Rep:Mod:certiorari3

2008-12-12T13:54:51Z

Sk1406:

= Third Year Computational Chemistry Lab, by Simon Krautwald =

== Module 3 - The Transition State ==

=== Tutorial ===

A structure for 1,5-hexadiene was drawn with the central C-C bond featuring the an ''anti'' arrangement of the R groups and then cleaned up using the "Clean" function. It was optimized using Gaussian at the HF/3-21G level. The same was done for a molecule with a gauche conformation at the central bond. Pertinent data from the analysis of the results are presented in the table below. The gauche form can be expected to have the higher energy due to the smaller dihedral angle (60 degrees as opposed to 180) between the more bulky R groups on the central C-C bond.

The anti energy obtained agrees with that of conformation anti4 in appendix 1, the gauche one with that of gauche3. Interestingly, the gauche conformation is of lower energy than the anti conformation, and the gauche3 conformation obtained is actually the lowest energy conformation overall.

{| class="wikitable" border="1"
|+ '''Selected Conformations of 1,5-Hexadiene'''
! [[Image:Sk1406_hexadiene_anti4_conf.jpg|Hexadiene anti4 conformation|thumb]] !! [[Image:Sk1406_hexadiene_gauche3_conf.jpg|Hexadiene gauche3 conformation|thumb]]
|}

For the generation of the anti2 conformation with Ci symmetry, the optimized anti4 conformation was taken as a starting point. In anti4, one of the dihedral angles of four carbon atoms is almost zero degrees, whereas the other one is 114.534. The zero degree one was manually set to -114.534 degrees to approximately give the molecule a centre of inversion. HF/3-21G optimization then followed. The energy obtained agreed with the one quoted in appendix 1. After symmetrizing the structure (Default Tolerance), the point group was identified as Ci.

Some bond lengths, bond angles and dihedral angles for the HF and DFT results are presented in the table. There are no significant differences. The B3LYP/6-31G(d) optimized geometry was then submitted again in order to calculate the vibrational frequencies. The job summary indicated zero imaginary frequencies, which means that the geometry was really optimized to a minimum.

From the output file of the frequency job, the following data was obtained:

Sum of electronic and zero-point Energies= -234.469195 (Potential Energy at 0K, E = Eelec + ZPE)

Sum of electronic and thermal Energies= -234.461847 (Energy at 298.15K and 1 atm, E = E + Evib + Erot + Etrans)

Sum of electronic and thermal Enthalpies= -234.460903 ( H = E + RT, important for dissociation reactions)

Sum of electronic and thermal Free Energies= -234.500782 (includes entropic contribution to free energy, G = H - TS)

include data for 0 K, comment on what the data means.

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

The allyl fragment was optimized at the HF/3-21G level. Following the instructions, the transition state of the Cope rearrangement was then set up manually by moving two allyl fragments into position. A picture of this is shown below. In it, the C-C distance of approximately 2.2 A is highlighted. Also, the chair shape, with all C-H bonds staggered, can be seen clearly. The TS optimization job was run and finished successfully - the summary indicated that there was one negative frequency of 817.977 cm-1.

[[Image:Sk1406_1st_guess_chair_TS.jpg|Initial Guess of the Chair TS Structure]]

The vibration is one that brings one terminus on each allyl fragment very close to one terminus on the other allyl fragment, while the other two termini are moved further away from one another. This is the Cope rearrangement, the formation of one sigma bond at the expense of another one being broken.

</jmol> '''3D view of the TS of the Cope Rearrangement''' <jmol>
<jmolApplet>
<title>TSCopeRearrange</title><color>white</color><size>300</size>
<script>zoom 80; cpk -25;frame 1; move 10 -20 10 0 0 0 0 0 3; delay 1;</script>
<uploadedFileContents>Sk1406_cope_rearrange_1st_ts.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable" border="1"
|+ '''Pictures for Chair Transition State Optimization'''
! [[Image:Sk1406_renumbered_SM_and_PDT.jpg|Renumbered Starting Material|thumb]] !! [[Image:Sk1406_1st_failed_QTS2_opt.jpg|Failed QST2 Optimization|thumb]]
|-
| [[Image:Sk1406_cope_boat_ts.jpg|Cope Boat TS|thumb]] || [[Image:Sk1406_vibration_boat_ts.jpg|Vibration in Cope Boat TS|thumb]]
|}

Thermochemical Data for the Chair TS at B3LYP/6-31G(d)/a.u.:

Sum of electronic and zero-point Energies= -234.414930

Sum of electronic and thermal Energies= -234.409009

Sum of electronic and thermal Enthalpies= -234.408065

Sum of electronic and thermal Free Energies= -234.443815

The first QTS2 optimization at HF/3-21G failed. An image is included showing the reason. Gaussian merely tried to connect the termini of the two allyl fragments from the geometry it was given, it did not rotate about bonds to find a chair or boat transition state. Hence the "crossover" or X-shaped transition state. d(C1-C6) = 4.32553 d(C3-C4)=3.48200, much longer than any forming or breaking C-C bond would be in reality, and much longer than the 2.02 A found for the chair TS using the above methods.

