File:DADA ALK 6-noeigen.cml

2010-11-12T14:39:44Z

Ef108:

Rep:Mod:enricof11phys

2010-11-12T14:36:44Z

Ef108:

==Module 3 - Phyisical computational chemistry==

This report is divided in two sections: the first one deals with the Cope rearrangement. The second concerns the Diels-Alder reaction.

===Cope rearrangement studies===

This section will look into the optimisation of the reactants and products for the Cope rearrangement and the boat and chair transition state localisation on the C6H10 potential energy surface. These considerations will allow us to determine the preferred reaction mechanism (lowest activation energy).

* '''Reactant optimisation to an energy minimum'''

Several isomers of 1,5-hexadiene exist:

{| class="wikitable" border="1"
|-
! Conformation !! Image !! Optimisation method/basis set!!Energy (hartree)!!Energy (kJ/mol)!!Point group
|-
! Anti2!![[Image:P1_Anti2.jpg|thumb|200px|]]!! HF/3-21G!!-231.69254!!-608,308.81!!Ci
|-
| Anti1||[[Image:P1_Anti1.jpg|thumb|200px|]]|| HF/3-21G||-231.69260||-608,308.97||C2
|-
| Gauche2||[[Image:P1_Gauche2.jpg|thumb|200px|]]|| HF/3-21G||-231.69167||-608,306.53||C2
|-
| Gauche3||[[Image:P1_Gauche3.jpg|thumb|200px|]]|| HF/3-21G||-231.69266||-608,309.13||C1
|-
! Anti2 !![[Image:P1_Anti2.jpg|thumb|200px|]]!! B3LYP/6-31G(d)!!-234.61172!!-615,973.11||Ci
|}

As can be noticed above, the geometry of Anti 2 does not change much, regardless of the level of theory adopted. However, the energy becomes lower whan we use a more precise basis set, as the structure gets stabilised even further.

* Frequency analysis allows us to determine that the structure of Anti 2 obtained is, in fact, a minimum. Since the low frequencies in the log file are more or less between +- 10 cm-1, we can conclude that the optimisation was successful (but not great).

From the log file:

Low frequencies --- -7.5940 0.0001 0.0005 0.0008 8.5899 13.2081

Low frequencies --- 74.7550 82.4948 121.8440

[[Image:IR_anti_DFT_freq.gif|thumb|580px|center|IR spectrum of Anti 2]]

There are no negative (imaginary) frequencies. This confirms that the structure is not a maximum (a T.S.).<ref>Higgins, ''J. Chem. Educ.'',''' 1995''', ''72'' (8),703. DOI: 10.1021/ed072p703</ref>

* Thermochemical analysis of Anti 2 revels that:

The sum of its electronic PE at 0K and its zero-point energy is -234.469182 hartree = - 615598.88 kJ/mol

The sum of its electronic PE at 298.15K, 1atm and thermal energies (vib, rot, trans contributions) is -234.461844 hartree = - 615579.62 kJ/mol

The sum of its electronic and thermal enthalpies (includes an RT correction) is -234.460900 hartree = - 615577.14 kJ/mol

The sum of its electronic and thermal free energies (includes entropy) is -234.500730 hartree = - 615681.71 kJ/mol

In fact, the first value Ee- + ZPE = -234.46918 au; that minus the ZPE 0.14254 au (from the log file) gives Ee-= -234.61172 au. This value matches the one previously obtained (see Anti 2, B3LYP/6-31G(d) method in the table at the start of this section).

* "Transition state optimisation"

The Optimisation of the chair TS of the Cope rearrangement was also done exploiting the HF/3-21G basis set and, while the first attempt was done using a force constant matrix, the second included redundant coordinates editing (first restricting the distance of the 2 fragments, then allowing them to reorientate). The two methods gave similar final structures. However, both optimisations did not run smoothly from the start. Firstly, an error message suggested the use of a single processor ratehr than 4 (as the jobs were being run on the laptop). Then, The initial structure of the two starting allyl fragments had to be modified to fit symmetry requirements. Only at this point the jobs run smoothly.

{| class="wikitable" border="1"
|+ Chair structure optimisation details
! !!Force constant!!Redundant
|-
| separation between fragments|| 2.02||2.02
|-
| bond breaking bond lengths|| 1.39||1.39
|-
| optimised fragments image||[[Image:1ikea_norm.jpg|thumb|widthpx|left]]||[[Image:2ikea_redundant.jpg|thumb|widthpx|left]]
|-
| Energy (au)|| -231.61932238||-231.61932198
|-
| Energy (kJ/mol)||-608116.57723 ||-608116.57618
|-
| Imaginary frequencies (cm-1)||818 (corresponds to Cope rearrangement)||818 (corresponds to Cope rearrangement)
|}

The boat transition structure, instead, was found by using QST2. The reactant and product - from which Gaussian interpolated the TS structure - were drawn in such a way that the structure resembled that of the boat TS in H.Jiao and P.v Ragué Schleyder's paper. <ref>H. Jiao, P. von Ragué Schleyer, ''Angewandte Chemie'', '''1995''', ''34'', 3, pp. 335, fig. 1.3b. DOI: 10.1002/anie.199503341</ref>. Also, the atom numbering of the reactant and product was matched as to allow Gaussian to recognise the Cope rearrangement, as shown below (all measurements are in Å, the central C-C-C-C dihedral angle is 0°).

{|class="wikitable" border="1"
|-
|[[Image:Ariel_QST_geo_in.jpg|thumb|600px|left]]
|}

Furthermore, I added an Opt=maxstep5 command to allow the TS not to be "missed" in the interpolation. The resulting output displays a single imaginary frequency at 836 cm-1, corresponding to the Cope rearrangement. Hence, the optimised TS structure is:

{|class="wikitable" border="1"
|+
|-
|[[Image:Ariel_QST_geo_out.jpg|thumb|400px|left]]
|}

Now, what will the optimised transition structures lead to?

* '''Intrinsic reaction coordinate''' (IRC) '''calculations'''

The IRC calculation was set up in the forward direction of the reaction coordinate (since it is symmetric). Force constants were calcualted at the beginning of the job. 50 points along the IRC were considered.

