px|Secondary orbital overlap in the endo-transition structure]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions. Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001

2009-11-13T13:27:29Z

Yi107: /* Chair Transition Structure */

=The Transition State=

The computational experiments involved the characterisation of transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

However, the molecular mechanics/force field methods that works well for structure determination (as in Module 1) cannot be used to study transition states in large molecules, as they do not describe bonds being made and broken, and changes in bonding type and electron distrbution. Instead, molecular-orbital based methods were used to solve the Schrodinger equation numerically and locate transition structures based on the local shape of potential energy surfaces. As well as showing what the transition states look like, reaction paths and barrier heights were also calculated.

==The Coper Rearrangement Tutorial==

{|
|[[Image:Cope_rearrange.gif|thumb|300px|left|Cope rearrangemnt of 1, 5-hexadiene ]]
The Cope rearrangement of 1, 5-hexadiene, which specifically involves a [3, 3] sigmatropic shift rearrangement, was studied to locate the low-energy minima and transition structures on the C6H10 potential energy surface, so that the preferred reaction mechanism could be determined.

It has been argued whether the mechanaism is concerted, stepwise or dissociative but it is now generally accepted that the reaction occurs in a concerted fashion via either a "''chair''" or a "''boat''" transition structure, with the ''boat'' transition structure lying several kcal/mol higher in energy. By using the B3LYP/6-31G* level of theory in Gaussian, the activation energies and enthalpies were calculated, which were then compared with literature values.
|}

{| align="center"
|- align="center"
|
[[Image:BoatChair_TS.gif|400px]]
|}

===Optimising the Reactants and Products===

Optimisation of 1, 5-hexadiene with an "''anti''" linkage for the central four C atoms was performed using the HF/3-21G level of theory and symmetrized to find its point group. Vibrational frequencies were then calculated and visualised, and potential energies corrected in order to compare them with experimental values. The same calculations were performed with another molecule of 1, 5-hexadiene with a "''gauche''" linkage, which would be expected to have a higher energy due to steric repulsion betweem the eclipsing carbon atoms. .

Results of the optimised ''anti-'' and ''gauche-'' structures based on HF/3-21G calculation method are shown below;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Conformer'''
| width="150" | '''Structure'''
| width="100" | '''Point Group'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
|- align="center"
| ''anti''
|
[[Image:1_5hexa_a_anti.gif|250px]]
| Ci
| -231.69253528
| -608303.5571
|- align="center"
| ''gauche''
|
[[Image:1_5hexa_b_gauche.gif|250px]]
| C1
| -231.69266121
| -608303.8879
|- align="center"
|}

The point group of the ''anti''-structure indicates that it has an inversion of symmetry, whilst the ''gauche''-structure lacks symmetry.

The energies of the ''anti-'' and ''gauche-'' structures were calculated as -231.69253528 and -231.69266121 Hartrees with an energy difference of 0.3308 kJmol-1, which indicates that the gauche conformation is in fact more stable; this is attributed to stereoelectronic effects in which there is an favourable interaction between the π orbital of the C=C bond and σ* orbital of the adjacent vinyl proton as shown belown in a Newman projection1;

{| align="center"
|- align="center"
|
[[Image:Newman_anti2.gif|380px]]
|}

By comparing the structures I have optimised with those shown in '''Appendix 1''', my structures correspond to ''anti2'' and ''gauche3'' conformers.

Reoptimisation of the Ci ''anti2'' conformation of 1, 5-hexadiene at the B3LYP/6-31G* level resulted in an overall geometry change with very similar bond lengths but a siginicant increase in the outer dihedral angles by 4° as shown below. In terms of the energy, a final energy of -234.61170277 Hartrees was calculated which is in good agreement with the one given in the table for the ''anti2'' conformer. The lowering of the energy compared to the energy calculated by the HF/3-21G method is due to the fact that the Hartree Fock method does not take into account electron distributions, which means that electronic effects such as CH-π interactions are not properly considered in the method2.
{|
|[[Image:1_5hexa_anti2_hf.gif|thumb|350px|left|Optimised structure of ''anti2'' conformer based on B3LYP/6-31G* method ]]
|[[Image:1_5hexa_anti2_dft.gif|thumb|350px|left|Optimised structure of ''anti2'' conformer based on Hartree-Fock/3-21G method ]]
|}

The table below compares the bond angles of the Ci ''anti2'' conformation for each method;

{| border="1" cellpadding="2"
! rowspan=2 |'''Calculation method'''
! colspan="3" | '''Torsional angle/°'''
|-
|width="140pt"|'''C6-C5-C4-C3'''
|width="140pt"|'''C5-C4-C3-C2'''
|width="140pt"|'''C4-C3-C2-C1'''
|-
|''HF/3-21G'' || 114.7 || -180.0 || 114.7
|-
|''DFT/6-31G*'' ||118.5 || -180.0 || -118.5
|}

The outer dihedral angles are complements of each other which supports the Ci symmetry exhibited by the ''anti2'' conformer

Frequency anaylsis confirmed that the optimium structure was a minimum as all the vibration frequencies were real and positive.
{| align="center"
|- align="center"
|
[[Image:1_5hexa_g_spectrum.jpg|thumb|450px|left|IR spectrum of Ci ''anti2'' conformation of 1, 5-hexadiene]]
|}

The table below shows the thermochemistry of ''anti2'' conformer;

{| border="1" cellpadding="2"
! colspan="1" | '''Thermochemistry '''
! colspan="1" | '''Energy'''
|-
|width="300pt"|''Sum of electronic and zero point energies/Hartrees'' i.e E = Eelec + ZPE
|width="170pt"|-234.469212
|-
|''Sum of electronic and thermal energies at 298.15K and 1atm/Hartrees'' i.e E = E + Evib + Erot + Etrans || -234.461856
|-
|''Sum of electronic and thermal enthalpies/Hartrees'' i.e H = E + RT || -234.460912
|-
|''Sum of electronic and thermal free energies/Hartrees '' i.e G = H - TS || -234.500821
|}

===Optimizing the "Chair" and "Boat" Transition Structures ===

A transition structure optimisation was set up by i) computing the force constants at the beginning of the calculation, ii) using redundant coordinate editor and iii) using QST2. The reaction coordinate was also visualised and the IRC ran and the activation energies for the Cope rearrangement were calculated via the ''chair'' and ''boat'' transition structures.

The ''chair'' and ''transition'' structures for the Cope rearrangement shown in '''Appendix 2''' both consist of two C3H5 allyl fragments positioned approximately 2.2 apart, one with C2h symmetry and and the other with C2v symmetry.

====Chair Transition Structure====
Firstly a suitable guess of the chair transition structure was constructed; an allyl fragment (CH2CHCH2) was drawn and then optimised using the HF/3-21G level of theory. The optimised allyl structure was then pasted twice into a new window so that the two fragments could be orientated into the chair conformer.

The chair transition structure optimisation was set up by both i and ii, where both methods used the HF/3-21G level of theory.

'''Optimisation to a TS(Berny)'''

This methods involves computing the force constant matrix (also known as the Hessian) in the first step of the optimisation which is then updated as the optimisation proceeds. The optimisation was set up so that the force constants were only calculated once with additional keywords, Opt=NoEigen, which prevents the calculation from crashing if more than one imaginary frequency is detected during the optimisation.

The frequency calculation gave an imaginary frequency of magnitude -817.96 cm-1, which confirmed the transition state was optimised successfully.
{|
{| align="center"
|- align="center"
|
|[[Image:chair_b_opt3.gif|thumb|250px|left|Optimised chair TS using Gaussian optimisation ]]
|[[Image:chair_b_optfreq.gif|thumb|250px|left|Vibration at -817.96cm-1 corresponding to the Cope rearrangement ]]
|}

'''Frozen coordinate method'''

In this method, the transition structure was generated by freezing the reaction coordinate, i.e the terminal carbons of each fragment which form/break a bond during rerrangement and then minimising the rest of the molecule using Opt=ModRedundant. Once the molecule was fully optimised, the reaction coordinate was unfrozen and optimisation to a transition structure was performed.

Comparison with the previous method give the same structure with a bond length between the terminal end of the allyl fragments as 2.02Å, suggesting that both methods are equally accurate. However, in some cases, if the guessed transition structure is not close enough to the correct structure, method i may fail as the curvature of the surface may be significantly different at points far removed from the transition structure. This would make the frozen cooodinate method more reliable as well as more time-efficient and less expensive as the whole Hessian may not need to be computed once this is done.
{|
{| align="center"
|- align="center"
|
|[[Image:chair_d_opt2.gif|thumb|250px|left|Optimised chair TS using frozen coordinate method ]]
|}

====Boat Transition Structure====

{|
|[[Image:boat_e0_input.gif|thumb|490px|left|Numbering of reactant and product]] The boat transition structure optimisation was set up by QST2 method at the HF/3-21G level of theory, which involves specifying the reactants and products for the reaction and then calculating the interpolation between the two structures to find the transition state betweeen them. This meant the numbering for the product molecule had to be changed so that it corresponded to the numbering obtained in if the reactant had rearranged. However, the method failed to locate the boat transition structure; the top allyl fragment was simply translated without the possibility of accounting for the rotation around the central bonds.
|}

Thus, the reactant and product geometries were modified so that the central dihedral C-C-C-C angle was changed to O° , whilst the central C-C-Cs were reduced to 100°. By using the same QST2 method, optimisation to a boat transition structure was successful, which was confirmed by frequency analysis; one imaginary freqency at -839.84cm-1.

{| align="center"
|- align="center"
|
[[Image:Boat_optfreq.gif|thumb|250px|Optimised boat TS including vibration at -839.84cm-1 corresponding to the Cope rearrangement ]]
|}

====Intrinsic Reaction Coordinate (IRC)====

The IRC method allows you to follow the minimum energy path from a transition structure down to its local minimum as the product on a potential energy surface. This was set up by computing the reaction coordinate in the forward direction only as it is symmetrical and calculating the force constants once. Also 50 points were considered along the IRC.

An IRC calculation for the optimised chair transition structure gave 17 intermediate geomtries. Since the minimum had not been reached yet as indicated by the RMS gradient along the IRC not equalling to zero, the last point on the IRC was ran for a normal optimisation. This resulted in the a minimum structure corresponding to the ''gauche2'' conformer with an energy of -231.691199702 Hartrees.

Re-running an IRC by specifying a larger number of points until a minimum was reached was not an option since the inital IRC calculated 17 intermediate geomtroes which is well within the number of points that was specified i.e 50. Therefore, in order to confirm a local minimum had been reached an IRC calculation was re-ran but with the force constants were computed at every step. As a result, 47 intermediate geometries were located with an IRC pathway reaching an asymptote and thus RMS gradient equalling to zero, which suggested that the local minimum had been reached. Nevertheless, the last point on IRC was ran for a normal optimisation and the local minimum was confirmed as ''gauche2''with an energy of -231.69166700 Hartrees. Thus, the IRC method determined the Cope rearrangement of the ''anti2'' conformation of 1, 5-hexadiene to give the ''gauche2'' conformer.

{| border="1" cellpadding="5"
|- align="center"
| width="200" | '''Property'''
| width="150" | '''Endo TS'''
| width="100" | '''Exo TS'''
|- align="center"
| ''Structure from side''
|
[[Image:chair_fi_ircgraph1.jpg|400px ]]
|
[[Image:chair_fiii_ircgraph1.jpg|400px ]]
|- align="center"
| ''RMS gradient along IRC''
|
[[Image:chair_fi_ircgraph2.jpg|400px ]]
|
[[Image:chair_fiii_ircgraph2.jpg|400px ]]
|- align="center"
| ''Structure''
|
[[Image:chair_fi_opt.gif|250px ]]
|
[[Image:chair_fiii_opt.gif|250px ]]
|- align="center"
| ''Energy/Hartrees''|| -231.69166702 || -23.69166700
|}

====Calculation Activation Energies====

Re-optimisations of the chair and boat transition structures were performed using the B3LYP/6-31G* level of theory followed by frequency calculations to confirm the optimisations were successful, and then compared with the HF/3-21G method. Additionally, the activation energies were also calculated for the reaction via both transition structures. The results are tabulated below;

{| border="1" cellpadding="5"
|- align="center"
! colspan="1" | '''Method'''
! colspan="3" | '''HF/3-21G'''
! colspan="3" | '''B3LYP/6-31G*'''
|- align="center"
|width="150pt" |
|width="200pt" | '''Electonic energy/Hartrees'''
|width="200pt" | '''Sum of electronic and zero point energies at OK/Hartrees'''
|width="200pt" | '''Sum of electronic and thermal energies energies at 298.15K/Hartrees'''
|width="200pt" | '''Electonic energy/Hartrees'''
|width="200pt" | '''Sum of electronic and zero point energies at OK/Hartrees'''
|width="200pt" | '''Sum of electronic and thermal energies energies at 298.15K/Hartrees'''
|- align="center"
| ''Chair TS'' || -231.619322 || -231.466697 || -231.461339 || -234.556983|| -234.414931 || -234.409010
|- align="center"
| ''Boat TS'' || -231.602802 || -231.450928 || -231.445298 || -234.543093 || -234.402340 || -234.396006
|- align="center"
| Reactant (anti2) || -231.692535 ||-231.539539 || -231.532565 || -234.611703 || -234.469212 || -234.461856
|}

Summary of activation energies/kcalmol-1

{| border="1" cellpadding="5"
|- align="center"
! colspan="1" | '''Method'''
! colspan="2" | '''HF/3-21G'''
! colspan="2" | '''B3LYP/6-31G*'''
|- align="center"
|width="150pt" |
|width="200pt" | '''at OK'''
|width="200pt" | '''at 298.15K'''
|width="200pt" | '''at 0K'''
|width="200pt" | '''at 298.15K'''
|- align="center"
| ''ΔE (Chair TS)'' || 45.70 ||44.69 || 34.06 || 33.16
|- align="center"
| ''ΔE (Boat TS)'' || 55.60 || 54.76 || 41.96|| 41.32
|}

At both levels of theory, the geomtries are reasonably similar, but energy differences between the reactant and the transition states are markedly different. By using B3LYP/6-31G* which is higher and more accurate level of theory, the energies of both transition states have decreased and the activation energies for both transition structures are in much better agreement with the experimental values of 33.5 ± 0.5 and 44.7 ± 2.0 kcalmol-1. For both levels of theory, the results are also consistent with the '''Appendix 2'''.