=== The Diels Alder Cycloaddition ===

The frontier molecular orbitals of butadiene are presented in the table below. The HOMO is antisymmetric with respect to the plane bisecting the central C-C bond, the LUMO is symmetric:

HOMO - a

LUMO - s

{| class="wikitable" border="1"
|+ '''The FMOs of Butadiene'''
! [[Image:Sk1406_cis_butadiene_homo.jpg|HOMO of Butadiene|thumb]] !! [[Image:Sk1406_cis_butadiene_lumo.jpg|LUMO of Butadiene|thumb]]
|}

This means that in any Diels Alder reaction of butadiene, either the HOMO of butadiene will have to overlap with an antisymmetric LUMO on the dienophile (such as the Pi* on ethylene) OR the LUMO of butadiene will have to overlap with a symmetric HOMO on the dienophile (such as the Pi orbital on ethylene). Which of the two processes is envisaged to happen usually depends on how electron rich or deficient the components are. For a normal electron demand DA, the diene is the electron rich component and the dienophile contributes the electron deficient double bond (as in the case of maleic anhydride).

{| class="wikitable" border="1"
|+ '''The Transition State of the Diels Alder Reaction'''
! [[Image:Sk1406_DA_TS_1.jpg|Diels Alder TS Image 1|thumb]] !! [[Image:Sk1406_DA_TS_2.jpg|Diels Alder TS Image 2|thumb]]
|-
| [[Image:Sk1406_da_ts_homo.jpg|Diels Alder TS HOMO|thumb]] || [[Image:Sk1406_da_ts_lumo.jpg|Diels Alder TS LUMO|thumb]]
|-
| [[Image:Sk1406_DA_TS_labels.jpg|Diels Alder TS Labels|thumb]]
|}

The HOMO of the transition state is still antisymmetric with respect to the plane bisecting the central bond, and the LUMO is still symmetric. This is the essence of the conservation of orbital symmetry. The orbitals involved in a pericyclic reaction have a certain symmetry to start with, they maintain that symmetry in the transition state, and in an ideal case the reactant orbitals smoothly transform into orbitals of the product with the same symmetry. Throughout the process, the symmetry of the orbitals is conserved.

In this case, the HOMO of the TS is formed from the HOMO of butadiene and the LUMO of ethylene as shown in the picture. One can clearly see that between each of the pairs of carbon atoms that form a new bond, there is an orbital lobe of one phase, which means that there is a bonding interaction. It was a key insight that many pericyclic processes are facile because throughout the reaction the maximum possible bonding is being maintained.

The average lengths of C-C bonds are as follows:

C-C single bond: 1.54 A

C-C double bond: 1.34 A

C-C triple bond: 1.20 A

C-C in benzene: 1.40 A

The table presents energies and geometrical parameters of the three DA transition states modelled. For the butadiene+ethylene system, the average bond length is about 1.38 A, i.e. significantly shorter than a single bond and somewhat longer than a C=C double bond. The two bonds that are being formed with a C-C distance of about 2.12 A are much longer than a typical C-C single bond.

{| class="wikitable" border="1"
|+ '''The Transition State of the Diels Alder Reaction, Endo and Exo'''
! [[Image:Sk1406_endo_ts_input.jpg|Endo TS Input Structure|thumb]] !! [[Image:Sk1406_endo_ts_homo.jpg|Endo TS HOMO|thumb]]
|-
| [[Image:Sk1406_exo_ts_input.jpg|Exo TS Input Structure|thumb]] || [[Image:Sk1406_exo_ts_homo.jpg|Exo TS HOMO|thumb]]
|}

The transition state was modelled according to the first method described in the instructions. The bicyclo[2.2.2]octane ring system was drawn and two methylene groups removed. This gave the "envelope" structure of an ethylene molecule approaching a butadiene molecule from the top face. The length of the two forming bonds was set to 2.2 A. This seemed like a reasonable value, as it had worked for the Cope rearrangement. A job of the type opt+freq with the AM1 method was started. Optimization to a TS (Berny), calculation of force constants once, and opt=noeigen. The job completed successfully with one imaginary frequency (indicating that Gaussian minimized to a TS) of -955.629 cm-1. Animating this vibration showed the atomic motion corresponding to and expected from the Diels Alder cycloaddition. The atoms of the ethylene molecule close in on the terminal atoms of butadiene in a concerted fashion. Pertinent geometrical data of the transition state are presented in the table.

The lowest positive frequency is 146.95 cm-1.

It is interesting to note that the bond lengths of a group of four bonds (that does not include the two new sigma bonds being formed) are almost equal at 1.38-1.39 A, intermediate in length of a C-C single and double bond. This partial bond length equalization supports the concept of an aromatic transition state!