{|class="wikitable" border="1"
|-
|[[Image:Ikea_IRC_graphs.gif|thumb|400px|left|Chair transition structure energy profile]]||[[Image:Ariel_IRC_graphs.gif|thumb|400px|left|Boat transition structure energy profile]]
|}

The structures obtained were minimised as usual, resulting in the following local minima of energy:

{|class="wikitable" border="3"
!CHAIR conformation local minimum!!BOAT conformation local minimum
|-
|<jmol> <jmolApplet> <uploadedFileContents>Ikea_IRC_mol.mol</uploadedFileContents> </jmolApplet> </jmol>||<jmol> <jmolApplet> <uploadedFileContents>Ariel_IRC_mol.mol</uploadedFileContents> </jmolApplet> </jmol>
|}

* '''Activation energy comparison''' (all in '''kJ/mol''')

{|class="wikitable" border="3"
!Level of theory||DFT/B3LYP/6-31G*||DFT/B3LYP/6-31G|| ||||HF/3-21G||HF/3-21G|| || ||
|-
| ||React.||T.S.||Energy difference = Activation energy|| ||React.||T.S.||Energy difference = Activation energy|| ||''Experiemntal values at 0K''
|-
|BOAT||-615.973||-615.793||180||||-608.309||-608.073||236|| ||187+-8.4
|-
|CHAIR||-615.973||-615.834||139|| ||-608.309||-608.117||192|| ||140+-2.1
|}

Hence, the experimental values are very close to teh computationally predicted ones using DFT/B3LYP/g-31G level of tgeory. The HF/3-21G theory is not precise enough to accurately predict the activation energies. However, it is still useful to have an idea of thir magnitude.

===Diels-Alder reaction===

This section will look into the transition structures of the Diels-Alder reaction to examine the nature of the reaction path. The discussion will then follow up on the regioselectivity of this reaction (endo/exo)

* The optimised geometry of cis-butadiene (B3LYP/3-21G basis set) is:

{| class="wikitable" border="1"
|-
| [[Image:BUH_optimised.jpg|thumb|200px|]]|| Notice how the optimised structure has a dihedral angle of 0° between the two extreme carbons.
|-
| HOMO [[Image:ef108buta_HOMO.jpg|thumb|200px|]]||LUMO [[Image:ef108buta_LUMO.jpg|thumb|200px|left]]||The HOMO and the LUMO of the molecule are shown on the left. One can notice how the HOMO is asymmetric with respect to the vertical plane, while the LUMO is symmetrical.
|}

Interestingly, the most external carbons have in the LUMO identical symmetry to the HOMO of ethene, suggesting a wonderful potential overlap.

Also, the alkenes have antibonding character in the LUMO. This orbital is empty, so that explains why they are higher order bonds.

* [[Image:DADA_CsSymmetry.jpg|thumb|150px|right|Cs symmetry - notice plane of symmetry]] The optimised geometry of the prototype Diels Alder reaction is below. This structure optimisation required the initial guess to be symmetrised. Hence, first the alkene was fitted to D2h symmetry. Separately, the diene was allowed to relax in a C2v symmetry conformation. The two structures were then pasted together and modified to fit Cs symmetry requirements. Interfragment distance was set to 2.2Å.

Furthermore, an "Opt=noEigen" command was added to allow the job to avoid eigenvalue checks. Finally, the optimised (output) transition state structure was again Cs symmetric and had the expected imaginary frequency at 818cm-1 and only 1 negative eigenvalue.

Moreover, the imaginary frequency, which can be seen on the right, corresponds to the movements of the bonds required to transform the reactants buatadiene+ethene in the Diels-Alder cyclic product. The bonds are forming synchronously. The lowest positive frequency of 166cm-1 represents a torsion of the dienophile with respect to the butadiene, leading, in such a way, to an asynchronous motion of the partly formed σ C-C bonds.

{| class="wikitable" border="1"
|+ Vibration motions
|-
|[[Image:DADA_alk_movie.gif|thumb|widthpx|right|Imaginary vibration motion]]||[[Image:DADA_166.gif|thumb|widthpx|right|166 cm-1 vibration]]
|}

{| class="wikitable" border="1"
|+ Optimised Diels-Alder transition state and frontier orbital representations
|-
|<jmol> <jmolAppletButton> <uploadedFileContents>DADA_ALK_6noeigen.mol</uploadedFileContents> <text>Optimised D-A Transition state</text> </jmolAppletButton> </jmol>
|-
|[[Image:DADA_A6.jpg|thumb|280px|]]||HOMO [[Image:DADA_HOMO.jpg|thumb|widthpx|]]||LUMO [[Image:DADA_LUMO.jpg|thumb|widthpx|]]
|}

The HOMO (and the LUMO) of this species are now symmetric with respect to the vertical central plane (differently to the butadiene above).

This fact testifies that the central butadiene bond has become stronger (higher order), while in butadiene, above, the HOMO had antibonding character for the central bond, and bonding character for the side olefinic bonds.

A closer look at the Transition state's MO allows us to realise that this orbital is the sum of the interaction between the ethene's HOMO (bonding and symmetric) and butadiene's LUMO (antibonding and symmetric). Ethene is acting as the electron rich substituent that donates to the LUMO of the electrophilic species. This interaction is allowed as the orbitals have the same character. Practically, though, this Diels-Alder reaction will not happen as readily as, say, that of butadiene with maleic anhydride, the reason being that the more the dienophile is electron rich, the faster the pericyclic rearrangement takes place.

Further considerations can be made regarding the C-C links. The partly formed σ C-C bond lengths are of 2.21Å (vs. lit. 1.526Å of ethane<ref>Lide, D.R., '''A survey on C-C bond lengths''', ''Tetrahedron'', '''1962''', ''17'', 125</ref>. Also, ''sp3'' C-''sp2'' C lit. 1.507Å; ''sp2'' C-''sp2'' C lit. 1.455Å.<ref>Allen, Kennard ''et al.'', ''J. Chem. Soc. Perkin Trans. II'', '''1987''', S1-S19</ref>

Moreover, the VdW radius of C is 1.70Å <ref>A. Bondi , ''J.Phys.Chem.'','''1964''', ''68'', 441-452</ref>. Hence, the partial σ C-C bond present in the transition state is actually longer than a normal C-C bond, but still shorter than the sum of the carbons' Van der Waals radii (3.40Å). The T.S. is, in fact, a transition from a non-bonding and non-interacting situation to a bonding one: in the transition state we can see how the carbons have entered each other's zone of influence.

* The optimised structures of the exo and endo products are, respectively:

{| class="wikitable" border="1"
|-
| <jmol> <jmolApplet> <uploadedFileContents>EXIT_optimised.mol</uploadedFileContents> </jmolApplet> </jmol> || <jmol> <jmolApplet> <uploadedFileContents>THEEND_optimised.mol</uploadedFileContents> </jmolApplet> </jmol>
|}

In order to obtain such optimised structures, it was necessary to modify the input geometries so as to fit symmetry requirements The EXO TS guess was fitted to Cs symmetry and optimised using the force constant method. The resulting structure had a single imaginary frequency at 648com-1, corresponding to the DA reaction.