Results show that the chair transition state is more stable than that of the boat with a lower activation energy of 33.16 kcalmol-1 at compared to 41.32kcalmol-1 at room temperature. Therefore, it can be concluded that the reaction mechanism of the Cope rearrangement prefers to proceed via the chair than the boat transition state.

====References====

# Nishio. M, Hirota. M, (1989). Tetrahedron. 45: 7201
# Rocque. B. G, Gonzales. J. M, Schaefer III. H. F, (2002). "An analysis of the conformers of 1,5-hexadiene" Molecular Physics. 100 (4): 441-446 {{DOI|10.1080/00268970110081412}}

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T13:18:53Z

Yi107: /* Optmisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations the AM1 semi-empirical molecular orbital was used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.71158
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.31661
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.15130
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the the van der Waals radii of the terminal carbon atoms are within each other to allow for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs2''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the carbon atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
| -0.34273
| -215.06616
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
| -0.04045
| -25.38274
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
| -0.34505
| -216.52198
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
| -0.03571
| -22.40835
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

{| align="center"
|- align="center"
|
|[[Image:Secondary_overlap.gif|thumb|350px|Secondary orbital overlap illustration]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions. Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T12:47:54Z

Yi107: /* The Diels Alder Cycloaddition */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations the AM1 semi-empirical molecular orbital was used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.71158
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.31661
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.15130
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs2''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the carbon atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
| -0.34273
| -215.06616
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
| -0.04045
| -25.38274
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
| -0.34505
| -216.52198
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
| -0.03571
| -22.40835
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

{| align="center"
|- align="center"
|
|[[Image:Secondary_overlap.gif|thumb|350px|Secondary orbital overlap illustration]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions. Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T12:47:33Z

Yi107: /* The Diels Alder Cycloaddition */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.71158
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.31661
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.15130
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs2''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the carbon atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
| -0.34273
| -215.06616
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
| -0.04045
| -25.38274
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
| -0.34505
| -216.52198
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
| -0.03571
| -22.40835
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

{| align="center"
|- align="center"
|
|[[Image:Secondary_overlap.gif|thumb|350px|Secondary orbital overlap illustration]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions. Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T12:44:27Z

Yi107: /* Cyclohexa-1,3-diene and Maleic Anhydride */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.71158
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.31661
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.15130
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the carbon atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
| -0.34273
| -215.06616
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
| -0.04045
| -25.38274
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
| -0.34505
| -216.52198
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
| -0.03571
| -22.40835
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

{| align="center"
|- align="center"
|
|[[Image:Secondary_overlap.gif|thumb|350px|Secondary orbital overlap illustration]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions. Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T12:42:33Z

Yi107: /* Conclusion */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.71158
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.31661
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.15130
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
| -0.34273
| -215.06616
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
| -0.04045
| -25.38274
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
| -0.34505
| -216.52198
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
| -0.03571
| -22.40835
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

{| align="center"
|- align="center"
|
|[[Image:Secondary_overlap.gif|thumb|350px|Secondary orbital overlap illustration]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions. Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001

2009-11-13T12:40:02Z

Yi107: /* The Coper Rearrangement Tutorial */

=The Transition State=

The computational experiments involved the characterisation of transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

However, the molecular mechanics/force field methods that works well for structure determination (as in Module 1) cannot be used to study transition states in large molecules, as they do not describe bonds being made and broken, and changes in bonding type and electron distrbution. Instead, molecular-orbital based methods were used to solve the Schrodinger equation numerically and locate transition structures based on the local shape of potential energy surfaces. As well as showing what the transition states look like, reaction paths and barrier heights were also calculated.

==The Coper Rearrangement Tutorial==

{|
|[[Image:Cope_rearrange.gif|thumb|300px|left|Cope rearrangemnt of 1, 5-hexadiene ]]
The Cope rearrangement of 1, 5-hexadiene, which specifically involves a [3, 3] sigmatropic shift rearrangement, was studied to locate the low-energy minima and transition structures on the C6H10 potential energy surface, so that the preferred reaction mechanism could be determined.

It has been argued whether the mechanaism is concerted, stepwise or dissociative but it is now generally accepted that the reaction occurs in a concerted fashion via either a "''chair''" or a "''boat''" transition structure, with the ''boat'' transition structure lying several kcal/mol higher in energy. By using the B3LYP/6-31G* level of theory in Gaussian, the activation energies and enthalpies were calculated, which were then compared with literature values.
|}

{| align="center"
|- align="center"
|
[[Image:BoatChair_TS.gif|400px]]
|}

===Optimising the Reactants and Products===

Optimisation of 1, 5-hexadiene with an "''anti''" linkage for the central four C atoms was performed using the HF/3-21G level of theory and symmetrized to find its point group. Vibrational frequencies were then calculated and visualised, and potential energies corrected in order to compare them with experimental values. The same calculations were performed with another molecule of 1, 5-hexadiene with a "''gauche''" linkage, which would be expected to have a higher energy due to steric repulsion betweem the eclipsing carbon atoms. .

Results of the optimised ''anti-'' and ''gauche-'' structures based on HF/3-21G calculation method are shown below;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Conformer'''
| width="150" | '''Structure'''
| width="100" | '''Point Group'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
|- align="center"
| ''anti''
|
[[Image:1_5hexa_a_anti.gif|250px]]
| Ci
| -231.69253528
| -608303.5571
|- align="center"
| ''gauche''
|
[[Image:1_5hexa_b_gauche.gif|250px]]
| C1
| -231.69266121
| -608303.8879
|- align="center"
|}

The point group of the ''anti''-structure indicates that it has an inversion of symmetry, whilst the ''gauche''-structure lacks symmetry.

The energies of the ''anti-'' and ''gauche-'' structures were calculated as -231.69253528 and -231.69266121 Hartrees with an energy difference of 0.3308 kJmol-1, which indicates that the gauche conformation is in fact more stable; this is attributed to stereoelectronic effects in which there is an favourable interaction between the π orbital of the C=C bond and σ* orbital of the adjacent vinyl proton as shown belown in a Newman projection1;

{| align="center"
|- align="center"
|
[[Image:Newman_anti2.gif|380px]]
|}

By comparing the structures I have optimised with those shown in '''Appendix 1''', my structures correspond to ''anti2'' and ''gauche3'' conformers.

Reoptimisation of the Ci ''anti2'' conformation of 1, 5-hexadiene at the B3LYP/6-31G* level resulted in an overall geometry change with very similar bond lengths but a siginicant increase in the outer dihedral angles by 4° as shown below. In terms of the energy, a final energy of -234.61170277 Hartrees was calculated which is in good agreement with the one given in the table for the ''anti2'' conformer. The lowering of the energy compared to the energy calculated by the HF/3-21G method is due to the fact that the Hartree Fock method does not take into account electron distributions, which means that electronic effects such as CH-π interactions are not properly considered in the method2.
{|
|[[Image:1_5hexa_anti2_hf.gif|thumb|350px|left|Optimised structure of ''anti2'' conformer based on B3LYP/6-31G* method ]]
|[[Image:1_5hexa_anti2_dft.gif|thumb|350px|left|Optimised structure of ''anti2'' conformer based on Hartree-Fock/3-21G method ]]
|}

The table below compares the bond angles of the Ci ''anti2'' conformation for each method;

{| border="1" cellpadding="2"
! rowspan=2 |'''Calculation method'''
! colspan="3" | '''Torsional angle/°'''
|-
|width="140pt"|'''C6-C5-C4-C3'''
|width="140pt"|'''C5-C4-C3-C2'''
|width="140pt"|'''C4-C3-C2-C1'''
|-
|''HF/3-21G'' || 114.7 || -180.0 || 114.7
|-
|''DFT/6-31G*'' ||118.5 || -180.0 || -118.5
|}

The outer dihedral angles are complements of each other which supports the Ci symmetry exhibited by the ''anti2'' conformer

Frequency anaylsis confirmed that the optimium structure was a minimum as all the vibration frequencies were real and positive.
{| align="center"
|- align="center"
|
[[Image:1_5hexa_g_spectrum.jpg|thumb|450px|left|IR spectrum of Ci ''anti2'' conformation of 1, 5-hexadiene]]
|}

The table below shows the thermochemistry of ''anti2'' conformer;

{| border="1" cellpadding="2"
! colspan="1" | '''Thermochemistry '''
! colspan="1" | '''Energy'''
|-
|width="300pt"|''Sum of electronic and zero point energies/Hartrees'' i.e E = Eelec + ZPE
|width="170pt"|-234.469212
|-
|''Sum of electronic and thermal energies at 298.15K and 1atm/Hartrees'' i.e E = E + Evib + Erot + Etrans || -234.461856
|-
|''Sum of electronic and thermal enthalpies/Hartrees'' i.e H = E + RT || -234.460912
|-
|''Sum of electronic and thermal free energies/Hartrees '' i.e G = H - TS || -234.500821
|}

===Optimizing the "Chair" and "Boat" Transition Structures ===

A transition structure optimisation was set up by i) computing the force constants at the beginning of the calculation, ii) using redundant coordinate editor and iii) using QST2. The reaction coordinate was also visualised and the IRC ran and the activation energies for the Cope rearrangement were calculated via the ''chair'' and ''boat'' transition structures.

The ''chair'' and ''transition'' structures for the Cope rearrangement shown in '''Appendix 2''' both consist of two C3H5 allyl fragments positioned approximately 2.2 apart, one with C2h symmetry and and the other with C2v symmetry.

====Chair Transition Structure====
Firstly a suitable guess of the chair transition structure was constructed; an allyl fragment (CH2CHCH2) was drawn and then optimised using the HF/3-21G level of theory. The optimised allyl structure was then pasted twice into a new window so that the two fragments could be orientated into the chair conformer.

The chair transition structure optimisation was set up by both i and ii, where both methods used the HF/3-21G level of theory.

'''Optimisation to a TS(Berny)'''

This methods involves computing the force constant matrix (also known as the Hessian) in the first step of the optimisation which is then updated as the optimisation proceeds. The optimisation was set up so that the force constants were only calculated once with additional keywords, Opt=NoEigen, which prevents the calculation from crashing if more than one imaginary frequency is detected during the optimisation.

The frequency calculation gave an imaginary frequency of magnitude -817.96 cm-1, which confirmed the transition state was optimised successfully.
{|
{| align="center"
|- align="center"
|
|[[Image:chair_b_opt3.gif|thumb|250px|left|Optimised chair TS using Gaussian optimisation ]]
|[[Image:chair_b_optfreq.gif|thumb|250px|left|Vibration at -817.96cm-1 corresponding to the Cope rearrangement ]]
|}

'''Frozen coordinate method'''

In this method, the transition structure was generated by freezing the reaction coordinate, i.e the terminal carbons of each fragment which form/break a bond during rerrangement and then minimising the rest of the molecule using Opt=ModRedundant. Once the molecule was fully optimised, the reaction coordinate was unfrozen and optimisation to a transition structure was performed.