=== References Mini Project ===

1. A. Neugebauer, G. Häfelinger, ''Int. J. Mol. Sci.'', '''2005''', 6, 157

2. Arduengo, A. J. et al., ''J. Am. Chem. Soc.'', '''1991''', 113, 361

3. A. J. Arduengo et al., ''J. Am. Chem. Soc.'', '''1992''', 114, 5530-5534

4. W. A. Herrmann, ''Angew. Chem. Int. Ed.'', '''2002''', 41, 1290

5. W. A. Herrmann et al., ''Angew. Chem. Int. Ed.'', '''1992''', 31, 1485

6. G. Frenking, C. Boehme, ''J. Am. Chem. Soc.'', '''1996''', 118, 2039-2046

Rep:Mod:certiorari3

2008-12-12T13:40:37Z

Sk1406:

= Third Year Computational Chemistry Lab, by Simon Krautwald =

== Module 3 - The Transition State ==

=== Tutorial ===

A structure for 1,5-hexadiene was drawn with the central C-C bond featuring the an ''anti'' arrangement of the R groups and then cleaned up using the "Clean" function. It was optimized using Gaussian at the HF/3-21G level. The same was done for a molecule with a gauche conformation at the central bond. Pertinent data from the analysis of the results are presented in the table below. The gauche form can be expected to have the higher energy due to the smaller dihedral angle (60 degrees as opposed to 180) between the more bulky R groups on the central C-C bond.

The anti energy obtained agrees with that of conformation anti4 in appendix 1, the gauche one with that of gauche3. Interestingly, the gauche conformation is of lower energy than the anti conformation, and the gauche3 conformation obtained is actually the lowest energy conformation overall.

{| class="wikitable" border="1"
|+ '''Selected Conformations of 1,5-Hexadiene'''
! [[Image:Sk1406_hexadiene_anti4_conf.jpg|Hexadiene anti4 conformation|thumb]] !! [[Image:Sk1406_hexadiene_gauche3_conf.jpg|Hexadiene gauche3 conformation|thumb]]
|}

For the generation of the anti2 conformation with Ci symmetry, the optimized anti4 conformation was taken as a starting point. In anti4, one of the dihedral angles of four carbon atoms is almost zero degrees, whereas the other one is 114.534. The zero degree one was manually set to -114.534 degrees to approximately give the molecule a centre of inversion. HF/3-21G optimization then followed. The energy obtained agreed with the one quoted in appendix 1. After symmetrizing the structure (Default Tolerance), the point group was identified as Ci.

Some bond lengths, bond angles and dihedral angles for the HF and DFT results are presented in the table. There are no significant differences. The B3LYP/6-31G(d) optimized geometry was then submitted again in order to calculate the vibrational frequencies. The job summary indicated zero imaginary frequencies, which means that the geometry was really optimized to a minimum.

From the output file of the frequency job, the following data was obtained:

Sum of electronic and zero-point Energies= -234.469195 (Potential Energy at 0K, E = Eelec + ZPE)

Sum of electronic and thermal Energies= -234.461847 (Energy at 298.15K and 1 atm, E = E + Evib + Erot + Etrans)

Sum of electronic and thermal Enthalpies= -234.460903 ( H = E + RT, important for dissociation reactions)

Sum of electronic and thermal Free Energies= -234.500782 (includes entropic contribution to free energy, G = H - TS)

include data for 0 K, comment on what the data means.

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

The allyl fragment was optimized at the HF/3-21G level. Following the instructions, the transition state of the Cope rearrangement was then set up manually by moving two allyl fragments into position. A picture of this is shown below. In it, the C-C distance of approximately 2.2 A is highlighted. Also, the chair shape, with all C-H bonds staggered, can be seen clearly. The TS optimization job was run and finished successfully - the summary indicated that there was one negative frequency of 817.977 cm-1.

[[Image:Sk1406_1st_guess_chair_TS.jpg|Initial Guess of the Chair TS Structure]]

The vibration is one that brings one terminus on each allyl fragment very close to one terminus on the other allyl fragment, while the other two termini are moved further away from one another. This is the Cope rearrangement, the formation of one sigma bond at the expense of another one being broken.

</jmol> '''3D view of the TS of the Cope Rearrangement''' <jmol>
<jmolApplet>
<title>TSCopeRearrange</title><color>white</color><size>300</size>
<script>zoom 80; cpk -25;frame 1; move 10 -20 10 0 0 0 0 0 3; delay 1;</script>
<uploadedFileContents>Sk1406_cope_rearrange_1st_ts.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable" border="1"
|+ '''Pictures for Chair Transition State Optimization'''
! [[Image:Sk1406_renumbered_SM_and_PDT.jpg|Renumbered Starting Material|thumb]] !! [[Image:Sk1406_1st_failed_QTS2_opt.jpg|Failed QST2 Optimization|thumb]]
|-
| [[Image:Sk1406_cope_boat_ts.jpg|Cope Boat TS|thumb]] || [[Image:Sk1406_vibration_boat_ts.jpg|Vibration in Cope Boat TS|thumb]]
|}