The ENDO t.s. conformer input structure was built by fitting the diene to Cs symmetry and allowing it to have a similar shape to that of the ENDO product of reaction. Separately, the anhydride was drawn to fit D2h symmetry. The maleic anhydide ring was then added, avoiding steric repulsions between the hydrogens, but still keeping the two species 2.2Å close. Finally, the molecule was fitted to Cs symmetry. The output had a single imaginary frequency at 643cm-1, corresponding to the Diels-Alder reaction.

The resulting energies are:

EXO T.S.: -605.60359 au = -1,590,012 kJ/mol

ENDO T.S.: -605.61037 au = -1,590,030 kJ/mol

Information about their geometry (all measures are in Å. The molecule has σv symmetry)

[[Image:THEENDTHEEXIT_geo.jpg|thumb|530px|left]]
{| class="wikitable" border="3"
|+ MOs
|-
| ENDO HOMO [[Image:THEEND_HOMO.jpg|thumb|widthpx|]] The image above shows the overlap between the diene and the dienophile|| ||EXO HOMO [[Image:EXIT_HOMO.jpg|thumb|widthpx|]]||EXO HOMO [[Image:EXIT_HOMOview.jpg|thumb|widthpx|left ]]
|-
| [[Image:THEEND_HOMO_orbconformholder.jpg|thumb|widthpx| ]] The image above displays the anti-bonding character of the interaction between the carbonyl oxygen and the ''sp2'' C - ''sp2'' C of the diene|| ||[[Image:EXIT_HOMO_orbconformholder.jpg|thumb|widthpx|]]||The upper images show the bonding overlap of the diene and the dienophile. The image on the left shows the slight bonding interaction between the oxygens of the carbonyls and the ''sp3'' C - ''sp2'' C of the diene.
|}

The MO images allow us to follow up with a few considerations. Firstly, in both the ENDO and EXO conformations there is a bonding overlap of the diene to the dienophile, in the locations where we expect the formation of 2 new σ bonds. Hence, the reaction "is working" as the species are starting to mix their electronic density.

Secondly, we notice that in the endo and the exo conformers there is a different overlap fashion of the carbonyls to the secondary orbitals of the diene that sits "opposite" to the carbonyls. In the endo structure, this interaction is antibonding; in the exo one, it is bonding. This suggests that the exo structure is more favoured, having a more constructive secondary orbital effect, a more stabilised conformation, a secondary driving force that pushes it towards reactivity. However, the structures' geometric data indicates that the endo's (O=C)-O-(C=O) to ''sp2'' C - ''sp2'' C distance is shorter by a factor of 0.09Å. The (O=C) to ''sp2'' C - ''sp2'' C distance, instead, is equal, suggesting that only the anhydride's central oxygen is bent "outwards" in the exo structure as opposed tot eh endo structure. Moreover, the anhydride sits closer to the diene in the ENDO conformer.

All this having been said, the energetic data indicates that the endo conformation is more stable by 18kJ/mol. Hence, despite the secondary orbital effect stabilisation in EXO, the endo structure is still the most stable conformer of the two. Most probably, the exo structure has an unfavourable strain due to the way it has to approach the diene: the Diels-Alder reaction works best when the dienophile approaches the diene from below or above. However, the exo conformer cannot allow access from above, due to the bridgehead's sterical interference. So the endo conformer is overall the winning isomer.

* Some effects have not been considered in these calculations. For instance, the electronic favourability of the interaction of the maleic anhydride with the diene (due to the electronic richness of the dienophile)<ref>D. Craig's lecture course "organic Synthesis II", Lecture 6, '''2010''', Imperial College London</ref>:

[[Image:mal_anh_effect.jpg|thumb|400px|left]]

==References==
<references />

File:Ariel IRC mol.mol

2010-11-12T14:35:39Z

Ef108:

2010-11-11T16:57:44Z

Ef108: /* Diels-Alder reaction */

==Module 3 - Phyisical computational chemistry==

===Cope rearrangement studies===

First, the reactant 1,5-hexadiene was analysed. Several isomers were optimised:

{| class="wikitable" border="1"
|-
! Conformation !! Optimisation method/basis set!!Energy (hartree)!!Energy (kJ/mol)!!Point group
|-
! Anti2 !! HF/3-21G!!-231.69254!!-608,308.81!!Ci
|-
| Anti1|| HF/3-21G||-231.69260||-608,308.97||C2
|-
| Gauche2|| HF/3-21G||-231.69167||-608,306.53||C2
|-
| Gauche3|| HF/3-21G||-231.69266||-608,309.13||C1
|-
! Anti2 !! B3LYP/6-31G(d)!!-234.61172!!-615,973.11||Ci
|}

The IR spectra of Anti2 is
[[Image:IR_anti_DFT_freq.gif|thumb|650px|left ]]

The sum of its electronic PE at 0K and its zero-point energy: -234.469182 hartree = - 615598.88 kJ/mol

The sum of its electronic PE at 298.15K, 1atm and thermal energies (vib, rot, trans contributions): -234.461844 hartree = - 615579.62 kJ/mol

The sum of its electronic and thermal enthalpies (includes an RT correction): -234.460900 hartree = - 615577.14 kJ/mol

The sum of its electronic and thermal free energies (includes entropy): -234.500730 hartree = - 615681.71 kJ/mol

The optimisation was successful but not great, as the low frequencies (from the log output file) are more or less between +-10cm-1. However, there is not much gap between the low and higher frequencies.

Low frequencies --- -7.5940 0.0001 0.0005 0.0008 8.5899 13.2081
Low frequencies --- 74.7550 82.4948 121.8440

The Optimisation of the chair TS of the Cope rearrangement was done always with HF/3-21G basis set and, while the first attempt was done using a force constant matrix, the second included redundant coordinates editing (first restricting the distance of the 2 fragments, then allowing them to reorientate). The two methods gave similar final structures.

{| class="wikitable" border="1"
|+ Chair structure optimisation details
! !!Force constant!!Redundant
|-
| separation between fragments|| 2.02||2.02
|-
| bond breaking bond lengths|| 1.39||1.39
|-
| optimised fragments image||[[Image:1ikea_norm.jpg|thumb|widthpx| ]]||[[Image:2ikea_redundant.jpg|thumb|widthpx| ]]
|-
| Energy (au)|| -231.61932238||-231.61932198
|-
| Energy (kJ/mol)||-608116.57723 ||-608116.57618
|-
| Point group||C1||C1
|}

The QST T.S. optimisation for the boat conformation displays one imaginary frequency, hence confirming the achievement of a true transition state.<ref>Higgins, ''J. Chem. Educ.'',''' 1995''', ''72'' (8),703. DOI: 10.1021/ed072p703</ref>

The structure yielded by the IRC calculation, followed by (i) optimisation of the last point is on the left, while the IRC calculation with force constant calculation at every step is on the right.