Comparison with the previous method give the same structure with a bond length between the terminal end of the allyl fragments as 2.02Å, suggesting that both methods are equally accurate. However, in some cases, if the guessed transition structure is not close enough to the correct structure, method i may fail as the curvature of the surface may be significantly different at points far removed from the transition structure. This would make the frozen cooodinate method more reliable as well as more time-efficient and less expensive as the whole Hessian may not need to be computed once this is done; differentiating along the reaction coordinate may give a good enough guess for the initial force constant matrix.
{|
{| align="center"
|- align="center"
|
|[[Image:chair_d_opt2.gif|thumb|250px|left|Optimised chair TS using frozen coordinate method ]]
|}

====Boat Transition Structure====

{|
|[[Image:boat_e0_input.gif|thumb|490px|left|Numbering of reactant and product]] The boat transition structure optimisation was set up by QST2 method at the HF/3-21G level of theory, which involves specifying the reactants and products for the reaction and then calculating the interpolation between the two structures to find the transition state betweeen them. This meant the numbering for the product molecule had to be changed so that it corresponded to the numbering obtained in if the reactant had rearranged. However, the method failed to locate the boat transition structure; the top allyl fragment was simply translated without the possibility of accounting for the rotation around the central bonds.
|}

Thus, the reactant and product geometries were modified so that the central dihedral C-C-C-C angle was changed to O° , whilst the central C-C-Cs were reduced to 100°. By using the same QST2 method, optimisation to a boat transition structure was successful, which was confirmed by frequency analysis; one imaginary freqency at -839.84cm-1.

{| align="center"
|- align="center"
|
[[Image:Boat_optfreq.gif|thumb|250px|Optimised boat TS including vibration at -839.84cm-1 corresponding to the Cope rearrangement ]]
|}

====Intrinsic Reaction Coordinate (IRC)====

The IRC method allows you to follow the minimum energy path from a transition structure down to its local minimum as the product on a potential energy surface. This was set up by computing the reaction coordinate in the forward direction only as it is symmetrical and calculating the force constants once. Also 50 points were considered along the IRC.

An IRC calculation for the optimised chair transition structure gave 17 intermediate geomtries. Since the minimum had not been reached yet as indicated by the RMS gradient along the IRC not equalling to zero, the last point on the IRC was ran for a normal optimisation. This resulted in the a minimum structure corresponding to the ''gauche2'' conformer with an energy of -231.691199702 Hartrees.

Re-running an IRC by specifying a larger number of points until a minimum was reached was not an option since the inital IRC calculated 17 intermediate geomtroes which is well within the number of points that was specified i.e 50. Therefore, in order to confirm a local minimum had been reached an IRC calculation was re-ran but with the force constants were computed at every step. As a result, 47 intermediate geometries were located with an IRC pathway reaching an asymptote and thus RMS gradient equalling to zero, which suggested that the local minimum had been reached. Nevertheless, the last point on IRC was ran for a normal optimisation and the local minimum was confirmed as ''gauche2''with an energy of -231.69166700 Hartrees. Thus, the IRC method determined the Cope rearrangement of the ''anti2'' conformation of 1, 5-hexadiene to give the ''gauche2'' conformer.

{| border="1" cellpadding="5"
|- align="center"
| width="200" | '''Property'''
| width="150" | '''Endo TS'''
| width="100" | '''Exo TS'''
|- align="center"
| ''Structure from side''
|
[[Image:chair_fi_ircgraph1.jpg|400px ]]
|
[[Image:chair_fiii_ircgraph1.jpg|400px ]]
|- align="center"
| ''RMS gradient along IRC''
|
[[Image:chair_fi_ircgraph2.jpg|400px ]]
|
[[Image:chair_fiii_ircgraph2.jpg|400px ]]
|- align="center"
| ''Structure''
|
[[Image:chair_fi_opt.gif|250px ]]
|
[[Image:chair_fiii_opt.gif|250px ]]
|- align="center"
| ''Energy/Hartrees''|| -231.69166702 || -23.69166700
|}

====Calculation Activation Energies====

Re-optimisations of the chair and boat transition structures were performed using the B3LYP/6-31G* level of theory followed by frequency calculations to confirm the optimisations were successful, and then compared with the HF/3-21G method. Additionally, the activation energies were also calculated for the reaction via both transition structures. The results are tabulated below;

{| border="1" cellpadding="5"
|- align="center"
! colspan="1" | '''Method'''
! colspan="3" | '''HF/3-21G'''
! colspan="3" | '''B3LYP/6-31G*'''
|- align="center"
|width="150pt" |
|width="200pt" | '''Electonic energy/Hartrees'''
|width="200pt" | '''Sum of electronic and zero point energies at OK/Hartrees'''
|width="200pt" | '''Sum of electronic and thermal energies energies at 298.15K/Hartrees'''
|width="200pt" | '''Electonic energy/Hartrees'''
|width="200pt" | '''Sum of electronic and zero point energies at OK/Hartrees'''
|width="200pt" | '''Sum of electronic and thermal energies energies at 298.15K/Hartrees'''
|- align="center"
| ''Chair TS'' || -231.619322 || -231.466697 || -231.461339 || -234.556983|| -234.414931 || -234.409010
|- align="center"
| ''Boat TS'' || -231.602802 || -231.450928 || -231.445298 || -234.543093 || -234.402340 || -234.396006
|- align="center"
| Reactant (anti2) || -231.692535 ||-231.539539 || -231.532565 || -234.611703 || -234.469212 || -234.461856
|}

Summary of activation energies/kcalmol-1

{| border="1" cellpadding="5"
|- align="center"
! colspan="1" | '''Method'''
! colspan="2" | '''HF/3-21G'''
! colspan="2" | '''B3LYP/6-31G*'''
|- align="center"
|width="150pt" |
|width="200pt" | '''at OK'''
|width="200pt" | '''at 298.15K'''
|width="200pt" | '''at 0K'''
|width="200pt" | '''at 298.15K'''
|- align="center"
| ''ΔE (Chair TS)'' || 45.70 ||44.69 || 34.06 || 33.16
|- align="center"
| ''ΔE (Boat TS)'' || 55.60 || 54.76 || 41.96|| 41.32
|}

At both levels of theory, the geomtries are reasonably similar, but energy differences between the reactant and the transition states are markedly different. By using B3LYP/6-31G* which is higher and more accurate level of theory, the energies of both transition states have decreased and the activation energies for both transition structures are in much better agreement with the experimental values of 33.5 ± 0.5 and 44.7 ± 2.0 kcalmol-1. For both levels of theory, the results are also consistent with the '''Appendix 2'''.

Results show that the chair transition state is more stable than that of the boat with a lower activation energy of 33.16 kcalmol-1 at compared to 41.32kcalmol-1 at room temperature. Therefore, it can be concluded that the reaction mechanism of the Cope rearrangement prefers to proceed via the chair than the boat transition state.

====References====

# Nishio. M, Hirota. M, (1989). Tetrahedron. 45: 7201
# Rocque. B. G, Gonzales. J. M, Schaefer III. H. F, (2002). "An analysis of the conformers of 1,5-hexadiene" Molecular Physics. 100 (4): 441-446 {{DOI|10.1080/00268970110081412}}

Rep:Mod3:Yuko.Isayama3001

2009-11-13T12:38:10Z

Yi107: /* The Transition State */

=The Transition State=

The computational experiments involved the characterisation of transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

However, the molecular mechanics/force field methods that works well for structure determination (as in Module 1) cannot be used to study transition states in large molecules, as they do not describe bonds being made and broken, and changes in bonding type and electron distrbution. Instead, molecular-orbital based methods were used to solve the Schrodinger equation numerically and locate transition structures based on the local shape of potential energy surfaces. As well as showing what the transition states look like, reaction paths and barrier heights were also calculated.

==The Coper Rearrangement Tutorial==

{|
|[[Image:Cope_rearrange.gif|thumb|300px|left|Cope rearrangemnt of 1, 5-hexadiene ]]
The Cope rearrangement of 1, 5-hexadiene, which specifically involves a [3, 3] sigmatropic shift rearrangement, was studied to locate the low-energy minima and transition structures on the C6H10 potential energy surface, so that the preferred reaction mechanism could be determined.

It has been argued whether the mechanaism is concerted, stepwise or dissociative but it is now generally accepted that the reaction occurs in a concerted fashion via either a "''chair''" or a "''boat''" transition structure, with the ''boat'' transition structure lying several kcal/mol higher in energy. By using the B3LYP/6-31G* level of theory in Gaussian, the activation energies and enthalpies were calculated, which were then compared with literature values.
|}

{| align="center"
|- align="center"
|
[[Image:BoatChair_TS.gif|400px]]
|}

===Optimising the Reactants and Products===

Optimisation of 1, 5-hexadiene with an "''anti''" linkage for the central four C atoms was performed using the HF/3-21G level of theory and symmetrized to find its point group. Vibrational frequencies were then calculated and visualised, and potential energies corrected in order to compare them with experimental values. The same calculations were performed with another molecule of 1, 5-hexadiene with a "''gauche''" linkage, which would be expected to have a higher energy due to steric repulsion betweem the eclipsing carbon atoms. .

Results of the optimised ''anti-'' and ''gauche-'' structures based on HF/3-21G calculation method are shown below;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Conformer'''
| width="150" | '''Structure'''
| width="100" | '''Point Group'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
|- align="center"
| ''anti''
|
[[Image:1_5hexa_a_anti.gif|250px]]
| Ci
| -231.69253528
| -608303.5571
|- align="center"
| ''gauche''
|
[[Image:1_5hexa_b_gauche.gif|250px]]
| C1
| -231.69266121
| -608303.8879
|- align="center"
|}

The point group of the ''anti''-structure indicates that it has an inversion of symmetry, whilst the ''gauche''-structure lacks symmetry.

The energies of the ''anti-'' and ''gauche-'' structures were calculated as -231.69253528 and -231.69266121 Hartrees with an energy difference of 0.3308 kJmol-1, which indicates that the gauche conformation is in fact more stable; this is attributed to stereoelectronic effects in which there is an favourable interaction between the π orbital of the C=C bond and σ* orbital of the adjacent vinyl proton as shown belown in a Newman projection-1;

{| align="center"
|- align="center"
|
[[Image:Newman_anti2.gif|380px]]
|}

By comparing the structures I have optimised with those shown in '''Appendix 1''', my structures correspond to ''anti2'' and ''gauche3'' conformers.

Reoptimisation of the Ci ''anti2'' conformation of 1, 5-hexadiene at the B3LYP/6-31G* level resulted in an overall geometry change with very similar bond lengths but a siginicant increase in the outer dihedral angles by 4° as shown below. In terms of the energy, a final energy of -234.61170277 Hartrees was calculated which is in good agreement with the one given in the table for the ''anti2'' conformer. The lowering of the energy compared to the energy calculated by the HF/3-21G method is due to the fact that the Hartree Fock method does not take into account electron distributions, which means that electronic effects such as CH-π interactions are not properly considered in the method2.
{|
|[[Image:1_5hexa_anti2_hf.gif|thumb|350px|left|Optimised structure of ''anti2'' conformer based on B3LYP/6-31G* method ]]
|[[Image:1_5hexa_anti2_dft.gif|thumb|350px|left|Optimised structure of ''anti2'' conformer based on Hartree-Fock/3-21G method ]]
|}

The table below compares the bond angles of the Ci ''anti2'' conformation for each method;

{| border="1" cellpadding="2"
! rowspan=2 |'''Calculation method'''
! colspan="3" | '''Torsional angle/°'''
|-
|width="140pt"|'''C6-C5-C4-C3'''
|width="140pt"|'''C5-C4-C3-C2'''
|width="140pt"|'''C4-C3-C2-C1'''
|-
|''HF/3-21G'' || 114.7 || -180.0 || 114.7
|-
|''DFT/6-31G*'' ||118.5 || -180.0 || -118.5
|}

The outer dihedral angles are complements of each other which supports the Ci symmetry exhibited by the ''anti2'' conformer

Frequency anaylsis confirmed that the optimium structure was a minimum as all the vibration frequencies were real and positive.
{| align="center"
|- align="center"
|
[[Image:1_5hexa_g_spectrum.jpg|thumb|450px|left|IR spectrum of Ci ''anti2'' conformation of 1, 5-hexadiene]]
|}

The table below shows the thermochemistry of ''anti2'' conformer;

{| border="1" cellpadding="2"
! colspan="1" | '''Thermochemistry '''
! colspan="1" | '''Energy'''
|-
|width="300pt"|''Sum of electronic and zero point energies/Hartrees'' i.e E = Eelec + ZPE
|width="170pt"|-234.469212
|-
|''Sum of electronic and thermal energies at 298.15K and 1atm/Hartrees'' i.e E = E + Evib + Erot + Etrans || -234.461856
|-
|''Sum of electronic and thermal enthalpies/Hartrees'' i.e H = E + RT || -234.460912
|-
|''Sum of electronic and thermal free energies/Hartrees '' i.e G = H - TS || -234.500821
|}

===Optimizing the "Chair" and "Boat" Transition Structures ===

A transition structure optimisation was set up by i) computing the force constants at the beginning of the calculation, ii) using redundant coordinate editor and iii) using QST2. The reaction coordinate was also visualised and the IRC ran and the activation energies for the Cope rearrangement were calculated via the ''chair'' and ''boat'' transition structures.

The ''chair'' and ''transition'' structures for the Cope rearrangement shown in '''Appendix 2''' both consist of two C3H5 allyl fragments positioned approximately 2.2 apart, one with C2h symmetry and and the other with C2v symmetry.