Thermochemical Data for the Chair TS at B3LYP/6-31G(d)/a.u.:

Sum of electronic and zero-point Energies= -234.414930

Sum of electronic and thermal Energies= -234.409009

Sum of electronic and thermal Enthalpies= -234.408065

Sum of electronic and thermal Free Energies= -234.443815

The first QTS2 optimization at HF/3-21G failed. An image is included showing the reason. Gaussian merely tried to connect the termini of the two allyl fragments from the geometry it was given, it did not rotate about bonds to find a chair or boat transition state. Hence the "crossover" or X-shaped transition state. d(C1-C6) = 4.32553 d(C3-C4)=3.48200, much longer than any forming or breaking C-C bond would be in reality, and much longer than the 2.02 A found for the chair TS using the above methods.

=== The Diels Alder Cycloaddition ===

The frontier molecular orbitals of butadiene are presented in the table below. The HOMO is antisymmetric with respect to the plane bisecting the central C-C bond, the LUMO is symmetric:

HOMO - a

LUMO - s

{| class="wikitable" border="1"
|+ '''The FMOs of Butadiene'''
! [[Image:Sk1406_cis_butadiene_homo.jpg|HOMO of Butadiene|thumb]] !! [[Image:Sk1406_cis_butadiene_lumo.jpg|LUMO of Butadiene|thumb]]
|}

This means that in any Diels Alder reaction of butadiene, either the HOMO of butadiene will have to overlap with an antisymmetric LUMO on the dienophile (such as the Pi* on ethylene) OR the LUMO of butadiene will have to overlap with a symmetric HOMO on the dienophile (such as the Pi orbital on ethylene). Which of the two processes is envisaged to happen usually depends on how electron rich or deficient the components are. For a normal electron demand DA, the diene is the electron rich component and the dienophile contributes the electron deficient double bond (as in the case of maleic anhydride).

{| class="wikitable" border="1"
|+ '''The Transition State of the Diels Alder Reaction'''
! [[Image:Sk1406_DA_TS_1.jpg|Diels Alder TS Image 1|thumb]] !! [[Image:Sk1406_DA_TS_2.jpg|Diels Alder TS Image 2|thumb]]
|-
| [[Image:Sk1406_da_ts_homo.jpg|Diels Alder TS HOMO|thumb]] || [[Image:Sk1406_da_ts_lumo.jpg|Diels Alder TS LUMO|thumb]]
|-
| [[Image:Sk1406_DA_TS_labels.jpg|Diels Alder TS Labels|thumb]]
|}

The HOMO of the transition state is still antisymmetric with respect to the plane bisecting the central bond, and the LUMO is still symmetric. This is the essence of the conservation of orbital symmetry. The orbitals involved in a pericyclic reaction have a certain symmetry to start with, they maintain that symmetry in the transition state, and in an ideal case the reactant orbitals smoothly transform into orbitals of the product with the same symmetry. Throughout the process, the symmetry of the orbitals is conserved.

The average lengths of C-C bonds are as follows:

C-C single bond: 1.54 A

C-C double bond: 1.34 A

C-C triple bond: 1.20 A

C-C in benzene: 1.40 A

The table presents energies and geometrical parameters of the three DA transition states modelled. For the butadiene+ethylene system, the average bond length is about 1.38 A, i.e. significantly shorter than a single bond and somewhat longer than a C=C double bond. The two bonds that are being formed with a C-C distance of about 2.12 A are much longer than a typical C-C single bond.

{| class="wikitable" border="1"
|+ '''The Transition State of the Diels Alder Reaction, Endo and Exo'''
! [[Image:Sk1406_endo_ts_input.jpg|Endo TS Input Structure|thumb]] !! [[Image:Sk1406_endo_ts_homo.jpg|Endo TS HOMO|thumb]]
|-
| [[Image:Sk1406_exo_ts_input.jpg|Exo TS Input Structure|thumb]] || [[Image:Sk1406_exo_ts_homo.jpg|Exo TS HOMO|thumb]]
|}

The transition state was modelled according to the first method described in the instructions. The bicyclo[2.2.2]octane ring system was drawn and two methylene groups removed. This gave the "envelope" structure of an ethylene molecule approaching a butadiene molecule from the top face. The length of the two forming bonds was set to 2.2 A. This seemed like a reasonable value, as it had worked for the Cope rearrangement. A job of the type opt+freq with the AM1 method was started. Optimization to a TS (Berny), calculation of force constants once, and opt=noeigen. The job completed successfully with one imaginary frequency (indicating that Gaussian minimized to a TS) of -955.629 cm-1. Animating this vibration showed the atomic motion corresponding to and expected from the Diels Alder cycloaddition. The atoms of the ethylene molecule close in on the terminal atoms of butadiene in a concerted fashion. Pertinent geometrical data of the transition state are presented in the table.

It is interesting to note that the bond lengths of a group of four bonds (that does not include the two new sigma bonds being formed) are almost equal at 1.38-1.39 A, intermediate in length of a C-C single and double bond. This partial bond length equalization supports the concept of an aromatic transition state!