<jmol> <jmolApplet> <uploadedFileContents>ikea_IRC2_optsd.mol</uploadedFileContents> </jmolApplet> </jmol><jmol> <jmolApplet> <uploadedFileContents>IRCoutput.mol</uploadedFileContents> </jmolApplet> </jmol>

===Diels-Alder reaction===

* The optimised geometry of cis-butadiene (B3LYP/3-21G basis set) is:

{| class="wikitable" border="1"
|-
| [[Image:BUH_optimised.jpg|thumb|300px|cell ]]|| Notice how the optimised structure has a dihedral angle of 0° between the two extreme carbons.
|-
| HOMO [[Image:ef108buta_HOMO.jpg|thumb|300px|cell ]]||LUMO [[Image:ef108buta_LUMO.jpg|thumb|widthpx|cell]]||The HOMO and the LUMO of the molecule are shown on the left. One can notice how the HOMO is asymeetric with respect to the vertical plane, while the LUMO is symmetrical.
|}

Interestingly, the most external carbons have in the LUMO identical symmetry to the HOMO of ethene, suggesting a wonderful potential overlap.

Also, the alkenes have antibonding character in the LUMO. This orbital is empty, so that explains why they are higher order bonds.

* The optimised geometry of the prototype Diels Alder reaction is below. This structure optimisation required the initial guess to be symmetrised. Hence, first the alkene was fitted to D2h symmetry. Separately, the diene was allowed to relax in a C2v symmetry conformation. [[Image:DADA_CsSymmetry.jpg|thumb|300px|right|Cs symmetry - notice plane of symmetry]]
The two structures were then pasted together and modified to fit Cs symmetry requirements. Interfragment distance was set to 2.2Å.

Furthermore, an "Opt=noEigen" command was added to allow the job to avoid eigenvalue checks. Finally, the optimised (output) transition state structure was again Cs symmetric and had the expected imaginary frequency at 818cm-1 and only 1 negative eigenvalue. [[Image:DADA_alk_movie.gif|thumb|widthpx|right|Imaginary vibration motion]]

Moreover, the imaginary frequency, which can be seen on the right, corresponds to the movements of the bonds required to transform the reactants buatadiene+ethene in the Diels-Alder cyclic product. The bonds are forming synchronously. The lowest positive frequency of 166cm-1 represents a torsion of the dienophile with respect to the butadiene, leading, in such a way, to an asynchronous motion of the partly formed σ C-C bonds. [[Image:DADA_166.gif|thumb|widthpx|right]]

{| class="wikitable" border="1"
|-
|<jmol> <jmolAppletButton> <uploadedFileContents>DADA_ALK_6noeigen.mol</uploadedFileContents> <text>Optimised D-A reactant</text> </jmolAppletButton> </jmol>
|-
|Optimised structure [[Image:DADA_A6.jpg|thumb|widthpx|cell ]]
|-
|HOMO [[Image:DADA_HOMO.jpg|thumb|widthpx|cell ]]
|-
|LUMO [[Image:DADA_LUMO.jpg|thumb|widthpx|cell]]
|}

The HOMO (and the LUMO) of this species are now symmetric with respect to the vertical central plane (differently to the butadiene above).

This fact testifies that the central butadiene bond has become stronger (higher order), while in butadiene, above, the HOMO had antibonding character for the central bond, and bonding character for the side olefinic bonds.

A closer look at the Transition state's MO allows us to realise that this orbital is the sum of the interaction between the ethene's HOMO (bonding and symmetric) and butadiene's LUMO (antibonding and symmetric). Ethene is acting as the electron rich substituent that donates to the LUMO of the electrophilic species. This interaction is allowed as the orbitals have the same character. Practically, though, this Diels-Alder reaction will not happen as readily as, say, that of butadiene with maleic anhydride, the reason being that the more the dienophile is electron rich, the faster the pericyclic rearrangement takes place.

Further considerations can be made regarding the C-C links. The partly formed σ C-C bond lengths are of 2.21Å (vs. lit. 1.526Å of ethane<ref>Lide, D.R., '''A survey on C-C bond lengths''', ''Tetrahedron'', '''1962''', ''17'', 125</ref>. Also, ''sp3'' C-''sp2'' C lit. 1.507Å; ''sp2'' C-''sp2'' C lit. 1.455Å.<ref>Allen, Kennard ''et al.'', ''J. Chem. Soc. Perkin Trans. II'', '''1987''', S1-S19</ref>

Moreover, the VdW radius of C is 1.70Å <ref>A. Bondi , ''J.Phys.Chem.'','''1964''', ''68'', 441-452</ref>. Hence, the partial σ C-C bond present in the transition state is actually longer than a normal C-C bond, but still shorter than the sum of the carbons' Van der Waals radii (3.40Å). The T.S. is, in fact, a transition from a non-bonding and non-interacting situation to a bonding one: in the transition state we can see how the carbons have entered each other's zone of influence.

* The optimised structures of the exo and endo products are, respectively:

{| class="wikitable" border="1"
|-
| <jmol> <jmolApplet> <uploadedFileContents>EXIT_optimised.mol</uploadedFileContents> </jmolApplet> </jmol> || <jmol> <jmolApplet> <uploadedFileContents>THEEND_optimised.mol</uploadedFileContents> </jmolApplet> </jmol>
|}

In order to obtain such optimised structures, it was necessary to modify the input geometries so as to fit symmetry requirements The EXO TS guess was fitted to Cs symmetry and optimised using the force constant method. The resulting structure had a single imaginary frequency at 648com-1, corresponding to the DA reaction.

The ENDO t.s. conformer input structure was built by fitting the diene to Cs symmetry and allowing it to have a similar shape to that of the ENDO product of reaction. Separately, the anhydride was drawn to fit D2h symmetry. The maleic anhydide ring was then added, avoiding steric repulsions between the hydrogens, but still keeping the two species 2.2Å close. Finally, the molecule was fitted to Cs symmetry. The output had a single imaginary frequency at 643cm-1, corresponding to the Diels-Alder reaction.