====Chair Transition Structure====
Firstly a suitable guess of the chair transition structure was constructed; an allyl fragment (CH2CHCH2) was drawn and then optimised using the HF/3-21G level of theory. The optimised allyl structure was then pasted twice into a new window so that the two fragments could be orientated into the chair conformer.

The chair transition structure optimisation was set up by both i and ii, where both methods used the HF/3-21G level of theory.

'''Optimisation to a TS(Berny)'''

This methods involves computing the force constant matrix (also known as the Hessian) in the first step of the optimisation which is then updated as the optimisation proceeds. The optimisation was set up so that the force constants were only calculated once with additional keywords, Opt=NoEigen, which prevents the calculation from crashing if more than one imaginary frequency is detected during the optimisation.

The frequency calculation gave an imaginary frequency of magnitude -817.96 cm-1, which confirmed the transition state was optimised successfully.
{|
{| align="center"
|- align="center"
|
|[[Image:chair_b_opt3.gif|thumb|250px|left|Optimised chair TS using Gaussian optimisation ]]
|[[Image:chair_b_optfreq.gif|thumb|250px|left|Vibration at -817.96cm-1 corresponding to the Cope rearrangement ]]
|}

'''Frozen coordinate method'''

In this method, the transition structure was generated by freezing the reaction coordinate, i.e the terminal carbons of each fragment which form/break a bond during rerrangement and then minimising the rest of the molecule using Opt=ModRedundant. Once the molecule was fully optimised, the reaction coordinate was unfrozen and optimisation to a transition structure was performed.

Comparison with the previous method give the same structure with a bond length between the terminal end of the allyl fragments as 2.02Å, suggesting that both methods are equally accurate. However, in some cases, if the guessed transition structure is not close enough to the correct structure, method i may fail as the curvature of the surface may be significantly different at points far removed from the transition structure. This would make the frozen cooodinate method more reliable as well as more time-efficient and less expensive as the whole Hessian may not need to be computed once this is done; differentiating along the reaction coordinate may give a good enough guess for the initial force constant matrix.
{|
{| align="center"
|- align="center"
|
|[[Image:chair_d_opt2.gif|thumb|250px|left|Optimised chair TS using frozen coordinate method ]]
|}

====Boat Transition Structure====

{|
|[[Image:boat_e0_input.gif|thumb|490px|left|Numbering of reactant and product]] The boat transition structure optimisation was set up by QST2 method at the HF/3-21G level of theory, which involves specifying the reactants and products for the reaction and then calculating the interpolation between the two structures to find the transition state betweeen them. This meant the numbering for the product molecule had to be changed so that it corresponded to the numbering obtained in if the reactant had rearranged. However, the method failed to locate the boat transition structure; the top allyl fragment was simply translated without the possibility of accounting for the rotation around the central bonds.
|}

Thus, the reactant and product geometries were modified so that the central dihedral C-C-C-C angle was changed to O° , whilst the central C-C-Cs were reduced to 100°. By using the same QST2 method, optimisation to a boat transition structure was successful, which was confirmed by frequency analysis; one imaginary freqency at -839.84cm-1.

{| align="center"
|- align="center"
|
[[Image:Boat_optfreq.gif|thumb|250px|Optimised boat TS including vibration at -839.84cm-1 corresponding to the Cope rearrangement ]]
|}

====Intrinsic Reaction Coordinate (IRC)====

The IRC method allows you to follow the minimum energy path from a transition structure down to its local minimum as the product on a potential energy surface. This was set up by computing the reaction coordinate in the forward direction only as it is symmetrical and calculating the force constants once. Also 50 points were considered along the IRC.

An IRC calculation for the optimised chair transition structure gave 17 intermediate geomtries. Since the minimum had not been reached yet as indicated by the RMS gradient along the IRC not equalling to zero, the last point on the IRC was ran for a normal optimisation. This resulted in the a minimum structure corresponding to the ''gauche2'' conformer with an energy of -231.691199702 Hartrees.

Re-running an IRC by specifying a larger number of points until a minimum was reached was not an option since the inital IRC calculated 17 intermediate geomtroes which is well within the number of points that was specified i.e 50. Therefore, in order to confirm a local minimum had been reached an IRC calculation was re-ran but with the force constants were computed at every step. As a result, 47 intermediate geometries were located with an IRC pathway reaching an asymptote and thus RMS gradient equalling to zero, which suggested that the local minimum had been reached. Nevertheless, the last point on IRC was ran for a normal optimisation and the local minimum was confirmed as ''gauche2''with an energy of -231.69166700 Hartrees. Thus, the IRC method determined the Cope rearrangement of the ''anti2'' conformation of 1, 5-hexadiene to give the ''gauche2'' conformer.

{| border="1" cellpadding="5"
|- align="center"
| width="200" | '''Property'''
| width="150" | '''Endo TS'''
| width="100" | '''Exo TS'''
|- align="center"
| ''Structure from side''
|
[[Image:chair_fi_ircgraph1.jpg|400px ]]
|
[[Image:chair_fiii_ircgraph1.jpg|400px ]]
|- align="center"
| ''RMS gradient along IRC''
|
[[Image:chair_fi_ircgraph2.jpg|400px ]]
|
[[Image:chair_fiii_ircgraph2.jpg|400px ]]
|- align="center"
| ''Structure''
|
[[Image:chair_fi_opt.gif|250px ]]
|
[[Image:chair_fiii_opt.gif|250px ]]
|- align="center"
| ''Energy/Hartrees''|| -231.69166702 || -23.69166700
|}

====Calculation Activation Energies====

Re-optimisations of the chair and boat transition structures were performed using the B3LYP/6-31G* level of theory followed by frequency calculations to confirm the optimisations were successful, and then compared with the HF/3-21G method. Additionally, the activation energies were also calculated for the reaction via both transition structures. The results are tabulated below;

{| border="1" cellpadding="5"
|- align="center"
! colspan="1" | '''Method'''
! colspan="3" | '''HF/3-21G'''
! colspan="3" | '''B3LYP/6-31G*'''
|- align="center"
|width="150pt" |
|width="200pt" | '''Electonic energy/Hartrees'''
|width="200pt" | '''Sum of electronic and zero point energies at OK/Hartrees'''
|width="200pt" | '''Sum of electronic and thermal energies energies at 298.15K/Hartrees'''
|width="200pt" | '''Electonic energy/Hartrees'''
|width="200pt" | '''Sum of electronic and zero point energies at OK/Hartrees'''
|width="200pt" | '''Sum of electronic and thermal energies energies at 298.15K/Hartrees'''
|- align="center"
| ''Chair TS'' || -231.619322 || -231.466697 || -231.461339 || -234.556983|| -234.414931 || -234.409010
|- align="center"
| ''Boat TS'' || -231.602802 || -231.450928 || -231.445298 || -234.543093 || -234.402340 || -234.396006
|- align="center"
| Reactant (anti2) || -231.692535 ||-231.539539 || -231.532565 || -234.611703 || -234.469212 || -234.461856
|}

Summary of activation energies/kcalmol-1

{| border="1" cellpadding="5"
|- align="center"
! colspan="1" | '''Method'''
! colspan="2" | '''HF/3-21G'''
! colspan="2" | '''B3LYP/6-31G*'''
|- align="center"
|width="150pt" |
|width="200pt" | '''at OK'''
|width="200pt" | '''at 298.15K'''
|width="200pt" | '''at 0K'''
|width="200pt" | '''at 298.15K'''
|- align="center"
| ''ΔE (Chair TS)'' || 45.70 ||44.69 || 34.06 || 33.16
|- align="center"
| ''ΔE (Boat TS)'' || 55.60 || 54.76 || 41.96|| 41.32
|}

At both levels of theory, the geomtries are reasonably similar, but energy differences between the reactant and the transition states are markedly different. By using B3LYP/6-31G* which is higher and more accurate level of theory, the energies of both transition states have decreased and the activation energies for both transition structures are in much better agreement with the experimental values of 33.5 ± 0.5 and 44.7 ± 2.0 kcalmol-1. For both levels of theory, the results are also consistent with the '''Appendix 2'''.

Results show that the chair transition state is more stable than that of the boat with a lower activation energy of 33.16 kcalmol-1 at compared to 41.32kcalmol-1 at room temperature. Therefore, it can be concluded that the reaction mechanism of the Cope rearrangement prefers to proceed via the chair than the boat transition state.

====References====

# Nishio. M, Hirota. M, (1989). Tetrahedron. 45: 7201
# Rocque. B. G, Gonzales. J. M, Schaefer III. H. F, (2002). "An analysis of the conformers of 1,5-hexadiene" Molecular Physics. 100 (4): 441-446 {{DOI|10.1080/00268970110081412}}

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T12:33:05Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.71158
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.31661
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.15130
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
| -0.34273
| -215.06616
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
| -0.04045
| -25.38274
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
| -0.34505
| -216.52198
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
| -0.03571
| -22.40835
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

{| align="center"
|- align="center"
|
|[[Image:Secondary_overlap.gif|thumb|350px|Secondary orbital overlap illustration]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T12:26:07Z

Yi107: /* Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.71158
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.31661
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.15130
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
| -0.34273
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
| -0.04045
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
| -0.34505
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
| -0.03571
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

{| align="center"
|- align="center"
|
|[[Image:Secondary_overlap.gif|thumb|350px|Secondary orbital overlap illustration]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T12:02:56Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -0.22736
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| -0.03015
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -0.26664
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 0.01881
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
| -0.34273
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
| -0.04045
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
| -0.34505
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
| -0.03571
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

{| align="center"
|- align="center"
|
|[[Image:Secondary_overlap.gif|thumb|350px|Secondary orbital overlap illustration]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T12:02:09Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -0.22736
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| -0.03015
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -0.26664
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 0.01881
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
| -0.34273
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
| -0.04045
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
| -0.34505
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
| -0.03571
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

{| align="center"
|- align="center"
|
|[[Image:Secondary_overlap.gif|350px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T12:01:29Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -0.22736
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| -0.03015
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -0.26664
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 0.01881
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
| -0.34273
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
| -0.04045
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
| -0.34505
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
| -0.03571
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

{| align="center"
|- align="center"
|
|[[Image:Secondary_overlap.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

File:Secondary overlap.gif

2009-11-13T12:00:33Z

Yi107:

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T11:49:43Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -0.22736
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| -0.03015
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -0.26664
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 0.01881
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
| -0.34273
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
| -0.04045
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
| -0.34505
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
| -0.03571
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T11:46:52Z

Yi107: /* Optmisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -0.22736
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| -0.03015
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -0.26664
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 0.01881
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T11:40:59Z

Yi107: /* Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -0.22736
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| -0.03015
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -0.26664
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 0.01881
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T11:40:04Z

Yi107: /* Optmisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -0.22736
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| -0.03015
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -0.26664
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 0.01881
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kcalmol-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T11:35:19Z

Yi107: /* Ethylene and ''Cis''-Butadiene */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -0.22736
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| -0.03015
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -0.26664
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 0.01881
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T11:35:01Z

Yi107: /* Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -0.22736
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| -0.03015
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -0.26664
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 0.01881
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T11:33:26Z

Yi107: /* Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees (AM1)'''
| width="200" | '''Energy/Hartrees (B3LYP/6-31G*)'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -0.22736
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| -0.03015
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
|
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T11:26:38Z

Yi107: /* Ethylene and ''Cis''-Butadiene */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T11:25:07Z

Yi107: /* Optmisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T11:02:41Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
! rowspan=2 | '''Endo TS''' || ''HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T11:00:45Z

Yi107: /* The Diels Alder Cycloaddition */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="100" |
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
|! rowspan=2 | '''Exo TS''' || ''HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:58:54Z

Yi107: /* Ethylene and ''Cis''-Butadiene */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:48:38Z

Yi107: /* Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as -155.98594956 and -78.58745828 Hartrees respectively -97882.58718 and -49314.33736kcamol-1.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:35:17Z

Yi107: /* References= */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References==

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:35:03Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|308px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:34:45Z

Yi107: /* Cyclohexa-1,3-diene and Maleic Anhydride */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:34:04Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_distances.gif|thumb|350px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:33:51Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_Tdistances.gif|thumb|350px|C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

File:Exo distances.gif

2009-11-13T10:33:03Z

Yi107:

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:32:38Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_distances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:32:21Z

Yi107: /* Cyclohexa-1,3-diene and Maleic Anhydride */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_disttances.gif|thumb|310px|C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

File:Endo distances.gif

2009-11-13T10:30:33Z

Yi107:

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:10:51Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|255px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:10:42Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|257px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:10:32Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|260px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:10:23Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|265px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:10:00Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:Initial_guess_endo.gif|left|thumb|270px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

File:Initial guess endo.gif

2009-11-13T10:09:35Z

Yi107:

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:04:26Z

Yi107: /* Optimisation and Molecular Orbitals of the Transition Structure */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|270px|Geometry of the initial guess transition structure]]
|[[Image:TS_c_guess.gif|left|thumb|225px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T10:04:02Z

Yi107: /* The Diels Alder Cycloaddition */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:Initial_guess_exo.gif|left|thumb|225px|Geometry of the initial guess transition structure]]
|[[Image:TS_c_guess.gif|left|thumb|225px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.