=== References Mini Project ===

1. A. Neugebauer, G. Häfelinger, ''Int. J. Mol. Sci.'', '''2005''', 6, 157

2. Arduengo, A. J. et al., ''J. Am. Chem. Soc.'', '''1991''', 113, 361

3. A. J. Arduengo et al., ''J. Am. Chem. Soc.'', '''1992''', 114, 5530-5534

4. W. A. Herrmann, ''Angew. Chem. Int. Ed.'', '''2002''', 41, 1290

5. W. A. Herrmann et al., ''Angew. Chem. Int. Ed.'', '''1992''', 31, 1485

6. G. Frenking, C. Boehme, ''J. Am. Chem. Soc.'', '''1996''', 118, 2039-2046

Rep:Mod:certiorari3

2008-12-12T12:11:19Z

Sk1406:

= Third Year Computational Chemistry Lab, by Simon Krautwald =

== Module 3 - The Transition State ==

=== Tutorial ===

A structure for 1,5-hexadiene was drawn with the central C-C bond featuring the an ''anti'' arrangement of the R groups and then cleaned up using the "Clean" function. It was optimized using Gaussian at the HF/3-21G level. The same was done for a molecule with a gauche conformation at the central bond. Pertinent data from the analysis of the results are presented in the table below. The gauche form can be expected to have the higher energy due to the smaller dihedral angle (60 degrees as opposed to 180) between the more bulky R groups on the central C-C bond.

The anti energy obtained agrees with that of conformation anti4 in appendix 1, the gauche one with that of gauche3. Interestingly, the gauche conformation is of lower energy than the anti conformation, and the gauche3 conformation obtained is actually the lowest energy conformation overall.

{| class="wikitable" border="1"
|+ '''Selected Conformations of 1,5-Hexadiene'''
! [[Image:Sk1406_hexadiene_anti4_conf.jpg|Hexadiene anti4 conformation|thumb]] !! [[Image:Sk1406_hexadiene_gauche3_conf.jpg|Hexadiene gauche3 conformation|thumb]]
|}

For the generation of the anti2 conformation with Ci symmetry, the optimized anti4 conformation was taken as a starting point. In anti4, one of the dihedral angles of four carbon atoms is almost zero degrees, whereas the other one is 114.534. The zero degree one was manually set to -114.534 degrees to approximately give the molecule a centre of inversion. HF/3-21G optimization then followed. The energy obtained agreed with the one quoted in appendix 1. After symmetrizing the structure (Default Tolerance), the point group was identified as Ci.

Some bond lengths, bond angles and dihedral angles for the HF and DFT results are presented in the table. There are no significant differences. The B3LYP/6-31G(d) optimized geometry was then submitted again in order to calculate the vibrational frequencies. The job summary indicated zero imaginary frequencies, which means that the geometry was really optimized to a minimum.

From the output file of the frequency job, the following data was obtained:

Sum of electronic and zero-point Energies= -234.469195 (Potential Energy at 0K, E = Eelec + ZPE)

Sum of electronic and thermal Energies= -234.461847 (Energy at 298.15K and 1 atm, E = E + Evib + Erot + Etrans)

Sum of electronic and thermal Enthalpies= -234.460903 ( H = E + RT, important for dissociation reactions)

Sum of electronic and thermal Free Energies= -234.500782 (includes entropic contribution to free energy, G = H - TS)

include data for 0 K, comment on what the data means.

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

The allyl fragment was optimized at the HF/3-21G level. Following the instructions, the transition state of the Cope rearrangement was then set up manually by moving two allyl fragments into position. A picture of this is shown below. In it, the C-C distance of approximately 2.2 A is highlighted. Also, the chair shape, with all C-H bonds staggered, can be seen clearly. The TS optimization job was run and finished successfully - the summary indicated that there was one negative frequency of 817.977 cm-1.

[[Image:Sk1406_1st_guess_chair_TS.jpg|Initial Guess of the Chair TS Structure]]

The vibration is one that brings one terminus on each allyl fragment very close to one terminus on the other allyl fragment, while the other two termini are moved further away from one another. This is the Cope rearrangement, the formation of one sigma bond at the expense of another one being broken.