The resulting energies are:

EXO T.S.: -605.60359 au = -1,590,012 kJ/mol

ENDO T.S.: -605.61037 au = -1,590,030 kJ/mol

Information about their geometry (all measures are in Å. The molecule has σv symmetry)
[[Image:THEENDTHEEXIT_geo.jpg|thumb|530px|left]]
{| class="wikitable" border="1"
|+ MOs
|-
| ENDO HOMO [[Image:THEEND_HOMO.jpg|thumb|widthpx|cell ]] The image above shows the overlap between the diene and the dienophile||EXO HOMO [[Image:EXIT_HOMO.jpg|thumb|widthpx|cell]]||EXO HOMO [[Image:EXIT_HOMOview.jpg|thumb|widthpx| ]]
|-
| [[Image:THEEND_HOMO_orbconformholder.jpg|thumb|widthpx| ]] The image above displays the anti-bonding character of the interaction between the carbonyl oxygen and the ''sp2'' C - ''sp2'' C of the diene|| [[Image:EXIT_HOMO_orbconformholder.jpg|thumb|widthpx|cell]]||The upper images show the bonding overlap of the diene and the dienophile. The image on the left shows the slight bonding interaction between the oxygens of the carbonyls and the ''sp3'' C - ''sp2'' C of the diene.
|}

The MO images allow us to follow up with a few considerations. Firstly, in both the ENDO and EXO conformations there is a bonding overlap of the diene to the dienophile, in the locations where we expect the formation of 2 new σ bonds. Hence, the reaction "is working" as the species are starting to mix their electronic density.

Secondly, we notice that in the endo and the exo conformers there is a different overlap fashion of the carbonyls to the secondary orbitals of the diene that sits "opposite" to the carbonyls. In the endo structure, this interaction is antibonding; in the exo one, it is bonding. This suggests that the exo structure is more favoured, having a more constructive secondary orbital effect, a more stabilised conformation, a secondary driving force that pushes it towards reactivity. However, the structures' geometric data indicates that the endo's (O=C)-O-(C=O) to ''sp2'' C - ''sp2'' C distance is shorter by a factor of 0.09Å. The (O=C) to ''sp2'' C - ''sp2'' C distance, instead, is equal, suggesting that only the anhydride's central oxygen is bent "outwards" in the exo structure as opposed tot eh endo structure. Moreover, the anhydride sits closer to the diene in the ENDO conformer.

All this having been said, the energetic data indicates that the endo conformation is more stable by 18kJ/mol. Hence, despite the secondary orbital effect stabilisation in EXO, the endo structure is still the most stable conformer of the two. Most probably, the exo structure has an unfavourable strain due to the way it has to approach the diene: the Diels-Alder reaction works best when the dienophile approaches the diene from below or above. However, the exo conformer cannot allow access from above, due to the bridgehead's sterical interference. So the endo conformer is overall the winning isomer.

* Some effects have not been considered in these calculations. For instance, the electronic favourability of the interaction of the maleic anhydride with the diene (due to the electronic richness of the dienophile)<ref>D. Craig's lecture course "organic Synthesis II", Lecture 6, '''2010''', Imperial College London</ref>:

[[Image:mal_anh_effect.jpg|thumb|400px|left]]

==References==
<references />

File:Mal anh effect.jpg

2010-11-11T16:56:23Z

Ef108:

Rep:Mod:enricof11phys

2010-11-11T16:51:46Z

Ef108: /* Module 3 - Phyisical computational chemistry */

==Module 3 - Phyisical computational chemistry==

===Cope rearrangement studies===

First, the reactant 1,5-hexadiene was analysed. Several isomers were optimised:

{| class="wikitable" border="1"
|-
! Conformation !! Optimisation method/basis set!!Energy (hartree)!!Energy (kJ/mol)!!Point group
|-
! Anti2 !! HF/3-21G!!-231.69254!!-608,308.81!!Ci
|-
| Anti1|| HF/3-21G||-231.69260||-608,308.97||C2
|-
| Gauche2|| HF/3-21G||-231.69167||-608,306.53||C2
|-
| Gauche3|| HF/3-21G||-231.69266||-608,309.13||C1
|-
! Anti2 !! B3LYP/6-31G(d)!!-234.61172!!-615,973.11||Ci
|}

The IR spectra of Anti2 is
[[Image:IR_anti_DFT_freq.gif|thumb|650px|left ]]

The sum of its electronic PE at 0K and its zero-point energy: -234.469182 hartree = - 615598.88 kJ/mol

The sum of its electronic PE at 298.15K, 1atm and thermal energies (vib, rot, trans contributions): -234.461844 hartree = - 615579.62 kJ/mol

The sum of its electronic and thermal enthalpies (includes an RT correction): -234.460900 hartree = - 615577.14 kJ/mol

The sum of its electronic and thermal free energies (includes entropy): -234.500730 hartree = - 615681.71 kJ/mol

The optimisation was successful but not great, as the low frequencies (from the log output file) are more or less between +-10cm-1. However, there is not much gap between the low and higher frequencies.

Low frequencies --- -7.5940 0.0001 0.0005 0.0008 8.5899 13.2081
Low frequencies --- 74.7550 82.4948 121.8440

The Optimisation of the chair TS of the Cope rearrangement was done always with HF/3-21G basis set and, while the first attempt was done using a force constant matrix, the second included redundant coordinates editing (first restricting the distance of the 2 fragments, then allowing them to reorientate). The two methods gave similar final structures.

{| class="wikitable" border="1"
|+ Chair structure optimisation details
! !!Force constant!!Redundant
|-
| separation between fragments|| 2.02||2.02
|-
| bond breaking bond lengths|| 1.39||1.39
|-
| optimised fragments image||[[Image:1ikea_norm.jpg|thumb|widthpx| ]]||[[Image:2ikea_redundant.jpg|thumb|widthpx| ]]
|-
| Energy (au)|| -231.61932238||-231.61932198
|-
| Energy (kJ/mol)||-608116.57723 ||-608116.57618
|-
| Point group||C1||C1
|}

The QST T.S. optimisation for the boat conformation displays one imaginary frequency, hence confirming the achievement of a true transition state.<ref>Higgins, ''J. Chem. Educ.'',''' 1995''', ''72'' (8),703. DOI: 10.1021/ed072p703</ref>

The structure yielded by the IRC calculation, followed by (i) optimisation of the last point is on the left, while the IRC calculation with force constant calculation at every step is on the right.

<jmol> <jmolApplet> <uploadedFileContents>ikea_IRC2_optsd.mol</uploadedFileContents> </jmolApplet> </jmol><jmol> <jmolApplet> <uploadedFileContents>IRCoutput.mol</uploadedFileContents> </jmolApplet> </jmol>

===Diels-Alder reaction===

* The optimised geometry of cis-butadiene (B3LYP/3-21G basis set) is:

{| class="wikitable" border="1"
|-
| [[Image:BUH_optimised.jpg|thumb|300px|cell ]]|| Notice how the optimised structure has a dihedral angle of 0° between the two extreme carbons.
|-
| HOMO [[Image:ef108buta_HOMO.jpg|thumb|300px|cell ]]||LUMO [[Image:ef108buta_LUMO.jpg|thumb|widthpx|cell]]||The HOMO and the LUMO of the molecule are shown on the left. One can notice how the HOMO is asymeetric with respect to the vertical plane, while the LUMO is symmetrical.
|}

Interestingly, the most external carbons have in the LUMO identical symmetry to the HOMO of ethene, suggesting a wonderful potential overlap.