File:Initial guess exo.gif

2009-11-13T10:03:35Z

Yi107:

Rep:Mod3:Yuko.Isayama3001

2009-11-13T02:25:30Z

Yi107: /* The Transition State */

=The Transition State=

The computational experiments involved the characterisation of transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

However, the molecular mechanics/force field methods that works well for structure determination (as in Module 1) cannot be used to study transition states in large molecules, as they do not describe bonds being made and broken, and changes in bonding type and electron distrbution. Instead, molecular-orbital based methods were used to solve the Schrodinger equation numerically and locate transition structures based on the local shape of potential energy surfaces. As well as showing what the transition states look like, reaction paths and barrier heights were also calculated.

==The Coper Rearrangement Tutorial==

{|
|[[Image:Cope_rearrange.gif|thumb|300px|left|Cope rearrangemnt of 1, 5-hexadiene ]]
The Cope rearrangement of 1, 5-hexadiene, which specifically involves a [3, 3] sigmatropic shift rearrangement, was studied to locate the low-energy minima and transition structures on the C6H10 potential energy surface, so that the preferred reaction mechanism could be determined.

It has been argued whether the mechanaism is concerted, stepwise or dissociative but it is now generally accepted that the reaction occurs in a concerted fashion via either a "''chair''" or a "''boat''" transition structure, with the ''boat'' transition structure lying several kcal/mol higher in energy. By using the B3LYP/6-31G* level of theory in Gaussian, the activation energies and enthalpies were calculated, which were then compared with literature values.
|}

{| align="center"
|- align="center"
|
[[Image:BoatChair_TS.gif|400px]]
|}

===Optimising the Reactants and Products===

Optimisation of 1, 5-hexadiene with an "''anti''" linkage for the central four C atoms was performed using the HF/3-21G level of theory and symmetrized to find its point group. Vibrational frequencies were then calculated and visualised, and potential energies corrected in order to compare them with experimental values. The same calculations were performed with another molecule of 1, 5-hexadiene with a "''gauche''" linkage, which would be expected to have a higher energy due to steric repulsion betweem the eclipsing carbon atoms. .

Results of the optimised ''anti-'' and ''gauche-'' structures based on HF/3-21G calculation method are shown below;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Conformer'''
| width="150" | '''Structure'''
| width="100" | '''Point Group'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
|- align="center"
| ''anti''
|
[[Image:1_5hexa_a_anti.gif|250px]]
| Ci
| -231.69253528
| -608303.5571
|- align="center"
| ''gauche''
|
[[Image:1_5hexa_b_gauche.gif|250px]]
| C1
| -231.69266121
| -608303.8879
|- align="center"
|}

The point group of the ''anti''-structure indicates that it has an inversion of symmetry, whilst the ''gauche''-structure lacks symmetry.

The energies of the ''anti-'' and ''gauche-'' structures were calculated as -231.69253528 and -231.69266121 Hartrees with an energy difference of 0.3308 kJmol-1, which indicates that the gauche conformation is in fact more stable; this is attributed to stereoelectronic effects in which there is an favourable interaction between the π orbital of the C=C bond and σ* orbital of the adjacent vinyl proton as shown belown in a Newman projection-1;

{| align="center"
|- align="center"
|
[[Image:Newman_anti2.gif|380px]]
|}

By comparing the structures I have optimised with those shown in '''Appendix 1''', my structures correspond to ''anti2'' and ''gauche3'' conformers.

Reoptimisation of the Ci ''anti2'' conformation of 1, 5-hexadiene at the B3LYP/6-31G* level resulted in an overall geometry change with very similar bond lengths but a siginicant increase in the outer dihedral angles by 4° as shown below. In terms of the energy, a final energy of -234.61170277 Hartrees was calculated which is in good agreement with the one given in the table for the ''anti2'' conformer. The lowering of the energy compared to the energy calculated by the HF/3-21G method is due to the fact that the Hartree Fock method does not take into account electron distributions, which means that electronic effects such as CH-π interactions are not properly considered in the method2.
{|
|[[Image:1_5hexa_anti2_hf.gif|thumb|350px|left|Optimised structure of ''anti2'' conformer based on B3LYP/6-31G* method ]]
|[[Image:1_5hexa_anti2_dft.gif|thumb|350px|left|Optimised structure of ''anti2'' conformer based on Hartree-Fock/3-21G method ]]
|}

The table below compares the bond angles of the Ci ''anti2'' conformation for each method;

{| border="1" cellpadding="2"
! rowspan=2 |'''Calculation method'''
! colspan="3" | '''Torsional angle/°'''
|-
|width="140pt"|'''C6-C5-C4-C3'''
|width="140pt"|'''C5-C4-C3-C2'''
|width="140pt"|'''C4-C3-C2-C1'''
|-
|''HF/3-21G'' || 114.7 || -180.0 || 114.7
|-
|''DFT/6-31G*'' ||118.5 || -180.0 || -118.5
|}

The outer dihedral angles are complements of each other which supports the Ci symmetry exhibited by the ''anti2'' conformer

Frequency anaylsis confirmed that the optimium structure was a minimum as all the vibration frequencies were real and positive.
{| align="center"
|- align="center"
|
[[Image:1_5hexa_g_spectrum.jpg|thumb|450px|left|IR spectrum of Ci ''anti2'' conformation of 1, 5-hexadiene]]
|}

The table below shows the thermochemistry of ''anti2'' conformer;

{| border="1" cellpadding="2"
! colspan="1" | '''Thermochemistry '''
! colspan="1" | '''Energy'''
|-
|width="300pt"|''Sum of electronic and zero point energies/Hartrees'' i.e E = Eelec + ZPE
|width="170pt"|-234.469212
|-
|''Sum of electronic and thermal energies at 298.15K and 1atm/Hartrees'' i.e E = E + Evib + Erot + Etrans || -234.461856
|-
|''Sum of electronic and thermal enthalpies/Hartrees'' i.e H = E + RT || -234.460912
|-
|''Sum of electronic and thermal free energies/Hartrees '' i.e G = H - TS || -234.500821
|}

====References====

# Nishio. M, Hirota. M, (1989). Tetrahedron. 45: 7201
# Rocque. B. G, Gonzales. J. M, Schaefer III. H. F, (2002). "An analysis of the conformers of 1,5-hexadiene" Molecular Physics. 100 (4): 441-446 {{DOI|10.1080/00268970110081412}}

===Optimizing the "Chair" and "Boat" Transition Structures ===

A transition structure optimisation was set up by i) computing the force constants at the beginning of the calculation, ii) using redundant coordinate editor and iii) using QST2. The reaction coordinate was also visualised and the IRC ran and the activation energies for the Cope rearrangement were calculated via the ''chair'' and ''boat'' transition structures.

The ''chair'' and ''transition'' structures for the Cope rearrangement shown in '''Appendix 2''' both consist of two C3H5 allyl fragments positioned approximately 2.2 apart, one with C2h symmetry and and the other with C2v symmetry.

====Chair Transition Structure====
Firstly a suitable guess of the chair transition structure was constructed; an allyl fragment (CH2CHCH2) was drawn and then optimised using the HF/3-21G level of theory. The optimised allyl structure was then pasted twice into a new window so that the two fragments could be orientated into the chair conformer.

The chair transition structure optimisation was set up by both i and ii, where both methods used the HF/3-21G level of theory.

'''Optimisation to a TS(Berny)'''

This methods involves computing the force constant matrix (also known as the Hessian) in the first step of the optimisation which is then updated as the optimisation proceeds. The optimisation was set up so that the force constants were only calculated once with additional keywords, Opt=NoEigen, which prevents the calculation from crashing if more than one imaginary frequency is detected during the optimisation.

The frequency calculation gave an imaginary frequency of magnitude -817.96 cm-1, which confirmed the transition state was optimised successfully.
{|
{| align="center"
|- align="center"
|
|[[Image:chair_b_opt3.gif|thumb|250px|left|Optimised chair TS using Gaussian optimisation ]]
|[[Image:chair_b_optfreq.gif|thumb|250px|left|Vibration at -817.96cm-1 corresponding to the Cope rearrangement ]]
|}

'''Frozen coordinate method'''

In this method, the transition structure was generated by freezing the reaction coordinate, i.e the terminal carbons of each fragment which form/break a bond during rerrangement and then minimising the rest of the molecule using Opt=ModRedundant. Once the molecule was fully optimised, the reaction coordinate was unfrozen and optimisation to a transition structure was performed.

Comparison with the previous method give the same structure with a bond length between the terminal end of the allyl fragments as 2.02Å, suggesting that both methods are equally accurate. However, in some cases, if the guessed transition structure is not close enough to the correct structure, method i may fail as the curvature of the surface may be significantly different at points far removed from the transition structure. This would make the frozen cooodinate method more reliable as well as more time-efficient and less expensive as the whole Hessian may not need to be computed once this is done; differentiating along the reaction coordinate may give a good enough guess for the initial force constant matrix.
{|
{| align="center"
|- align="center"
|
|[[Image:chair_d_opt2.gif|thumb|250px|left|Optimised chair TS using frozen coordinate method ]]
|}

====Boat Transition Structure====

{|
|[[Image:boat_e0_input.gif|thumb|490px|left|Numbering of reactant and product]] The boat transition structure optimisation was set up by QST2 method at the HF/3-21G level of theory, which involves specifying the reactants and products for the reaction and then calculating the interpolation between the two structures to find the transition state betweeen them. This meant the numbering for the product molecule had to be changed so that it corresponded to the numbering obtained in if the reactant had rearranged. However, the method failed to locate the boat transition structure; the top allyl fragment was simply translated without the possibility of accounting for the rotation around the central bonds.
|}

Thus, the reactant and product geometries were modified so that the central dihedral C-C-C-C angle was changed to O° , whilst the central C-C-Cs were reduced to 100°. By using the same QST2 method, optimisation to a boat transition structure was successful, which was confirmed by frequency analysis; one imaginary freqency at -839.84cm-1.

{| align="center"
|- align="center"
|
[[Image:Boat_optfreq.gif|thumb|250px|Optimised boat TS including vibration at -839.84cm-1 corresponding to the Cope rearrangement ]]
|}

====Intrinsic Reaction Coordinate (IRC)====

The IRC method allows you to follow the minimum energy path from a transition structure down to its local minimum as the product on a potential energy surface. This was set up by computing the reaction coordinate in the forward direction only as it is symmetrical and calculating the force constants once. Also 50 points were considered along the IRC.

An IRC calculation for the optimised chair transition structure gave 17 intermediate geomtries. Since the minimum had not been reached yet as indicated by the RMS gradient along the IRC not equalling to zero, the last point on the IRC was ran for a normal optimisation. This resulted in the a minimum structure corresponding to the ''gauche2'' conformer with an energy of -231.691199702 Hartrees.

Re-running an IRC by specifying a larger number of points until a minimum was reached was not an option since the inital IRC calculated 17 intermediate geomtroes which is well within the number of points that was specified i.e 50. Therefore, in order to confirm a local minimum had been reached an IRC calculation was re-ran but with the force constants were computed at every step. As a result, 47 intermediate geometries were located with an IRC pathway reaching an asymptote and thus RMS gradient equalling to zero, which suggested that the local minimum had been reached. Nevertheless, the last point on IRC was ran for a normal optimisation and the local minimum was confirmed as ''gauche2''with an energy of -231.69166700 Hartrees. Thus, the IRC method determined the Cope rearrangement of the ''anti2'' conformation of 1, 5-hexadiene to give the ''gauche2'' conformer.