</jmol> '''3D view of the TS of the Cope Rearrangement''' <jmol>
<jmolApplet>
<title>TSCopeRearrange</title><color>white</color><size>300</size>
<script>zoom 80; cpk -25;frame 1; move 10 -20 10 0 0 0 0 0 3; delay 1;</script>
<uploadedFileContents>Sk1406_cope_rearrange_1st_ts.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable" border="1"
|+ '''Pictures for Chair Transition State Optimization'''
! [[Image:Sk1406_renumbered_SM_and_PDT.jpg|Renumbered Starting Material|thumb]] !! [[Image:Sk1406_1st_failed_QTS2_opt.jpg|Failed QST2 Optimization|thumb]]
|-
| [[Image:Sk1406_cope_boat_ts.jpg|Cope Boat TS|thumb]] || [[Image:Sk1406_vibration_boat_ts.jpg|Vibration in Cope Boat TS|thumb]]
|}

Thermochemical Data for the Chair TS at B3LYP/6-31G(d)/a.u.:

Sum of electronic and zero-point Energies= -234.414930

Sum of electronic and thermal Energies= -234.409009

Sum of electronic and thermal Enthalpies= -234.408065

Sum of electronic and thermal Free Energies= -234.443815

The first QTS2 optimization at HF/3-21G failed. An image is included showing the reason. Gaussian merely tried to connect the termini of the two allyl fragments from the geometry it was given, it did not rotate about bonds to find a chair or boat transition state. Hence the "crossover" or X-shaped transition state. d(C1-C6) = 4.32553 d(C3-C4)=3.48200, much longer than any forming or breaking C-C bond would be in reality, and much longer than the 2.02 A found for the chair TS using the above methods.

=== The Diels Alder Cycloaddition ===

The frontier molecular orbitals of butadiene are presented in the table below. The HOMO is antisymmetric with respect to the plane bisecting the central C-C bond, the LUMO is symmetric:

HOMO - a

LUMO - s

{| class="wikitable" border="1"
|+ '''The FMOs of Butadiene'''
! [[Image:Sk1406_cis_butadiene_homo.jpg|HOMO of Butadiene|thumb]] !! [[Image:Sk1406_cis_butadiene_lumo.jpg|LUMO of Butadiene|thumb]]
|}

This means that in any Diels Alder reaction of butadiene, either the HOMO of butadiene will have to overlap with an antisymmetric LUMO on the dienophile (such as the Pi* on ethylene) OR the LUMO of butadiene will have to overlap with a symmetric HOMO on the dienophile (such as the Pi orbital on ethylene). Which of the two processes is envisaged to happen usually depends on how electron rich or deficient the components are. For a normal electron demand DA, the diene is the electron rich component and the dienophile contributes the electron deficient double bond (as in the case of maleic anhydride).

{| class="wikitable" border="1"
|+ '''The Transition State of the Diels Alder Reaction'''
! [[Image:Sk1406_DA_TS_1.jpg|Diels Alder TS Image 1|thumb]] !! [[Image:Sk1406_DA_TS_2.jpg|Diels Alder TS Image 2|thumb]]
|-
| [[Image:Sk1406_da_ts_homo.jpg|Diels Alder TS HOMO|thumb]] || [[Image:Sk1406_da_ts_lumo.jpg|Diels Alder TS LUMO|thumb]]
|-
| [[Image:Sk1406_DA_TS_labels.jpg|Diels Alder TS Labels|thumb]]
|}

The HOMO of the transition state is still antisymmetric with respect to the plane bisecting the central bond, and the LUMO is still symmetric. This is the essence of the conservation of orbital symmetry. The orbitals involved in a pericyclic reaction have a certain symmetry to start with, they maintain that symmetry in the transition state, and in an ideal case the reactant orbitals smoothly transform into orbitals of the product with the same symmetry. Throughout the process, the symmetry of the orbitals is conserved.

{| class="wikitable" border="1"
|+ '''The Transition State of the Diels Alder Reaction, Endo and Exo'''
! [[Image:Sk1406_endo_ts_input.jpg|Endo TS Input Structure|thumb]] !! [[Image:Sk1406_endo_ts_homo.jpg|Endo TS HOMO|thumb]]
|-
| [[Image:Sk1406_exo_ts_input.jpg|Exo TS Input Structure|thumb]] || [[Image:Sk1406_exo_ts_homo.jpg|Exo TS HOMO|thumb]]
|}

The transition state was modelled according to the first method described in the instructions. The bicyclo[2.2.2]octane ring system was drawn and two methylene groups removed. This gave the "envelope" structure of an ethylene molecule approaching a butadiene molecule from the top face. The length of the two forming bonds was set to 2.2 A. This seemed like a reasonable value, as it had worked for the Cope rearrangement. A job of the type opt+freq with the AM1 method was started. Optimization to a TS (Berny), calculation of force constants once, and opt=noeigen. The job completed successfully with one imaginary frequency (indicating that Gaussian minimized to a TS) of -955.629 cm-1. Animating this vibration showed the atomic motion corresponding to and expected from the Diels Alder cycloaddition. The atoms of the ethylene molecule close in on the terminal atoms of butadiene in a concerted fashion. Pertinent geometrical data of the transition state are presented in the table.

It is interesting to note that the bond lengths of a group of four bonds (that does not include the two new sigma bonds being formed) are almost equal at 1.38-1.39 A, intermediate in length of a C-C single and double bond. This partial bond length equalization supports the concept of an aromatic transition state!