Also, the alkenes have antibonding character in the LUMO. This orbital is empty, so that explains why they are higher order bonds.

* The optimised geometry of the prototype Diels Alder reaction is below. This structure optimisation required the initial guess to be symmetrised. Hence, first the alkene was fitted to D2h symmetry. Separately, the diene was allowed to relax in a C2v symmetry conformation. [[Image:DADA_CsSymmetry.jpg|thumb|300px|right|Cs symmetry - notice plane of symmetry]]
The two structures were then pasted together and modified to fit Cs symmetry requirements. Interfragment distance was set to 2.2Å.

Furthermore, an "Opt=noEigen" command was added to allow the job to avoid eigenvalue checks. Finally, the optimised (output) transition state structure was again Cs symmetric and had the expected imaginary frequency at 818cm-1 and only 1 negative eigenvalue. [[Image:DADA_alk_movie.gif|thumb|widthpx|right|Imaginary vibration motion]]

Moreover, the imaginary frequency, which can be seen on the right, corresponds to the movements of the bonds required to transform the reactants buatadiene+ethene in the Diels-Alder cyclic product. The bonds are forming synchronously. The lowest positive frequency of 166cm-1 represents a torsion of the dienophile with respect to the butadiene, leading, in such a way, to an asynchronous motion of the partly formed σ C-C bonds. [[Image:DADA_166.gif|thumb|widthpx|right]]

{| class="wikitable" border="1"
|-
|<jmol> <jmolAppletButton> <uploadedFileContents>DADA_ALK_6noeigen.mol</uploadedFileContents> <text>Optimised D-A reactant</text> </jmolAppletButton> </jmol>
|-
|Optimised structure [[Image:DADA_A6.jpg|thumb|widthpx|cell ]]
|-
|HOMO [[Image:DADA_HOMO.jpg|thumb|widthpx|cell ]]
|-
|LUMO [[Image:DADA_LUMO.jpg|thumb|widthpx|cell]]
|}

The HOMO (and the LUMO) of this species are now symmetric with respect to the vertical central plane (differently to the butadiene above).

This fact testifies that the central butadiene bond has become stronger (higher order), while in butadiene, above, the HOMO had antibonding character for the central bond, and bonding character for the side olefinic bonds.

A closer look at the Transition state's MO allows us to realise that this orbital is the sum of the interaction between the ethene's HOMO (bonding and symmetric) and butadiene's LUMO (antibonding and symmetric). Ethene is acting as the electron rich substituent that donates to the LUMO of the electrophilic species. This interaction is allowed as the orbitals have the same character. Practically, though, this Diels-Alder reaction will not happen as readily as, say, that of butadiene with maleic anhydride, the reason being that the more the dienophile is electron rich, the faster the pericyclic rearrangement takes place.

Further considerations can be made regarding the C-C links. The partly formed σ C-C bond lengths are of 2.21Å (vs. lit. 1.526Å of ethane<ref>Lide, D.R., '''A survey on C-C bond lengths''', ''Tetrahedron'', '''1962''', ''17'', 125</ref>. Also, ''sp3'' C-''sp2'' C lit. 1.507Å; ''sp2'' C-''sp2'' C lit. 1.455Å.<ref>Allen, Kennard ''et al.'', ''J. Chem. Soc. Perkin Trans. II'', '''1987''', S1-S19</ref>

Moreover, the VdW radius of C is 1.70Å <ref>A. Bondi , ''J.Phys.Chem.'','''1964''', ''68'', 441-452</ref>. Hence, the partial σ C-C bond present in the transition state is actually longer than a normal C-C bond, but still shorter than the sum of the carbons' Van der Waals radii (3.40Å). The T.S. is, in fact, a transition from a non-bonding and non-interacting situation to a bonding one: in the transition state we can see how the carbons have entered each other's zone of influence.

* The optimised structures of the exo and endo products are:

{| class="wikitable" border="1"
|-
| <jmol> <jmolApplet> <uploadedFileContents>EXIT_optimised.mol</uploadedFileContents> </jmolApplet> </jmol> || <jmol> <jmolApplet> <uploadedFileContents>THEEND_optimised.mol</uploadedFileContents> </jmolApplet> </jmol>
|}

In order to obtain such optimised structures, it was necessary to modify the input geometries so as to fit symmetry requirements The EXO TS guess was fitted to Cs symmetry and optimised using the force constant method. The resulting structure had a single imaginary frequency at 648com-1, corresponding to the DA reaction.

The ENDO t.s. conformer input structure was built by fitting the diene to Cs symmetry and allowing it to have a similar shape to that of the ENDO product of reaction. Separately, the anhydride was drawn to fit D2h symmetry. The maleic anhydide ring was then added, avoiding steric repulsions between the hydrogens, but still keeping the two species 2.2Å close. Finally, the molecule was fitted to Cs symmetry. The output had a single imaginary frequency at 643cm-1, corresponding to the Diels-Alder reaction.

The resulting energies are:

EXO T.S.: -605.60359 au = -1,590,012 kJ/mol

ENDO T.S.: -605.61037 au = -1,590,030 kJ/mol

Information about their geometry (all measures are in Å. The molecule has σv symmetry)
[[Image:THEENDTHEEXIT_geo.jpg|thumb|530px|left]]
{| class="wikitable" border="1"
|+ MOs
|-
| ENDO HOMO [[Image:THEEND_HOMO.jpg|thumb|widthpx|cell ]] The image above shows the overlap between the diene and the dienophile||EXO HOMO [[Image:EXIT_HOMO.jpg|thumb|widthpx|cell]]||EXO HOMO [[Image:EXIT_HOMOview.jpg|thumb|widthpx| ]]
|-
| [[Image:THEEND_HOMO_orbconformholder.jpg|thumb|widthpx| ]] The image above displays the anti-bonding character of the interaction between the carbonyl oxygen and the ''sp2'' C - ''sp2'' C of the diene|| [[Image:EXIT_HOMO_orbconformholder.jpg|thumb|widthpx|cell]]||The upper images show the bonding overlap of the diene and the dienophile. The image on the left shows the slight bonding interaction between the oxygens of the carbonyls and the ''sp3'' C - ''sp2'' C of the diene.
|}

The MO images allow us to follow up with a few considerations. Firstly, in both the ENDO and EXO conformations there is a bonding overlap of the diene to the dienophile, in the locations where we expect the formation of 2 new σ bonds. Hence, the reaction "is working" as the species are starting to mix their electronic density.