{| border="1" cellpadding="5"
|- align="center"
| width="200" | '''Property'''
| width="150" | '''Endo TS'''
| width="100" | '''Exo TS'''
|- align="center"
| ''Structure from side''
|
[[Image:chair_fi_ircgraph1.jpg|400px ]]
|
[[Image:chair_fiii_ircgraph1.jpg|400px ]]
|- align="center"
| ''RMS gradient along IRC''
|
[[Image:chair_fi_ircgraph2.jpg|400px ]]
|
[[Image:chair_fiii_ircgraph2.jpg|400px ]]
|- align="center"
| ''Structure''
|
[[Image:chair_fi_opt.gif|250px ]]
|
[[Image:chair_fiii_opt.gif|250px ]]
|- align="center"
| ''Energy/Hartrees''|| -231.69166702 || -23.69166700
|}

====Calculation Activation Energies====

Re-optimisations of the chair and boat transition structures were performed using the B3LYP/6-31G* level of theory followed by frequency calculations to confirm the optimisations were successful, and then compared with the HF/3-21G method. Additionally, the activation energies were also calculated for the reaction via both transition structures. The results are tabulated below;

{| border="1" cellpadding="5"
|- align="center"
! colspan="1" | '''Method'''
! colspan="3" | '''HF/3-21G'''
! colspan="3" | '''B3LYP/6-31G*'''
|- align="center"
|width="150pt" |
|width="200pt" | '''Electonic energy/Hartrees'''
|width="200pt" | '''Sum of electronic and zero point energies at OK/Hartrees'''
|width="200pt" | '''Sum of electronic and thermal energies energies at 298.15K/Hartrees'''
|width="200pt" | '''Electonic energy/Hartrees'''
|width="200pt" | '''Sum of electronic and zero point energies at OK/Hartrees'''
|width="200pt" | '''Sum of electronic and thermal energies energies at 298.15K/Hartrees'''
|- align="center"
| ''Chair TS'' || -231.619322 || -231.466697 || -231.461339 || -234.556983|| -234.414931 || -234.409010
|- align="center"
| ''Boat TS'' || -231.602802 || -231.450928 || -231.445298 || -234.543093 || -234.402340 || -234.396006
|- align="center"
| Reactant (anti2) || -231.692535 ||-231.539539 || -231.532565 || -234.611703 || -234.469212 || -234.461856
|}

Summary of activation energies/kcalmol-1

{| border="1" cellpadding="5"
|- align="center"
! colspan="1" | '''Method'''
! colspan="2" | '''HF/3-21G'''
! colspan="2" | '''B3LYP/6-31G*'''
|- align="center"
|width="150pt" |
|width="200pt" | '''at OK'''
|width="200pt" | '''at 298.15K'''
|width="200pt" | '''at 0K'''
|width="200pt" | '''at 298.15K'''
|- align="center"
| ''ΔE (Chair TS)'' || 45.70 ||44.69 || 34.06 || 33.16
|- align="center"
| ''ΔE (Boat TS)'' || 55.60 || 54.76 || 41.96|| 41.32
|}

At both levels of theory, the geomtries are reasonably similar, but energy differences between the reactant and the transition states are markedly different. By using B3LYP/6-31G* which is higher and more accurate level of theory, the energies of both transition states have decreased and the activation energies for both transition structures are in much better agreement with the experimental values of 33.5 ± 0.5 and 44.7 ± 2.0 kcalmol-1. For both levels of theory, the results are also consistent with the '''Appendix 2'''.

Results show that the chair transition state is more stable than that of the boat with a lower activation energy of 33.16 kcalmol-1 at compared to 41.32kcalmol-1 at room temperature. Therefore, it can be concluded that the reaction mechanism of the Cope rearrangement prefers to proceed via the chair than the boat transition state.

Rep:Mod3:Yuko.Isayama3001

2009-11-13T02:24:43Z

Yi107: /* Optimising the Reactants and Products */

=The Transition State=

The computational experiments involved the characterisation of transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

However, the molecular mechanics/force field methods that works well for structure determination (as in Module 1) cannot be used to study transition states in large molecules, as they do not describe bonds being made and broken, and changes in bonding type and electron distrbution. Instead, molecular-orbital based methods were used to solve the Schrodinger equation numerically and locate transition structures based on the local shape of potential energy surfaces. As well as showing what the transition states look like, reaction paths and barrier heights were also calculated.

==The Coper Rearrangement Tutorial==

{|
|[[Image:Cope_rearrange.gif|thumb|300px|left|Cope rearrangemnt of 1, 5-hexadiene ]]
The Cope rearrangement of 1, 5-hexadiene, which specifically involves a [3, 3] sigmatropic shift rearrangement, was studied to locate the low-energy minima and transition structures on the C6H10 potential energy surface, so that the preferred reaction mechanism could be determined.

It has been argued whether the mechanaism is concerted, stepwise or dissociative but it is now generally accepted that the reaction occurs in a concerted fashion via either a "''chair''" or a "''boat''" transition structure, with the ''boat'' transition structure lying several kcal/mol higher in energy. By using the B3LYP/6-31G* level of theory in Gaussian, the activation energies and enthalpies were calculated, which were then compared with literature values.
|}

{| align="center"
|- align="center"
|
[[Image:BoatChair_TS.gif|400px]]
|}

===Optimising the Reactants and Products===

Optimisation of 1, 5-hexadiene with an "''anti''" linkage for the central four C atoms was performed using the HF/3-21G level of theory and symmetrized to find its point group. Vibrational frequencies were then calculated and visualised, and potential energies corrected in order to compare them with experimental values. The same calculations were performed with another molecule of 1, 5-hexadiene with a "''gauche''" linkage, which would be expected to have a higher energy due to steric repulsion betweem the eclipsing carbon atoms. .

Results of the optimised ''anti-'' and ''gauche-'' structures based on HF/3-21G calculation method are shown below;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Conformer'''
| width="150" | '''Structure'''
| width="100" | '''Point Group'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
|- align="center"
| ''anti''
|
[[Image:1_5hexa_a_anti.gif|250px]]
| Ci
| -231.69253528
| -608303.5571
|- align="center"
| ''gauche''
|
[[Image:1_5hexa_b_gauche.gif|250px]]
| C1
| -231.69266121
| -608303.8879
|- align="center"
|}

The point group of the ''anti''-structure indicates that it has an inversion of symmetry, whilst the ''gauche''-structure lacks symmetry.

The energies of the ''anti-'' and ''gauche-'' structures were calculated as -231.69253528 and -231.69266121 Hartrees with an energy difference of 0.3308 kJmol-1, which indicates that the gauche conformation is in fact more stable; this is attributed to stereoelectronic effects in which there is an favourable interaction between the π orbital of the C=C bond and σ* orbital of the adjacent vinyl proton as shown belown in a Newman projection-1;

{| align="center"
|- align="center"
|
[[Image:Newman_anti2.gif|380px]]
|}

By comparing the structures I have optimised with those shown in '''Appendix 1''', my structures correspond to ''anti2'' and ''gauche3'' conformers.

Reoptimisation of the Ci ''anti2'' conformation of 1, 5-hexadiene at the B3LYP/6-31G* level resulted in an overall geometry change with very similar bond lengths but a siginicant increase in the outer dihedral angles by 4° as shown below. In terms of the energy, a final energy of -234.61170277 Hartrees was calculated which is in good agreement with the one given in the table for the ''anti2'' conformer. The lowering of the energy compared to the energy calculated by the HF/3-21G method is due to the fact that the Hartree Fock method does not take into account electron distributions, which means that electronic effects such as CH-π interactions are not properly considered in the method2.
{|
|[[Image:1_5hexa_anti2_hf.gif|thumb|350px|left|Optimised structure of ''anti2'' conformer based on B3LYP/6-31G* method ]]
|[[Image:1_5hexa_anti2_dft.gif|thumb|350px|left|Optimised structure of ''anti2'' conformer based on Hartree-Fock/3-21G method ]]
|}

The table below compares the bond angles of the Ci ''anti2'' conformation for each method;

{| border="1" cellpadding="2"
! rowspan=2 |'''Calculation method'''
! colspan="3" | '''Torsional angle/°'''
|-
|width="140pt"|'''C6-C5-C4-C3'''
|width="140pt"|'''C5-C4-C3-C2'''
|width="140pt"|'''C4-C3-C2-C1'''
|-
|''HF/3-21G'' || 114.7 || -180.0 || 114.7
|-
|''DFT/6-31G*'' ||118.5 || -180.0 || -118.5
|}

The outer dihedral angles are complements of each other which supports the Ci symmetry exhibited by the ''anti2'' conformer

Frequency anaylsis confirmed that the optimium structure was a minimum as all the vibration frequencies were real and positive.
{| align="center"
|- align="center"
|
[[Image:1_5hexa_g_spectrum.jpg|thumb|450px|left|IR spectrum of Ci ''anti2'' conformation of 1, 5-hexadiene]]
|}

The table below shows the thermochemistry of ''anti2'' conformer;

{| border="1" cellpadding="2"
! colspan="1" | '''Thermochemistry '''
! colspan="1" | '''Energy'''
|-
|width="300pt"|''Sum of electronic and zero point energies/Hartrees'' i.e E = Eelec + ZPE
|width="170pt"|-234.469212
|-
|''Sum of electronic and thermal energies at 298.15K and 1atm/Hartrees'' i.e E = E + Evib + Erot + Etrans || -234.461856
|-
|''Sum of electronic and thermal enthalpies/Hartrees'' i.e H = E + RT || -234.460912
|-
|''Sum of electronic and thermal free energies/Hartrees '' i.e G = H - TS || -234.500821
|}

====References====

# Nishio. M, Hirota. M, (1989). Tetrahedron. 45: 7201
# Rocque. B. G, Gonzales. J. M, Schaefer III. H. F, (2002). "An analysis of the conformers of 1,5-hexadiene" Molecular Physics. 100 (4): 441-446 {{DOI|10.1080/00268970110081412}}

===Optimizing the "Chair" and "Boat" Transition Structures ===

A transition structure optimisation was set up by i) computing the force constants at the beginning of the calculation, ii) using redundant coordinate editor and iii) using QST2. The reaction coordinate was also visualised and the IRC ran and the activation energies for the Cope rearrangement were calculated via the ''chair'' and ''boat'' transition structures.

The ''chair'' and ''transition'' structures for the Cope rearrangement shown in '''Appendix 2''' both consist of two C3H5 allyl fragments positioned approximately 2.2 apart, one with C2h symmetry and and the other with C2v symmetry.

====Chair Transition Structure====
Firstly a suitable guess of the chair transition structure was constructed; an allyl fragment (CH2CHCH2) was drawn and then optimised using the HF/3-21G level of theory. The optimised allyl structure was then pasted twice into a new window so that the two fragments could be orientated into the chair conformer.

The chair transition structure optimisation was set up by both i and ii, where both methods used the HF/3-21G level of theory.

'''Optimisation to a TS(Berny)'''

This methods involves computing the force constant matrix (also known as the Hessian) in the first step of the optimisation which is then updated as the optimisation proceeds. The optimisation was set up so that the force constants were only calculated once with additional keywords, Opt=NoEigen, which prevents the calculation from crashing if more than one imaginary frequency is detected during the optimisation.

The frequency calculation gave an imaginary frequency of magnitude -817.96 cm-1, which confirmed the transition state was optimised successfully.
{|
{| align="center"
|- align="center"
|
|[[Image:chair_b_opt3.gif|thumb|250px|left|Optimised chair TS using Gaussian optimisation ]]
|[[Image:chair_b_optfreq.gif|thumb|250px|left|Vibration at -817.96cm-1 corresponding to the Cope rearrangement ]]
|}

'''Frozen coordinate method'''

In this method, the transition structure was generated by freezing the reaction coordinate, i.e the terminal carbons of each fragment which form/break a bond during rerrangement and then minimising the rest of the molecule using Opt=ModRedundant. Once the molecule was fully optimised, the reaction coordinate was unfrozen and optimisation to a transition structure was performed.

Comparison with the previous method give the same structure with a bond length between the terminal end of the allyl fragments as 2.02Å, suggesting that both methods are equally accurate. However, in some cases, if the guessed transition structure is not close enough to the correct structure, method i may fail as the curvature of the surface may be significantly different at points far removed from the transition structure. This would make the frozen cooodinate method more reliable as well as more time-efficient and less expensive as the whole Hessian may not need to be computed once this is done; differentiating along the reaction coordinate may give a good enough guess for the initial force constant matrix.
{|
{| align="center"
|- align="center"
|
|[[Image:chair_d_opt2.gif|thumb|250px|left|Optimised chair TS using frozen coordinate method ]]
|}

====Boat Transition Structure====

{|
|[[Image:boat_e0_input.gif|thumb|490px|left|Numbering of reactant and product]] The boat transition structure optimisation was set up by QST2 method at the HF/3-21G level of theory, which involves specifying the reactants and products for the reaction and then calculating the interpolation between the two structures to find the transition state betweeen them. This meant the numbering for the product molecule had to be changed so that it corresponded to the numbering obtained in if the reactant had rearranged. However, the method failed to locate the boat transition structure; the top allyl fragment was simply translated without the possibility of accounting for the rotation around the central bonds.
|}

Thus, the reactant and product geometries were modified so that the central dihedral C-C-C-C angle was changed to O° , whilst the central C-C-Cs were reduced to 100°. By using the same QST2 method, optimisation to a boat transition structure was successful, which was confirmed by frequency analysis; one imaginary freqency at -839.84cm-1.

{| align="center"
|- align="center"
|
[[Image:Boat_optfreq.gif|thumb|250px|Optimised boat TS including vibration at -839.84cm-1 corresponding to the Cope rearrangement ]]
|}

====Intrinsic Reaction Coordinate (IRC)====

The IRC method allows you to follow the minimum energy path from a transition structure down to its local minimum as the product on a potential energy surface. This was set up by computing the reaction coordinate in the forward direction only as it is symmetrical and calculating the force constants once. Also 50 points were considered along the IRC.

An IRC calculation for the optimised chair transition structure gave 17 intermediate geomtries. Since the minimum had not been reached yet as indicated by the RMS gradient along the IRC not equalling to zero, the last point on the IRC was ran for a normal optimisation. This resulted in the a minimum structure corresponding to the ''gauche2'' conformer with an energy of -231.691199702 Hartrees.

Re-running an IRC by specifying a larger number of points until a minimum was reached was not an option since the inital IRC calculated 17 intermediate geomtroes which is well within the number of points that was specified i.e 50. Therefore, in order to confirm a local minimum had been reached an IRC calculation was re-ran but with the force constants were computed at every step. As a result, 47 intermediate geometries were located with an IRC pathway reaching an asymptote and thus RMS gradient equalling to zero, which suggested that the local minimum had been reached. Nevertheless, the last point on IRC was ran for a normal optimisation and the local minimum was confirmed as ''gauche2''with an energy of -231.69166700 Hartrees. Thus, the IRC method determined the Cope rearrangement of the ''anti2'' conformation of 1, 5-hexadiene to give the ''gauche2'' conformer.

{| border="1" cellpadding="5"
|- align="center"
| width="200" | '''Property'''
| width="150" | '''Endo TS'''
| width="100" | '''Exo TS'''
|- align="center"
| ''Structure from side''
|
[[Image:chair_fi_ircgraph1.jpg|400px ]]
|
[[Image:chair_fiii_ircgraph1.jpg|400px ]]
|- align="center"
| ''RMS gradient along IRC''
|
[[Image:chair_fi_ircgraph2.jpg|400px ]]
|
[[Image:chair_fiii_ircgraph2.jpg|400px ]]
|- align="center"
| ''Structure''
|
[[Image:chair_fi_opt.gif|250px ]]
|
[[Image:chair_fiii_opt.gif|250px ]]
|- align="center"
| ''Energy/Hartrees''|| -231.69166702 || -23.69166700
|}

====Calculation Activation Energies====

Re-optimisations of the chair and boat transition structures were performed using the B3LYP/6-31G* level of theory followed by frequency calculations to confirm the optimisations were successful, and then compared with the HF/3-21G method. Additionally, the activation energies were also calculated for the reaction via both transition structures. The results are tabulated below;

{| border="1" cellpadding="5"
|- align="center"
! colspan="1" | '''Method'''
! colspan="3" | '''HF/3-21G'''
! colspan="3" | '''B3LYP/6-31G*'''
|- align="center"
|width="150pt" |
|width="200pt" | '''Electonic energy/Hartrees'''
|width="200pt" | '''Sum of electronic and zero point energies at OK/Hartrees'''
|width="200pt" | '''Sum of electronic and thermal energies energies at 298.15K/Hartrees'''
|width="200pt" | '''Electonic energy/Hartrees'''
|width="200pt" | '''Sum of electronic and zero point energies at OK/Hartrees'''
|width="200pt" | '''Sum of electronic and thermal energies energies at 298.15K/Hartrees'''
|- align="center"
| ''Chair TS'' || -231.619322 || -231.466697 || -231.461339 || -234.556983|| -234.414931 || -234.409010
|- align="center"
| ''Boat TS'' || -231.602802 || -231.450928 || -231.445298 || -234.543093 || -234.402340 || -234.396006
|- align="center"
| Reactant (anti2) || -231.692535 ||-231.539539 || -231.532565 || -234.611703 || -234.469212 || -234.461856
|}

Summary of activation energies/kcalmol-1

{| border="1" cellpadding="5"
|- align="center"
! colspan="1" | '''Method'''
! colspan="2" | '''HF/3-21G'''
! colspan="2" | '''B3LYP/6-31G*'''
|- align="center"
|width="150pt" |
|width="200pt" | '''at OK'''
|width="200pt" | '''at 298.15K'''
|width="200pt" | '''at 0K'''
|width="200pt" | '''at 298.15K'''
|- align="center"
| ''ΔE (Chair TS)'' || 45.70 ||44.69 || 34.06 || 33.16
|- align="center"
| ''ΔE (Boat TS)'' || 55.60 || 54.76 || 41.96|| 41.32
|}

At both levels of theory, the geomtries are reasonably similar, but energy differences between the reactant and the transition states are markedly different. By using B3LYP/6-31G* which is higher and more accurate level of theory, the energies of both transition states have decreased and the activation energies for both transition structures are in much better agreement with the experimental values of 33.5 ± 0.5 and 44.7 ± 2.0 kcalmol-1. For both levels of theory, the results are also consistent with the '''Appendix 2'''.

Results show that the chair transition state is more stable than that of the boat with a lower activation energy of 33.16 kcalmol-1 at compared to 41.32kcalmol-1 at room temperature. Therefore, it can be concluded that the reaction mechanism of the Cope rearrangement prefers to proceed via the chair than the boat transition state.

Rep:Mod3:Yuko.Isayama3001

2009-11-13T02:11:10Z

Yi107: /* The Transition State */

=The Transition State=

The computational experiments involved the characterisation of transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

However, the molecular mechanics/force field methods that works well for structure determination (as in Module 1) cannot be used to study transition states in large molecules, as they do not describe bonds being made and broken, and changes in bonding type and electron distrbution. Instead, molecular-orbital based methods were used to solve the Schrodinger equation numerically and locate transition structures based on the local shape of potential energy surfaces. As well as showing what the transition states look like, reaction paths and barrier heights were also calculated.

==The Coper Rearrangement Tutorial==

{|
|[[Image:Cope_rearrange.gif|thumb|300px|left|Cope rearrangemnt of 1, 5-hexadiene ]]
The Cope rearrangement of 1, 5-hexadiene, which specifically involves a [3, 3] sigmatropic shift rearrangement, was studied to locate the low-energy minima and transition structures on the C6H10 potential energy surface, so that the preferred reaction mechanism could be determined.

It has been argued whether the mechanaism is concerted, stepwise or dissociative but it is now generally accepted that the reaction occurs in a concerted fashion via either a "''chair''" or a "''boat''" transition structure, with the ''boat'' transition structure lying several kcal/mol higher in energy. By using the B3LYP/6-31G* level of theory in Gaussian, the activation energies and enthalpies were calculated, which were then compared with literature values.
|}

{| align="center"
|- align="center"
|
[[Image:BoatChair_TS.gif|400px]]
|}

===Optimising the Reactants and Products===

Optimisation of 1, 5-hexadiene with an "''anti''" linkage for the central four C atoms was performed using the HF/3-21G level of theory and symmetrized to find its point group. Vibrational frequencies were then calculated and visualised, and potential energies corrected in order to compare them with experimental values. The same calculations were performed with another molecule of 1, 5-hexadiene with a "''gauche''" linkage, which would be expected to have a higher energy due to steric repulsion betweem the eclipsing carbon atoms. .

Results of the optimised ''anti-'' and ''gauche-'' structures based on HF/3-21G calculation method are shown below;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Conformer'''
| width="150" | '''Structure'''
| width="100" | '''Point Group'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
|- align="center"
| ''anti''
|
[[Image:1_5hexa_a_anti.gif|250px]]
| Ci
| -231.69253528
| -608303.5571
|- align="center"
| ''gauche''
|
[[Image:1_5hexa_b_gauche.gif|250px]]
| C1
| -231.69266121
| -608303.8879
|- align="center"
|}

The point group of the ''anti''-structure indicates that it has an inversion of symmetry, whilst the ''gauche''-structure lacks symmetry.

The energies of the ''anti-'' and ''gauche-'' structures were calculated as -231.69253528 and -231.69266121 Hartrees with an energy difference of 0.3308 kJmol-1, which indicates that the gauche conformation is in fact more stable; this is attributed to stereoelectronic effects in which there is an favourable interaction between the π orbital of the C=C bond and σ* orbital of the adjacent vinyl proton as shown belown in a Newman projection;

{| align="center"
|- align="center"
|
[[Image:Newman_anti2.gif|380px]]
|}

By comparing the structures I have optimised with those shown in '''Appendix 1''', my structures correspond to ''anti2'' and ''gauche3'' conformers.

Reoptimisation of the Ci ''anti2'' conformation of 1, 5-hexadiene at the B3LYP/6-31G* level resulted in an overall geometry change with very similar bond lengths but a siginicant increase in the outer dihedral angles by 4° as shown below. In terms of the energy, a final energy of -234.61170277 Hartrees was calculated which is in good agreement with the one given in the table for the ''anti2'' conformer. The lowering of the energy compared to the energy calculated by the HF/3-21G method is due to the fact that the Hartree Fock method does not take into account electron distributions, which means that electronic effects such as CH-π interactions are not properly considered in the method.
{|
|[[Image:1_5hexa_anti2_hf.gif|thumb|350px|left|Optimised structure of ''anti2'' conformer based on B3LYP/6-31G* method ]]
|[[Image:1_5hexa_anti2_dft.gif|thumb|350px|left|Optimised structure of ''anti2'' conformer based on Hartree-Fock/3-21G method ]]
|}

The table below compares the bond angles of the Ci ''anti2'' conformation for each method;

{| border="1" cellpadding="2"
! rowspan=2 |'''Calculation method'''
! colspan="3" | '''Torsional angle/°'''
|-
|width="140pt"|'''C6-C5-C4-C3'''
|width="140pt"|'''C5-C4-C3-C2'''
|width="140pt"|'''C4-C3-C2-C1'''
|-
|''HF/3-21G'' || 114.7 || -180.0 || 114.7
|-
|''DFT/6-31G*'' ||118.5 || -180.0 || -118.5
|}

The outer dihedral angles are complements of each other which supports the Ci symmetry exhibited by the ''anti2'' conformer

Frequency anaylsis confirmed that the optimium structure was a minimum as all the vibration frequencies were real and positive.
{| align="center"
|- align="center"
|
[[Image:1_5hexa_g_spectrum.jpg|thumb|450px|left|IR spectrum of Ci ''anti2'' conformation of 1, 5-hexadiene]]
|}

The table below shows the comparison of the thermochemistry properties of the ''anti2'' conformer at 0K and 298.15K;

{| border="1" cellpadding="2"
! colspan="1" | '''Thermochemistry properties'''
! colspan="1" | '''Energy at OK and 1atm'''
! colspan="1" | '''Energy at 298.15K and 1atm'''
|-
|width="300pt"|''Sum of electronic and zero point energies/Hartrees'' i.e E = Eelec + ZPE
|width="170pt"|-234.469212
|width="170pt"|
|-
|''Sum of electronic and thermal energies at 298.15K and 1atm/Hartrees'' i.e E = E + Evib + Erot + Etrans || -234.461856 ||
|-
|''Sum of electronic and thermal enthalpies/Hartrees'' i.e H = E + RT || -234.460912 ||
|-
|''Sum of electronic and thermal free energies/Hartrees '' i.e G = H - TS || -234.500821 ||
|}

====References====

# Nishio, M.; Hirota, M. Tetrahedron 1989, 45, 7201

===Optimizing the "Chair" and "Boat" Transition Structures ===

A transition structure optimisation was set up by i) computing the force constants at the beginning of the calculation, ii) using redundant coordinate editor and iii) using QST2. The reaction coordinate was also visualised and the IRC ran and the activation energies for the Cope rearrangement were calculated via the ''chair'' and ''boat'' transition structures.

The ''chair'' and ''transition'' structures for the Cope rearrangement shown in '''Appendix 2''' both consist of two C3H5 allyl fragments positioned approximately 2.2 apart, one with C2h symmetry and and the other with C2v symmetry.

====Chair Transition Structure====
Firstly a suitable guess of the chair transition structure was constructed; an allyl fragment (CH2CHCH2) was drawn and then optimised using the HF/3-21G level of theory. The optimised allyl structure was then pasted twice into a new window so that the two fragments could be orientated into the chair conformer.

The chair transition structure optimisation was set up by both i and ii, where both methods used the HF/3-21G level of theory.

'''Optimisation to a TS(Berny)'''

This methods involves computing the force constant matrix (also known as the Hessian) in the first step of the optimisation which is then updated as the optimisation proceeds. The optimisation was set up so that the force constants were only calculated once with additional keywords, Opt=NoEigen, which prevents the calculation from crashing if more than one imaginary frequency is detected during the optimisation.

The frequency calculation gave an imaginary frequency of magnitude -817.96 cm-1, which confirmed the transition state was optimised successfully.
{|
{| align="center"
|- align="center"
|
|[[Image:chair_b_opt3.gif|thumb|250px|left|Optimised chair TS using Gaussian optimisation ]]
|[[Image:chair_b_optfreq.gif|thumb|250px|left|Vibration at -817.96cm-1 corresponding to the Cope rearrangement ]]
|}

'''Frozen coordinate method'''

In this method, the transition structure was generated by freezing the reaction coordinate, i.e the terminal carbons of each fragment which form/break a bond during rerrangement and then minimising the rest of the molecule using Opt=ModRedundant. Once the molecule was fully optimised, the reaction coordinate was unfrozen and optimisation to a transition structure was performed.

Comparison with the previous method give the same structure with a bond length between the terminal end of the allyl fragments as 2.02Å, suggesting that both methods are equally accurate. However, in some cases, if the guessed transition structure is not close enough to the correct structure, method i may fail as the curvature of the surface may be significantly different at points far removed from the transition structure. This would make the frozen cooodinate method more reliable as well as more time-efficient and less expensive as the whole Hessian may not need to be computed once this is done; differentiating along the reaction coordinate may give a good enough guess for the initial force constant matrix.
{|
{| align="center"
|- align="center"
|
|[[Image:chair_d_opt2.gif|thumb|250px|left|Optimised chair TS using frozen coordinate method ]]
|}

====Boat Transition Structure====

{|
|[[Image:boat_e0_input.gif|thumb|490px|left|Numbering of reactant and product]] The boat transition structure optimisation was set up by QST2 method at the HF/3-21G level of theory, which involves specifying the reactants and products for the reaction and then calculating the interpolation between the two structures to find the transition state betweeen them. This meant the numbering for the product molecule had to be changed so that it corresponded to the numbering obtained in if the reactant had rearranged. However, the method failed to locate the boat transition structure; the top allyl fragment was simply translated without the possibility of accounting for the rotation around the central bonds.
|}

Thus, the reactant and product geometries were modified so that the central dihedral C-C-C-C angle was changed to O° , whilst the central C-C-Cs were reduced to 100°. By using the same QST2 method, optimisation to a boat transition structure was successful, which was confirmed by frequency analysis; one imaginary freqency at -839.84cm-1.

{| align="center"
|- align="center"
|
[[Image:Boat_optfreq.gif|thumb|250px|Optimised boat TS including vibration at -839.84cm-1 corresponding to the Cope rearrangement ]]
|}

====Intrinsic Reaction Coordinate (IRC)====

The IRC method allows you to follow the minimum energy path from a transition structure down to its local minimum as the product on a potential energy surface. This was set up by computing the reaction coordinate in the forward direction only as it is symmetrical and calculating the force constants once. Also 50 points were considered along the IRC.

An IRC calculation for the optimised chair transition structure gave 17 intermediate geomtries. Since the minimum had not been reached yet as indicated by the RMS gradient along the IRC not equalling to zero, the last point on the IRC was ran for a normal optimisation. This resulted in the a minimum structure corresponding to the ''gauche2'' conformer with an energy of -231.691199702 Hartrees.

Re-running an IRC by specifying a larger number of points until a minimum was reached was not an option since the inital IRC calculated 17 intermediate geomtroes which is well within the number of points that was specified i.e 50. Therefore, in order to confirm a local minimum had been reached an IRC calculation was re-ran but with the force constants were computed at every step. As a result, 47 intermediate geometries were located with an IRC pathway reaching an asymptote and thus RMS gradient equalling to zero, which suggested that the local minimum had been reached. Nevertheless, the last point on IRC was ran for a normal optimisation and the local minimum was confirmed as ''gauche2''with an energy of -231.69166700 Hartrees. Thus, the IRC method determined the Cope rearrangement of the ''anti2'' conformation of 1, 5-hexadiene to give the ''gauche2'' conformer.

{| border="1" cellpadding="5"
|- align="center"
| width="200" | '''Property'''
| width="150" | '''Endo TS'''
| width="100" | '''Exo TS'''
|- align="center"
| ''Structure from side''
|
[[Image:chair_fi_ircgraph1.jpg|400px ]]
|
[[Image:chair_fiii_ircgraph1.jpg|400px ]]
|- align="center"
| ''RMS gradient along IRC''
|
[[Image:chair_fi_ircgraph2.jpg|400px ]]
|
[[Image:chair_fiii_ircgraph2.jpg|400px ]]
|- align="center"
| ''Structure''
|
[[Image:chair_fi_opt.gif|250px ]]
|
[[Image:chair_fiii_opt.gif|250px ]]
|- align="center"
| ''Energy/Hartrees''|| -231.69166702 || -23.69166700
|}

====Calculation Activation Energies====

Re-optimisations of the chair and boat transition structures were performed using the B3LYP/6-31G* level of theory followed by frequency calculations to confirm the optimisations were successful, and then compared with the HF/3-21G method. Additionally, the activation energies were also calculated for the reaction via both transition structures. The results are tabulated below;

{| border="1" cellpadding="5"
|- align="center"
! colspan="1" | '''Method'''
! colspan="3" | '''HF/3-21G'''
! colspan="3" | '''B3LYP/6-31G*'''
|- align="center"
|width="150pt" |
|width="200pt" | '''Electonic energy/Hartrees'''
|width="200pt" | '''Sum of electronic and zero point energies at OK/Hartrees'''
|width="200pt" | '''Sum of electronic and thermal energies energies at 298.15K/Hartrees'''
|width="200pt" | '''Electonic energy/Hartrees'''
|width="200pt" | '''Sum of electronic and zero point energies at OK/Hartrees'''
|width="200pt" | '''Sum of electronic and thermal energies energies at 298.15K/Hartrees'''
|- align="center"
| ''Chair TS'' || -231.619322 || -231.466697 || -231.461339 || -234.556983|| -234.414931 || -234.409010
|- align="center"
| ''Boat TS'' || -231.602802 || -231.450928 || -231.445298 || -234.543093 || -234.402340 || -234.396006
|- align="center"
| Reactant (anti2) || -231.692535 ||-231.539539 || -231.532565 || -234.611703 || -234.469212 || -234.461856
|}

Summary of activation energies/kcalmol-1

{| border="1" cellpadding="5"
|- align="center"
! colspan="1" | '''Method'''
! colspan="2" | '''HF/3-21G'''
! colspan="2" | '''B3LYP/6-31G*'''
|- align="center"
|width="150pt" |
|width="200pt" | '''at OK'''
|width="200pt" | '''at 298.15K'''
|width="200pt" | '''at 0K'''
|width="200pt" | '''at 298.15K'''
|- align="center"
| ''ΔE (Chair TS)'' || 45.70 ||44.69 || 34.06 || 33.16
|- align="center"
| ''ΔE (Boat TS)'' || 55.60 || 54.76 || 41.96|| 41.32
|}

At both levels of theory, the geomtries are reasonably similar, but energy differences between the reactant and the transition states are markedly different. By using B3LYP/6-31G* which is higher and more accurate level of theory, the energies of both transition states have decreased and the activation energies for both transition structures are in much better agreement with the experimental values of 33.5 ± 0.5 and 44.7 ± 2.0 kcalmol-1. For both levels of theory, the results are also consistent with the '''Appendix 2'''.

Results show that the chair transition state is more stable than that of the boat with a lower activation energy of 33.16 kcalmol-1 at compared to 41.32kcalmol-1 at room temperature. Therefore, it can be concluded that the reaction mechanism of the Cope rearrangement prefers to proceed via the chair than the boat transition state.

Rep:Mod3:Yuko.Isayama3001Ex2

2009-11-13T02:06:06Z

Yi107: /* The Diels Alder Cycloaddition */

=The Diels Alder Cycloaddition=

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and ''cis''-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations both the AM1 semi-empirical molecular orbital and B3LYP/6-31G* methods were used.

==Ethylene and ''Cis''-Butadiene==

{| align="center"
|- align="center"
|
|[[Image:DA_ethylenebutadiene.gif|thumb|300px|left|Diels-Alder reaction between ethylene and ''cis''-butadiene ]]
|}

===Optimisation and Molecular Orbitals of ''Cis''-Butadiene and Ethylene===

Optimisation of ''cis''-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1. The B3LYP/6-31G* level of theory calculated the energies as.

{| align="center"
|- align="center"
|
|[[Image:Butadiene_opt.gif|thumb|133px |''Cis''-butadiene ]]
|[[Image:Ethylene_opt.gif|thumb|158px | Ethylene ]]
|}

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown) based on the AM1 semi-emprical method;

{| align="center"
|- align="center"
|
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]
|}

{| border="1" cellpadding="5"
|- align="center"
| width="100" | '''Reactant'''
| width="150" | '''Molecular Orbital'''
! colspan="2" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
! rowspan=2 | '''''cis''-butadiene''' ||''HOMO''
|
[[Image:Butadiene_b_HOMO2.gif|120px]]
|
[[Image:Butadiene_b_HOMO.gif|150px]]
| -0.34381
| -215.74387
| Anti-symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Butadiene_b_LUMO2.gif|120px]]
|
[[Image:Butadiene_b_LUMO.gif|150px]]
| 0.01707
| 10.67393
| Symmetric
|- align="center"
! rowspan=2 | '''ethylene''' ||''HOMO''
|
[[Image:ethylene_b_HOMO2.gif|100px]]
|
[[Image:ethylene_b_HOMO.gif|150px]]
| -0.38775
| -243.15415
| Symmetric
|- align="center"
|'''''LUMO'''''
|
[[Image:Ethylene_b_LUMO2.gif|100px]]
|
[[Image:ethylene_b_LUMO.gif|150px]]
| 0.05283
| 33.12916
| Anti-symmetric
|}

===Optmisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_b_guess.gif|left|thumb|225px|Geometry of the guessed transition structure]]
The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.
|}

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt_ifreq.gif|left|thumb|225px|Vibration at -956.57cm-1 corresponding to the reaction path at the transition state]]
|[[Image:TS_b_opt_freq.gif|left|thumb|225px|Vibration at cm-1 corresponding to the 'rocking' motion of ethylene]]
|}

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

{| align="center"
|- align="center"
|
|[[Image:TS_b_opt.gif|thumb|300px]]
|}

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the terminal carbon atoms of each reactant are within their van der Waals radii and approaching each other for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''HOMO''
|
[[Image:TS_b_opt_HOMO2.gif|150px]]
| -0.32396
| -203.28782
| Anti-symmetric
|- align="center"
| ''LUMO''
|
[[Image:TS_b_opt_LUMO2.gif|150px]]
| 0.02319
| 14.55193
| Symmetric
|}

By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of ''cis''-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by ''Conservation of Orbital Symmetry''3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the ''cis''-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(-253.83kJ-1), thereby implying low kinetic stability.

===References===
# Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
# Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{DOI|10.1021/j100785a001}}
# Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 {{DOI|10.1021/ar50001a003}}

==Cyclohexa-1,3-diene and Maleic Anhydride==

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the ''endo''-isomer or the ''exo''-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the ''endo''-adduct. The reaction is said to be kinetically controlled which suggests that the ''exo''-transition state is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_reaction.gif|thumb|650px|left|Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1 ]]
|}

===Optimisation and Molecular Orbitals of the Transition Structure===

{|
|[[Image:TS_c_guess.gif|left|thumb|225px|Geometry of the initial guess transition structure]]
|[[Image:TS_c_guess.gif|left|thumb|225px|Geometry of guessed struture of ''endo''-transition state ]]
The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the ''endo''-/''exo''- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.
|}

Optimisation was successful and gave the ''exo''-transition structure. In order to locate the ''endo''-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the ''endo''-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

{| border="1" cellpadding="5"
|- align="center"
| width="200" |
| width="150" | '''Exo TS'''
| width="150" | '''Endo TS'''
|- align="center"
| ''Orientation of Hs''
|
[[Image:exo_Hs.gif|180px ]]
|
[[Image:endo_Hs.gif|180px ]]
|- align="center"
| ''Structure from side''
|
[[Image:exo_TS2.gif|200px ]]
|
[[Image:endo_TS.gif|200px ]]
|- align="center"
| ''Energy/Hartrees''|| -0.05041981 || -0.05150473
|- align="center"
| ''Energy/kcalmol-1''|| -31.63888 || -32.31968
|- align="center"
| ''Imaginary frequency/cm-1''|| -812.17 || -806.49
|}

One can distungish between the geometries of the structures because in the ''exo''-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In the''Italic text'' endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the ''endo''-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the ''exo''-transition structure corresponds to the product formed under thermodynamic control.

The C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

{| align="center"
|- align="center"
|
|[[Image:Exo_TS3.gif|thumb|350px|Other C-C distances of exo-transiton structure]]
|[[Image:Endo_TS4.gif|thumb|310px|Other C-C distances of endo-transiton structure]]
|}

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the ''exo''- and 2.16Å in the ''endo''-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the ''endo'' supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the ''exo''.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the C atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;
{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecular Orbital'''
! width="150" | '''Molecular Orbital Image'''
| width="200" | '''Energy/Hartrees'''
| width="200" | '''Energy/kcalmol-1'''
| width="200" | '''Symmetry w.r.t the plane'''
|- align="center"
| ''Exo HOMO''
|
[[Image:Exo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Exo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Endo HOMO''
|
[[Image:Endo_HOMO.gif|150px]]
|
|
| Anti-symmetric
|- align="center"
| ''Exo-LUMO''
|
[[Image:Endo_LUMO.gif|150px]]
|
|
| Anti-symmetric
|}

Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for ''endo''-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

{| align="center"
|- align="center"
|
|[[Image:EndoExo_orbitals.gif|550px]]
|}

==References===

# Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
# Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

==Conclusion==

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions Furthermore, by studying the molecular orbitals of the transition structures we can apply the ''Conservation of Orbital Symmetry'' to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.