=== References Mini Project ===

1. A. Neugebauer, G. Häfelinger, ''Int. J. Mol. Sci.'', '''2005''', 6, 157

2. Arduengo, A. J. et al., ''J. Am. Chem. Soc.'', '''1991''', 113, 361

3. A. J. Arduengo et al., ''J. Am. Chem. Soc.'', '''1992''', 114, 5530-5534

4. W. A. Herrmann, ''Angew. Chem. Int. Ed.'', '''2002''', 41, 1290

5. W. A. Herrmann et al., ''Angew. Chem. Int. Ed.'', '''1992''', 31, 1485

6. G. Frenking, C. Boehme, ''J. Am. Chem. Soc.'', '''1996''', 118, 2039-2046

Rep:Mod:certiorari3

2008-12-12T12:07:25Z

Sk1406:

= Third Year Computational Chemistry Lab, by Simon Krautwald =

== Module 3 - The Transition State ==

=== Tutorial ===

A structure for 1,5-hexadiene was drawn with the central C-C bond featuring the an ''anti'' arrangement of the R groups and then cleaned up using the "Clean" function. It was optimized using Gaussian at the HF/3-21G level. The same was done for a molecule with a gauche conformation at the central bond. Pertinent data from the analysis of the results are presented in the table below. The gauche form can be expected to have the higher energy due to the smaller dihedral angle (60 degrees as opposed to 180) between the more bulky R groups on the central C-C bond.

The anti energy obtained agrees with that of conformation anti4 in appendix 1, the gauche one with that of gauche3. Interestingly, the gauche conformation is of lower energy than the anti conformation, and the gauche3 conformation obtained is actually the lowest energy conformation overall.

{| class="wikitable" border="1"
|+ '''Selected Conformations of 1,5-Hexadiene'''
! [[Image:Sk1406_hexadiene_anti4_conf.jpg|Hexadiene anti4 conformation|thumb]] !! [[Image:Sk1406_hexadiene_gauche3_conf.jpg|Hexadiene gauche3 conformation|thumb]]
|}

For the generation of the anti2 conformation with Ci symmetry, the optimized anti4 conformation was taken as a starting point. In anti4, one of the dihedral angles of four carbon atoms is almost zero degrees, whereas the other one is 114.534. The zero degree one was manually set to -114.534 degrees to approximately give the molecule a centre of inversion. HF/3-21G optimization then followed. The energy obtained agreed with the one quoted in appendix 1. After symmetrizing the structure (Default Tolerance), the point group was identified as Ci.

Some bond lengths, bond angles and dihedral angles for the HF and DFT results are presented in the table. There are no significant differences. The B3LYP/6-31G(d) optimized geometry was then submitted again in order to calculate the vibrational frequencies. The job summary indicated zero imaginary frequencies, which means that the geometry was really optimized to a minimum.

From the output file of the frequency job, the following data was obtained:

Sum of electronic and zero-point Energies= -234.469195 (Potential Energy at 0K, E = Eelec + ZPE)

Sum of electronic and thermal Energies= -234.461847 (Energy at 298.15K and 1 atm, E = E + Evib + Erot + Etrans)

Sum of electronic and thermal Enthalpies= -234.460903 ( H = E + RT, important for dissociation reactions)

Sum of electronic and thermal Free Energies= -234.500782 (includes entropic contribution to free energy, G = H - TS)

include data for 0 K, comment on what the data means.

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

The allyl fragment was optimized at the HF/3-21G level. Following the instructions, the transition state of the Cope rearrangement was then set up manually by moving two allyl fragments into position. A picture of this is shown below. In it, the C-C distance of approximately 2.2 A is highlighted. Also, the chair shape, with all C-H bonds staggered, can be seen clearly. The TS optimization job was run and finished successfully - the summary indicated that there was one negative frequency of 817.977 cm-1.

[[Image:Sk1406_1st_guess_chair_TS.jpg|Initial Guess of the Chair TS Structure]]

The vibration is one that brings one terminus on each allyl fragment very close to one terminus on the other allyl fragment, while the other two termini are moved further away from one another. This is the Cope rearrangement, the formation of one sigma bond at the expense of another one being broken.

</jmol> '''3D view of the TS of the Cope Rearrangement''' <jmol>
<jmolApplet>
<title>TSCopeRearrange</title><color>white</color><size>300</size>
<script>zoom 80; cpk -25;frame 1; move 10 -20 10 0 0 0 0 0 3; delay 1;</script>
<uploadedFileContents>Sk1406_cope_rearrange_1st_ts.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable" border="1"
|+ '''Pictures for Chair Transition State Optimization'''
! [[Image:Sk1406_renumbered_SM_and_PDT.jpg|Renumbered Starting Material|thumb]] !! [[Image:Sk1406_1st_failed_QTS2_opt.jpg|Failed QST2 Optimization|thumb]]
|-
| [[Image:Sk1406_cope_boat_ts.jpg|Cope Boat TS|thumb]] || [[Image:Sk1406_vibration_boat_ts.jpg|Vibration in Cope Boat TS|thumb]]
|}

Thermochemical Data for the Chair TS at B3LYP/6-31G(d)/a.u.:

Sum of electronic and zero-point Energies= -234.414930

Sum of electronic and thermal Energies= -234.409009

Sum of electronic and thermal Enthalpies= -234.408065

Sum of electronic and thermal Free Energies= -234.443815

The first QTS2 optimization at HF/3-21G failed. An image is included showing the reason. Gaussian merely tried to connect the termini of the two allyl fragments from the geometry it was given, it did not rotate about bonds to find a chair or boat transition state. Hence the "crossover" or X-shaped transition state. d(C1-C6) = 4.32553 d(C3-C4)=3.48200, much longer than any forming or breaking C-C bond would be in reality, and much longer than the 2.02 A found for the chair TS using the above methods.