Secondly, we notice that in the endo and the exo conformers there is a different overlap fashion of the carbonyls to the secondary orbitals of the diene that sits "opposite" to the carbonyls. In the endo structure, this interaction is antibonding; in the exo one, it is bonding. This suggests that the exo structure is more favoured, having a more constructive secondary orbital effect, a more stabilised conformation, a secondary driving force that pushes it towards reactivity. However, the structures' geometric data indicates that the endo's (O=C)-O-(C=O) to ''sp2'' C - ''sp2'' C distance is shorter by a factor of 0.09Å. The (O=C) to ''sp2'' C - ''sp2'' C distance, instead, is equal, suggesting that only the anhydride's central oxygen is bent "outwards" in the exo structure as opposed tot eh endo structure. Moreover, the anhydride sits closer to the diene in the ENDO conformer.

All this having been said, the energetic data indicates that the endo conformation is more stable by 18kJ/mol. Hence, despite the secondary orbital effect stabilisation in EXO, the endo structure is still the most stable conformer of the two. Most probably, the exo structure has an unfavourable strain due to the way it has to approach the diene: the Diels-Alder reaction works best when the dienophile approaches the diene from below or above. However, the exo conformer cannot allow access from above, due to the bridgehead's sterical interference. So the endo conformer is overall the winning isomer.

* Some effects have not been considered in these calculations. For instance, the electronic favourability of the interaction of the maleic anhydride with the diene (due to the electronic richness of the dienophile)<ref>D. Craig's lecture course "organic Synthesis II", Lecture 6, '''2010''', Imperial College London</ref>:

[[Image:mal_anh_effect.jpg|thumb|400px|left]]

==References==
<references />

Rep:Mod:enricof11phys

2010-11-11T16:44:20Z

2010-11-11T15:17:29Z

Ef108: /* Diels-Alder reaction */

==Module 3 - Phyisical computational chemistry==

===Cope rearrangement studies===

First, the reactant 1,5-hexadiene was analysed. Several isomers were optimised:

{| class="wikitable" border="1"
|-
! Conformation !! Optimisation method/basis set!!Energy (hartree)!!Energy (kJ/mol)!!Point group
|-
! Anti2 !! HF/3-21G!!-231.69254!!-608,308.81!!Ci
|-
| Anti1|| HF/3-21G||-231.69260||-608,308.97||C2
|-
| Gauche2|| HF/3-21G||-231.69167||-608,306.53||C2
|-
| Gauche3|| HF/3-21G||-231.69266||-608,309.13||C1
|-
! Anti2 !! B3LYP/6-31G(d)!!-234.61172!!-615,973.11||Ci
|}

The IR spectra of Anti2 is
[[Image:IR_anti_DFT_freq.gif|thumb|650px|left ]]

The sum of its electronic PE at 0K and its zero-point energy: -234.469182 hartree = - 615598.88 kJ/mol

The sum of its electronic PE at 298.15K, 1atm and thermal energies (vib, rot, trans contributions): -234.461844 hartree = - 615579.62 kJ/mol

The sum of its electronic and thermal enthalpies (includes an RT correction): -234.460900 hartree = - 615577.14 kJ/mol

The sum of its electronic and thermal free energies (includes entropy): -234.500730 hartree = - 615681.71 kJ/mol

The optimisation was successful but not great, as the low frequencies (from the log output file) are more or less between +-10cm-1. However, there is not much gap between the low and higher frequencies.

Low frequencies --- -7.5940 0.0001 0.0005 0.0008 8.5899 13.2081
Low frequencies --- 74.7550 82.4948 121.8440

The Optimisation of the chair TS of the Cope rearrangement was done always with HF/3-21G basis set and, while the first attempt was done using a force constant matrix, the second included redundant coordinates editing (first restricting the distance of the 2 fragments, then allowing them to reorientate). The two methods gave similar final structures.

{| class="wikitable" border="1"
|+ Chair structure optimisation details
! !!Force constant!!Redundant
|-
| separation between fragments|| 2.02||2.02
|-
| bond breaking bond lengths|| 1.39||1.39
|-
| optimised fragments image||[[Image:1ikea_norm.jpg|thumb|widthpx| ]]||[[Image:2ikea_redundant.jpg|thumb|widthpx| ]]
|-
| Energy (au)|| -231.61932238||-231.61932198
|-
| Energy (kJ/mol)||-608116.57723 ||-608116.57618
|-
| Point group||C1||C1
|}

The QST T.S. optimisation for the boat conformation displays one imaginary frequency, hence confirming the achievement of a true transition state.<ref>Higgins, ''J. Chem. Educ.'',''' 1995''', ''72'' (8),703. DOI: 10.1021/ed072p703</ref>

The structure yielded by the IRC calculation, followed by (i) optimisation of the last point is on the left, while the IRC calculation with force constant calculation at every step is on the right.

<jmol> <jmolApplet> <uploadedFileContents>ikea_IRC2_optsd.mol</uploadedFileContents> </jmolApplet> </jmol><jmol> <jmolApplet> <uploadedFileContents>IRCoutput.mol</uploadedFileContents> </jmolApplet> </jmol>

===Diels-Alder reaction===

* The optimised geometry of cis-butadiene is:

{| class="wikitable" border="1"
|-
| [[Image:BUH_optimised.jpg|thumb|300px|cell ]]|| Notice how the optimised structure has a dihedral angle of 0° between the two extreme carbons.
|-
| HOMO [[Image:ef108buta_HOMO.jpg|thumb|300px|cell ]]||LUMO [[Image:ef108buta_LUMO.jpg|thumb|widthpx|cell]]||The HOMO and the LUMO of the molecule are shown on the left. One can notice how the HOMO is asymeetric with respect to the vertical plane, while the LUMO is symmetrical.
|}

Interestingly, the most external carbons have in the LUMO identical symmetry to the HOMO of ethene, suggesting a wonderful potential overlap.

Also, the alkenes have antibonding character in the LUMO. This orbital is empty, so that explains why they are higher order bonds.

* The optimised geometry of the prototype Diels Alder reaction is below. This structure optimisation required the initial guess to be symmetrised. Hence, first the alkene was fitted to D2h symmetry. Separately, the diene was allowed to relax in a C2v symmetry conformation. [[Image:DADA_CsSymmetry.jpg|thumb|300px|right|Cs symmetry - notice plane of symmetry]]
The two structures were then pasted together and modified to fit Cs symmetry requirements. Interfragment distance was set to 2.2Å.

Furthermore, an "Opt=noEigen" command was added to allow the job to avoid eigenvalue checks. Finally, the optimised (output) transition state structure was again Cs symmetric and had the expected imaginary frequency at 818cm-1 and only 1 negative eigenvalue. [[Image:DADA_alk_movie.gif|thumb|widthpx|right|Imaginary vibration motion]]

Moreover, the imaginary frequency, which can be seen on the right, corresponds to the movements of the bonds required to transform the reactants buatadiene+ethene in the Diels-Alder cyclic product. The bonds are forming synchronously. The lowest positive frequency of 166cm-1 represents a torsion of the dienophile with respect to the butadiene, leading, in such a way, to an asynchronous motion of the partly formed σ C-C bonds. [[Image:DADA_166.gif|thumb|widthpx|right]]

{| class="wikitable" border="1"
|-
|<jmol> <jmolAppletButton> <uploadedFileContents>DADA_ALK_6noeigen.mol</uploadedFileContents> <text>Optimised D-A reactant</text> </jmolAppletButton> </jmol>
|-
|Optimised structure [[Image:DADA_A6.jpg|thumb|widthpx|cell ]]
|-
|HOMO [[Image:DADA_HOMO.jpg|thumb|widthpx|cell ]]
|-
|LUMO [[Image:DADA_LUMO.jpg|thumb|widthpx|cell]]
|}

The HOMO (and the LUMO) of this species are now symmetric with respect to the vertical central plane (differently to the butadiene above).

This fact testifies that the central butadiene bond has become stronger (higher order), while in butadiene, above, the HOMO had antibonding character for the central bond, and bonding character for the side olefinic bonds.

A closer look at the Transition state's MO allows us to realise that this orbital is the sum of the interaction between the ethene's HOMO (bonding and symmetric) and butadiene's LUMO (antibonding and symmetric). Ethene is acting as the electron rich substituent that donates to the LUMO of the electrophilic species. This interaction is allowed as the orbitals have the same character. Practically, though, this Diels-Alder reaction will not happen as readily as, say, that of butadiene with maleic anhydride, the reason being that the more the dienophile is electron rich, the faster the pericyclic rearrangement takes place.

Further considerations can be made regarding the C-C links. The partly formed σ C-C bond lengths are of 2.21Å (vs. lit. 1.526Å of ethane<ref>Lide, D.R., '''A survey on C-C bond lengths''', ''Tetrahedron'', '''1962''', ''17'', 125</ref>. Also, ''sp3'' C-''sp2'' C lit. 1.507Å; ''sp2'' C-''sp2'' C lit. 1.455Å.<ref>Allen, Kennard ''et al.'', ''J. Chem. Soc. Perkin Trans. II'', '''1987''', S1-S19</ref>

Moreover, the VdW radius of C is 1.70Å <ref>A. Bondi , ''J.Phys.Chem.'','''1964''', ''68'', 441-452</ref>. Hence, the partial σ C-C bond present in the transition state is actually longer than a normal C-C bond, but still shorter than the sum of the carbons' Van der Waals radii (3.40Å). The T.S. is, in fact, a transition from a non-bonding and non-interacting situation to a bonding one: in the transition state we can see how the carbons have entered each other's zone of influence.

* The optimised structures of the exo and endo products are:

{| class="wikitable" border="1"
|-
| <jmol> <jmolApplet> <uploadedFileContents>EXIT_optimised.mol</uploadedFileContents> </jmolApplet> </jmol> || <jmol> <jmolApplet> <uploadedFileContents>THEEND_optimised.mol</uploadedFileContents> </jmolApplet> </jmol>
|}

In order to obtain such optimised structures, it was necessary to modify the input geometries so as to fit symmetry requirements The EXO TS guess was fitted to Cs symmetry and optimised using the force constant method. The resulting structure had a single imaginary frequency at 648com-1, corresponding to the DA reaction.

The ENDO t.s. conformer input structure was built by fitting the diene to Cs symmetry and allowing it to have a similar shape to that of the ENDO product of reaction. Separately, the anhydride was drawn to fit D2h symmetry. The maleic anhydide ring was then added, avoiding steric repulsions between the hydrogens, but still keeping the two species 2.2Å close. Finally, the molecule was fitted to Cs symmetry. The output had a single imaginary frequency at 643cm-1, corresponding to the Diels-Alder reaction.

The resulting energies are:

EXO T.S.: -605.60359 au = -1,590,012 kJ/mol

ENDO T.S.: -605.61037 au = -1,590,030 kJ/mol

Information about their geometry (all measures are in Å)

First, we must optimise the reactants. This is done with a B3LYP/3-21G basis set (i), which was preferred to 6311-G(d) because the low frequency values were closer to zero in the former case.

Low frequencies --- -16.0631 -2.9994 -0.0003 -0.0001 0.0005 16.8130
Low frequencies --- 151.4150 284.8688 483.5358

vs

Low frequencies --- -125.1038 -15.4980 -5.1944 -0.0012 -0.0009 -0.0006
Low frequencies --- 9.4217 297.5104 517.9157

The optimised structure has a dihedral angle of 31.5°. The structure yielded had relative energy of -155.135459 au = -407308.2 kJ/mol vs -155.9864 au, -155.9859 au of some other tested optimisation methods (some with starting dihedral angle of 30°). This structure was chosen as it was the best compromise between stability and low frequency closeness to 0 or low frequency-"higher" frequency gap.

[[Image:ef108buta_HOMO.jpg|thumb|widthpx|left]]

This HOMO orbital is AS (ungerade) with respect to the vertical plane along the centre of the molecule.

[[Image:ef108buta_LUMO.jpg|thumb|widthpx|left]]

This LUMO orbital is S (gerade) with respect to the vertical plane along the centre of the molecule.

The search of the T.S. was done overcoming a series of issues concerning:
- symmetry
- eigenvalue checks

For what concerns symmetry, the molecule has to be modified until Gaussian could recognise Cs symmetry. Only then the T.S. could be found.
Secondly, the eigenvalue check at the beginning of the calculation has to be aborted, as Gaussian was getting confused between the eigenvalue due to the imaginary frequency and another, due to other bond stretches.

The sought after structure was then achieved:

[[Image:DADA_CsSymmetry.jpg|thumb|250px|left]][[Image:DADA_alk_movie.gif|thumb|300px|]]

The image on the left is useful as it shows that there is Cs symmetry in the molecule (a plane of symmetry is present). The motion image, instead, displays the imaginary vibration: one can notice that this motion corresponds to the conversion of the reactant to the product.

Now we can compare the HOMO of this TS to the previously displayed HOMO and LUMO of butadiene:

[[Image:DADA_HOMO.jpg|thumb|200px|left]]

<references />