=== The Diels Alder Cycloaddition ===

The frontier molecular orbitals of butadiene are presented in the table below. The HOMO is antisymmetric with respect to the plane bisecting the central C-C bond, the LUMO is symmetric:

HOMO - a

LUMO - s

{| class="wikitable" border="1"
|+ '''The FMOs of Butadiene'''
! [[Image:Sk1406_cis_butadiene_homo.jpg|HOMO of Butadiene|thumb]] !! [[Image:Sk1406_cis_butadiene_lumo.jpg|LUMO of Butadiene|thumb]]
|}

This means that in any Diels Alder reaction of butadiene, either the HOMO of butadiene will have to overlap with an antisymmetric LUMO on the dienophile (such as the Pi* on ethylene) OR the LUMO of butadiene will have to overlap with a symmetric HOMO on the dienophile (such as the Pi orbital on ethylene). Which of the two processes is envisaged to happen usually depends on how electron rich or deficient the components are. For a normal electron demand DA, the diene is the electron rich component and the dienophile contributes the electron deficient double bond (as in the case of maleic anhydride).

{| class="wikitable" border="1"
|+ '''The Transition State of the Diels Alder Reaction'''
! [[Image:Sk1406_DA_TS_1.jpg|Diels Alder TS Image 1|thumb]] !! [[Image:Sk1406_DA_TS_2.jpg|Diels Alder TS Image 2|thumb]]
|-
| [[Image:Sk1406_da_ts_homo.jpg|Diels Alder TS HOMO|thumb]] || [[Image:Sk1406_da_ts_lumo.jpg|Diels Alder TS Labels|thumb]]
|-
| [[Image:Sk1406_DA_TS_labels.jpg|Diels Alder TS Labels|thumb]]
|}

{| class="wikitable" border="1"
|+ '''The Transition State of the Diels Alder Reaction'''
! [[Image:Sk1406_endo_ts_input.jpg|Endo TS Input Structure|thumb]] !! [[Image:Sk1406_endo_ts_homo.jpg|Endo TS HOMO|thumb]]
|-
| [[Image:Sk1406_exo_ts_input.jpg|Exo TS Input Structure|thumb]] || [[Image:Sk1406_exo_ts_homo.jpg|Exo TS HOMO|thumb]]
|}

The transition state was modelled according to the first method described in the instructions. The bicyclo[2.2.2]octane ring system was drawn and two methylene groups removed. This gave the "envelope" structure of an ethylene molecule approaching a butadiene molecule from the top face. The length of the two forming bonds was set to 2.2 A. This seemed like a reasonable value, as it had worked for the Cope rearrangement. A job of the type opt+freq with the AM1 method was started. Optimization to a TS (Berny), calculation of force constants once, and opt=noeigen. The job completed successfully with one imaginary frequency (indicating that Gaussian minimized to a TS) of -955.629 cm-1. Animating this vibration showed the atomic motion corresponding to and expected from the Diels Alder cycloaddition. The atoms of the ethylene molecule close in on the terminal atoms of butadiene in a concerted fashion. Pertinent geometrical data of the transition state are presented in the table.

It is interesting to note that the bond lengths of a group of four bonds (that does not include the two new sigma bonds being formed) are almost equal at 1.38-1.39 A, intermediate in length of a C-C single and double bond. This partial bond length equalization supports the concept of an aromatic transition state!

=== References Mini Project ===

1. A. Neugebauer, G. Häfelinger, ''Int. J. Mol. Sci.'', '''2005''', 6, 157

2. Arduengo, A. J. et al., ''J. Am. Chem. Soc.'', '''1991''', 113, 361

3. A. J. Arduengo et al., ''J. Am. Chem. Soc.'', '''1992''', 114, 5530-5534

4. W. A. Herrmann, ''Angew. Chem. Int. Ed.'', '''2002''', 41, 1290

5. W. A. Herrmann et al., ''Angew. Chem. Int. Ed.'', '''1992''', 31, 1485

6. G. Frenking, C. Boehme, ''J. Am. Chem. Soc.'', '''1996''', 118, 2039-2046

2008-12-12T11:32:02Z

Sk1406:

Rep:Mod:certiorari3

Rep:Mod:certiorari3

2008-12-11T15:05:02Z

Sk1406: