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Rep:Mod:hz2b

2012-03-01T12:53:50Z

Fs1309: Created page with "afkluhqO ;L"

afkluhqO ;L

Rep:Mod:fs1309module 3

2011-11-11T12:41:15Z

Fs1309:

3rd year computational lab Module 3 Transition states and reactivity.

Abstract:

This module aims to characterize transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions. This can be achieved by applying molecular orbital-based methods, solving the Schrodinger equation numerically, and locating transition structures based on the local shape of a potential energy surface. Together with showing what transition structures look like, reaction paths and barrier heights can also be calculated.

Part 1:

The Cope Rearrangement Tutorial [[Image:pic1.jpg|right|150px|Cope rearrangement]]

1)Optimizing the Reactants at HF/3-21G level theory. The energy of different conformers can be found in the summary table after optimization, and the symmetry is determined using '''Symmetrize''' under Edit menu. The table below shows the structures of optimized conformers and their energies.

{| class="wikitable" border="1"
|+ Table showing different conformers and their energy and comparisons to contents in appendix 1
! Conformer !! Structure !!point group!!Energy (Comparison to literature value) / a.u.!!Relative energy /kcalmol-1!!Summary Table
|-
| gauche1 ||[[Image:Structure_gauche_1.JPG|thumb|widthpx| ]]||C2||-231.68771613 (-231.68772 )||3.10 || [[Image:Summary_of_gauche_1.JPG|thumb|150px|Summary table for gauche 1]]
|-
| gauche2 ||[[Image:Structure_gauche_2.JPG|thumb|widthpx| ]]||C2||-231.69166702 (-231.69167 )||0.62 || [[Image:Summary_of_gauche_2.JPG|thumb|150px|Summary table for gauche 2]]
|-
| gauche3 ||[[Image:Structure_gauche_3.JPG|thumb|widthpx| ]]||C1||-231.69266120 (-231.69266 )||0.00 || [[Image:Summary_of_gauche_3.JPG|thumb|150px|Summary table for gauche 3]]
|-
| gauche4 ||[[Image:Structure_gauche_4.JPG|thumb|widthpx| ]]||C2||-231.69153032 (-231.69153 )||0.71 || [[Image:Summary_of_gauche_4.JPG|thumb|150px|Summary table for gauche 4]]
|-
| gauche5 ||[[Image:Structure_gauche_5.JPG|thumb|widthpx| ]]||C1||-231.68961572 (-231.68962 )||1.91 || [[Image:Summary_of_gauche_5.JPG|thumb|150px|Summary table for gauche 5]]
|-
| gauche6 ||[[Image:Structure_gauche_6.JPG|thumb|widthpx| ]]||C1||-231.68916017 (-231.68916 )||2.20|| [[Image:Summary_of_gauche_6.JPG|thumb|150px|Summary table for gauche 6]]
|-
| anti1 ||[[Image:Structrue_anti_1.jpg|thumb|widthpx| ]]||C2||-231.69260220 (-231.69260 )||0.04 || [[Image:Summary_of_anti_1.jpg|thumb|150px|Summary table for anti 1]]
|-
| anti2 ||[[Image:Structrue_anti_2.jpg|thumb|widthpx| ]]||Ci||-231.69253494 (-231.69254 )||0.08 || [[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table for anti 2]]
|-
| anti3 ||[[Image:Structrue_anti_3.jpg|thumb|widthpx| ]]||C2h||-231.68907066 (-231.68907 )||2.25 || [[Image:Summary_of_anti_3.jpg|thumb|150px|Summary table for anti 3]]||
|-
| anti4 ||[[Image:Structrue_anti_4.jpg|thumb|widthpx| ]]||C1||-231.69097054 (-231.69097 )||1.06|| [[Image:Summary_of_anti_4.jpg|thumb|150px|Summary table for anti 4]]
|}

Reoptimization and frequency analysis of Anti 2 conformer at B3LYP/6-31G* level after optimization at HF/6-31G level of theory.

Section 1 Optimization
{| class="wikitable" border="1"
|+ Comparison of results between HF/3-21G and B3LYP/6-31G*
! Method !! Structure!! Energy / a.u. (literature value)!!Summary table
|-
| HF/3-21G ||[[Image:Structrue_anti_2_HF.JPG|thumb|widthpx| ]] ||-231.692535 (-231.692535 )||[[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table]]
|-
| B3LYP/6-31G* || [[Image:Structrue_anti_2_DFT.JPG|thumb|widthpx| ]]||-234.611699 (-234.611710 )||[[Image:Summary_of_anti_2_dft.JPG|thumb|150px|Summary table]]
|}

Change in structure: [[Image:Comparison_2.JPG|right|200px|Comparison]]
The two structure are very similar, the small differences is found after comparing their total energies and geometric parameters such as bond angle, dihedral angle and bone length data obtained for the identical molecule but with different level of theory. It is noted that: 1)The total energy predicted at HF/6-31G level is much lower than what was obtained at B3LYP/6-31G* level, the relative energy is 2) The bond lengths obtained at HF/3-21G level are in general slightly shorter than those obtained at B3LYP/6-31G* level; 3) The most significant differences are found in the dihedral angle between central atoms and alkene carbon atoms, e.g: H(9)-C(6)-C(2)-C(1) C(7)-C(6)-C(2)-C(1). The maximum difference in dihedral angle is around 4°.

Section 2 Frequency analysis
[[Image:IR_spectrum 2.JPG|right|250px|Infra red spectrum ]]

No imaginary frequencies are found after checking the vibration results and spectrum, this means the optimized structure is not a transition structure. The thermochemistry data below are obtained from the output file.
Sum of electronic and zero-point Energies(E=Eelec+ZPE)= -234.469231
Sum of electronic and thermal Energies(E=E+Evib+Erot+Etrans)=-234.461865
Sum of electronic and thermal Enthalpies(E=E+RT)=-234.460920
Sum of electronic and thermal Free Energies(G=H-TS)=-234.500877

2) Optimizing the "Chair" and "Boat" Transition Structures

Section 1. Single allyl fragment optimization using the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Results of single allyl fragment optimization
! Structure of allyl fragement !! Summary table!!Comparison to transition structure
|-
| [[Image:Allyl.JPG|thumb|150px|Structure of Allyl fragment]] || [[Image:Summary.JPG|thumb|150px|Summary table of allyl fragment]]|| [[Image:Chair_HF.JPG|thumb|150px| ]]
|}

The structure of single allyl fragment look like one half of the transition structures shown.

Section 2. Chair two allyl fragments optimization

{| class="wikitable" border="1"
|+ Comparison of optimized structures using different settings
! Optimization setting !! Transition Structure !! Summary table!!Bond forming /breaking distance/ Å
|-
| Method in (b) ||[[Image:Opt_b.JPG|thumb|150px|Transition structure obtained from method 1]] ||[[Image:Summary_table_opt_b.JPG|thumb|150px|Summary table]]||2.02||
|-
| Method in (c)||[[Image:Opt_c.JPG|thumb|150px|Transition structure obtained from method 2]] ||[[Image:Summary_table_opt_c.JPG|thumb|150px|Summary table]]|| 2.20||
|-
| Method in (d)|| [[Image:Opt_d.JPG|thumb|150px|Transition structure obtained from method 3]] ||[[Image:Summary_table_opt_d.JPG|thumb|150px|Summary table]]|| 2.02||
|}

[[Image:Animation_of_imaginary_freq_b.gif|right|150px|Imaginary frequency at -817.87cm-1]]
This animation of imaginary frequency at -817.87cm-1 (as shown on the right) corresponds to the Cope rearrangement as it shows both bond forming and breaking at different ends of two allyl fragments in the transition structure .

Section 3 Optimization of the boat transition structure using QST2 method

The reactant and product were firstly numbered using ''atom list'' under edit menu, the first QST2 trial failed. After modification by changing the central C-C-C-C (C2-C3-C4-C5) dihedral angle to 0o, followed by reduce the inside angle (C2-C3-C4 and C3-C4-C5) to 100o, a more reasonable boat transition structure was obtained.

{| class="wikitable" border="1"
|+ Table showing labeling of atoms in reactants and products
! Component !! Picture of component!!Picture of component (modified)
|-
| Reactant || [[Image:Labeling_of_reactant.JPG|thumb|widthpx|cLabeling in reatant]] ||[[Image:Labeling_of_modified_reactant.JPG|thumb|widthpx|Labeling in modified reactant]] ||
|-
| Product || [[Image:Labeling_of_product.JPG|thumb|widthpx|cLabeling in product]] ||[[Image:Labeling_of_modified_product.JPG|thumb|widthpx|cLabeling in modified product]] ||
|-
| Transition structure || -- ||[[Image:Transition_state_1.JPG|thumb|widthpx| ]] ||
|}

The imaginary frequency was found at -840.01 cm-1. The corresponding motion is shown on the right. [[Image:Imaginary_frequency.JPG|right|150px|Motion corresponding to the imaginary frequency]]

f) Optimization of chair transition structure using IRC method

IRC method is used here to predict which conformer the reaction paths from the transitions structures will lead to.

{| class="wikitable" border="1"
|+ Table showing conformations and energies of IRC methods
! Method !!Description of method!! Conformations !! Energy / a.u.
|-
| Initial Method ||minimization with 50 points along IRC ||[[Image:Chair_IRC_initial_stucture.JPG|thumb|150px| ]]||-231.68321543
|-
| Method 1 ||Normal minimization using the last point on IRC after initial method || [[Image:Method_1.JPG|thumb|150px| ]]||-231.69166702
|-
| Method 2 ||Minimization with 200 points along IRC|| [[Image:Method_2.JPG|thumb|150px| ]]||-231.61932195
|-
| Method 3 ||IRC with force constant specified at every step || [[Image:Method_3.JPG|thumb|150px| ]]||-231.69165600
|}
Method 1: take the last point on the IRC and run a normal minimization;
Method 2: restart the IRC and specify a larger number of points until it reaches a minimum;
Method 3: redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches.

Similar conformers are obtained from method 1 and 3, which indicates the transition structures connect to the Gauche 2 conformer.

Activation energy analysis.

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from HF/3-21G
! !! Electronic energy (literature)/a.u.!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-231.619322 (-231.619322 )||-231.466696 (-231.466705)|| -231.477029(-234.461346)||[[Image:Chair_HF.JPG|thumb|100px| ]]|| [[Image:Chair_HF_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-231.602802 (-231.602802 )||-231.450929 (-231.450929 )|| -231.445301(-234.445300)||[[Image:Boat_HF.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 ||-231.692535 (-231.692535 )||-231.539541 (-231.539539|| -231.532569 -234.532566)||[[Image:Structrue_anti_2.jpg|thumb|100px| ]]|| [[Image:Summary_of_anti_2.jpg|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from B3LYP/6-31G*
! !! Electronic energy /a.u.(literature)!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-234.556983 (-234.556983 )||-234.414919 (-234.414919 )||-234.409010 (-234.408998)||[[Image:Chair_dft.JPG|thumb|100px| ]]|| [[Image:Chair_dft_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-234.543093 (-234.543093 )||-234.402340(-234.402340 )||(-234.396006)||[[Image:Boat_dft.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 || -234.611699 (-234.611710 )||-231.469242(-234.469203 )||-234.461865(-234.461856)||[[Image:DFT_method_anti_2.JPG|thumb|100px| ]]|| [[Image:Summary_of_anti_2_dft.JPG|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary table of activation energy obtained at different theory level and temperature
! Transition structure !! HF/3-21G at 0K /(kcal/mol)!!HF/3-21G at 298.15K/(kcal/mol)!!B3LYP/6-31G* at 0K/(kcal/mol)!!B3LYP/6-31G* at 298.15K/(kcal/mol)!!Expt. /(kcal/mol)
|-
| Chair ||45.71 (45.70) ||44.69(44.69)||34.09(34.06)||33.23(33.17)||33.5±0.5
|-
| Boat ||55.60 (55.60) ||55.12(54.76)||41.98(41.96)||(41.32)||44.7±2.0
|}
The numbers in bracket are literature values in appendix 2.

Comment on the results: The electronic energy and the sum of electronic and zero point energies both match the literature values very well, but the actual calculated values of the sum of electronic and thermal energies show a small difference with data given in appendix 2. This could only due to errors introduced during the calculation, as overall activation energies still match the literature value very well.

Part 2 Exercise AM1 semi empirical orbital method is used here for initial calculation, followed by calculation at HF/3-21G theory level for further transition structure optimization.

Section 1 Optimization of cis butadiene and determination of the symmetry of corresponding HOMO and LUMO [[Image:Am_1.JPG|right|150px|Summary table ]]

{| class="wikitable" border="1"
|+ Table of cis-butadiene's HOMO and LUMO and their symmetries
! Orbital !! Plot of orbital!!Symmetry with respect to the plane
|-
| HOMO || [[Image:HOMO.jpg|thumb|100px|HOMO]]|| [[Image:HOMO_symmetry_plane.jpg|thumb|100px|anti-symmetric with respect to the plane]] ||
|-
| LUMO || [[Image:LUMO.jpg|thumb|100px|LUMO]]|| [[Image:LUMO_symmetry_plane.jpg|thumb|100px|symmetric with respect to the plane]]||
|}

Section 2 Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path.

{| class="wikitable" border="1"
|+ Table of HOMO and LUMO to illustrate symmetry in the transition structure
! MO !! Picture of MO!!Symmetry of MO!!Interacting orbitals
|-
| HOMO ||[[Image:HOMO 1 .jpg |thumb|100px| ]]||Anti-symmetric with respect to the symmetry plane|| [[Image:Homo_of_diene.JPG|thumb|widthpx| ]]
|-
| LUMO || [[Image:LUMO 2 .jpg |thumb|100px| ]]||Symmetric with respect to the symmetry plane||[[Image:Lumo_of_diene.JPG|thumb|widthpx| ]]
|}

The Diels Alder reaction here, which involves two new α bonds forming due to the interaction between the diene's HOMO/LUMO and dienophile's LUMO/HOMO interaction, is a class of pericyclic reactions. Such reaction can only proceed if the π/π* orbitals involved have correct symmetry. According to the selection rules in pericyclic reaction, such 6 electrons system can interact if the stereochemistry of two interacting orbitals are supra facial or two anti-facial. The HOMO and LUMO obtained from the transition structures both are consistent with the stereochemistry in the selection rules, as the HOMO show suprafacial interaction between diene and dienophile's interacting orbitals (HOMO of diene and LUMO of dieneophile), and LUMO show suprafacial interaction between diene and dienophile's interacting orbitals (LUMO of diene and HOMO of dieneophile).

[[Image:Transition_structure 1.JPG|thumb|200px|Labeling of transition structure]]

{| class="wikitable" border="1"
|+ Table comparing bond length in transition structure and typical sp3 and sp2 C-C bond lengths
! Level of theory!!Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !!Bonding between (n)C and (n')C !! Bond length/Å
|-
| Semi-empirical AM1||(2)C --(12)C and (3)C --(9)C || 2.12||(2)C --(1)C and (3)C --(4)C||1.38||(1)C and (4)C||1.40||(1)C and (4)C||1.38
|-
| HF/3-21G||(2)C --(12)C and (3)C --(9)C || 2.21||(2)C --(1)C and (3)C --(4)C||1.37||(1)C and (4)C||1.39||(1)C and (4)C||1.38
|}

n and n' here are used to indicate the bonding carbon atoms. The 6 electrons system can interact when stereochemistry of two interacting orbitals are supra facial or two anti-facial.

[[Image:Positive_frequency.JPG|left|200px| ]] Similar structures were obtained for AM1 and HF/3-21G method, the only difference is the distance between diene and dienophile. According to the literature, the typical bond lengths of sp3 and sp2 C-C bond are 1.54Å and 1.34Å respectively, the van der waal's radius of carbon is 1.70Å. The newly form α bonds origin from 1) breaking of C-C double, 2) two partly formed α bonds between diene and dienophile. The first cases can be proven as the double bonds in dienophile and diene are longer than the typical carbon carbon double bond length, but shorter than the typical C-C α bond;[[Image:Animation 2.JPG|thumb|200px| Animation of imaginary frequency]] and the α bond length in the cie-butadiene has shortened significantly. As the diene and dienophile are two separate components before the Diels Alder reaction, a typical carbon van der waal's radius can be used here to approximate the distance between these carbons before the reaction, which is around 3.40Å (=2*1.70Å). While in the transition structure, this distance has been shortened significantly to 2.12Å. This can be further proven by looking at the animation of imaginary frequency at -955.87cm-1, the ends of dienophile and diene are getting closer to each other. This also proves the fact that two new α bonds are partly forming in the transition structure. The diene and dienophile do not approach to each other to form α bonds between them in the animation of the lowest positive frequency(as shown in the left).

Section 3 Diels Alder reaction between cyclohexa-1,3-diene reaction with maleic anhydride:

This reaction can proceed as the π/π* orbitals involved have correct symmetry.
{| class="wikitable" border="1"
|+ Table showing structure, energies and summary table of endo and exo transition structure
! Type of transition structure!!Transition structure by AM1!! Energy / a.u.!!Summary table!!Transition structure by HF/3-21G!! Energy / a.u.!!Summary table
|-
| Endo || [[Image:Endo.JPG|thumb|150px|Endo structure]]||-0.05150440||[[Image:Summary_table_endo.JPG|thumb|150px|Summary table of Endo]]||[[Image:Hf.jpg|thumb|150px| ]]||-605.61036805||[[Image:Hf_summary.JPG|thumb|150px| ]]
|-
| Exo || [[Image:Exo.JPG|thumb|150px|Exo structure]]||-0.05041965||[[Image:Summary_table_exo.JPG|thumb|150px|Summary table of Exo]]||[[Image:Exo_hf.JPG|150px| ]]||-605.60359120||[[Image:Exo_hf_summary.JPG|thumb|150px| ]]
|}

[[Image:Electronic_repulsion.JPG|right|200px|Electronic repulsion between C-H α orbital and C=O π orbital]]The endo transition structure is lower in energy than the exo structure by 0.71kcal/mol if calculation is done with semi-empirical AM1 method, but opposite results were obtained for HF/3-21G method. The structural different between the endo and exo is due to the different orientations of maleic anhydride. A possible reason for exo form is more strained is due to the electronic repulsion between electrons in C-H α orbital (atom 1 and 2) and C=O π orbital (atom 3 and 4) in the exo form (as shown on the right). This results in an increase in energy of the transition structure. Such interaction does not happen in the endo form as the C-H α orbitals are now very far apart from each other.

{| class="wikitable" border="1"
|+ Table showing HOMO and their nodal properties in endo and exo form
! Transition structure !! Picture of HOMO!!Nodal property!!Illustration of secondary orbital interactions!!
|-
| Endo || [[Image:Homo_endo.jpg|thumb|150px| ]]||Two nodal points between the -(C=O)-O-(C=O)- fragment and the remainder of the system||[[Image:Orbital_interaction_1.JPG|thumb|150px|Secondary orbital interaction]]
|-
| Exo || [[Image:Homo_exo.jpg|thumb|150px| ]]||One nodal points between the -(C=O)-O-(C=O)- fragment and the remainder of the system||[[Image:No_Orbital_interaction.JPG|thumb|150px|No secondary orbital interaction]]
|}

[[Image:Stabilization.JPG|right|150px| ]]The secondary orbital interaction is a class of electronic effect which can be rationalized here as the interactions between C=C π orbital and the C=O π* orbital as they have both correct symmetry and orientation. The resultant effect can stabilize the system by trading off the weakening the C=O double bond.

The secondary orbital overlap effect had been neglected in the AM1 calculation because the endo transition structure is higher in energy than than of exo transition structure, which contradicts with the experimental observations. As in reality, the endo product predominate over hermodynamically more stable exo productthe as it is the kinetically favorable product unless thermodynamical condition is applied. This is due to the secondary orbital overlap effect in the endo form transition state, such effect can stabilize the endo transition structure and provide a lower energy pathway for the reaction to proceed despite the fact that the exo product is thermodynamically more stable as it has less strain compare the to the endo product.

Reference:
#Yi Li, K. N. Houk J. Am. Chem. Soc., 1993, 115 (16), pp 7478–7485
#Shogo SakaiJ. Phys. Chem. A, 2000, 104 (5), pp 922–927
#Fleming, Ian Pericyclic reactions : Oxford University Press 1998

File:Orbital interaction 1.JPG

2011-11-11T12:41:08Z

Fs1309:

Rep:Mod:fs1309module 3

2011-11-11T12:38:49Z

Fs1309:

3rd year computational lab Module 3 Transition states and reactivity.

Abstract:

This module aims to characterize transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions. This can be achieved by applying molecular orbital-based methods, solving the Schrodinger equation numerically, and locating transition structures based on the local shape of a potential energy surface. Together with showing what transition structures look like, reaction paths and barrier heights can also be calculated.

Part 1:

The Cope Rearrangement Tutorial [[Image:pic1.jpg|right|150px|Cope rearrangement]]

1)Optimizing the Reactants at HF/3-21G level theory. The energy of different conformers can be found in the summary table after optimization, and the symmetry is determined using '''Symmetrize''' under Edit menu. The table below shows the structures of optimized conformers and their energies.

{| class="wikitable" border="1"
|+ Table showing different conformers and their energy and comparisons to contents in appendix 1
! Conformer !! Structure !!point group!!Energy (Comparison to literature value) / a.u.!!Relative energy /kcalmol-1!!Summary Table
|-
| gauche1 ||[[Image:Structure_gauche_1.JPG|thumb|widthpx| ]]||C2||-231.68771613 (-231.68772 )||3.10 || [[Image:Summary_of_gauche_1.JPG|thumb|150px|Summary table for gauche 1]]
|-
| gauche2 ||[[Image:Structure_gauche_2.JPG|thumb|widthpx| ]]||C2||-231.69166702 (-231.69167 )||0.62 || [[Image:Summary_of_gauche_2.JPG|thumb|150px|Summary table for gauche 2]]
|-
| gauche3 ||[[Image:Structure_gauche_3.JPG|thumb|widthpx| ]]||C1||-231.69266120 (-231.69266 )||0.00 || [[Image:Summary_of_gauche_3.JPG|thumb|150px|Summary table for gauche 3]]
|-
| gauche4 ||[[Image:Structure_gauche_4.JPG|thumb|widthpx| ]]||C2||-231.69153032 (-231.69153 )||0.71 || [[Image:Summary_of_gauche_4.JPG|thumb|150px|Summary table for gauche 4]]
|-
| gauche5 ||[[Image:Structure_gauche_5.JPG|thumb|widthpx| ]]||C1||-231.68961572 (-231.68962 )||1.91 || [[Image:Summary_of_gauche_5.JPG|thumb|150px|Summary table for gauche 5]]
|-
| gauche6 ||[[Image:Structure_gauche_6.JPG|thumb|widthpx| ]]||C1||-231.68916017 (-231.68916 )||2.20|| [[Image:Summary_of_gauche_6.JPG|thumb|150px|Summary table for gauche 6]]
|-
| anti1 ||[[Image:Structrue_anti_1.jpg|thumb|widthpx| ]]||C2||-231.69260220 (-231.69260 )||0.04 || [[Image:Summary_of_anti_1.jpg|thumb|150px|Summary table for anti 1]]
|-
| anti2 ||[[Image:Structrue_anti_2.jpg|thumb|widthpx| ]]||Ci||-231.69253494 (-231.69254 )||0.08 || [[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table for anti 2]]
|-
| anti3 ||[[Image:Structrue_anti_3.jpg|thumb|widthpx| ]]||C2h||-231.68907066 (-231.68907 )||2.25 || [[Image:Summary_of_anti_3.jpg|thumb|150px|Summary table for anti 3]]||
|-
| anti4 ||[[Image:Structrue_anti_4.jpg|thumb|widthpx| ]]||C1||-231.69097054 (-231.69097 )||1.06|| [[Image:Summary_of_anti_4.jpg|thumb|150px|Summary table for anti 4]]
|}

Reoptimization and frequency analysis of Anti 2 conformer at B3LYP/6-31G* level after optimization at HF/6-31G level of theory.

Section 1 Optimization
{| class="wikitable" border="1"
|+ Comparison of results between HF/3-21G and B3LYP/6-31G*
! Method !! Structure!! Energy / a.u. (literature value)!!Summary table
|-
| HF/3-21G ||[[Image:Structrue_anti_2_HF.JPG|thumb|widthpx| ]] ||-231.692535 (-231.692535 )||[[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table]]
|-
| B3LYP/6-31G* || [[Image:Structrue_anti_2_DFT.JPG|thumb|widthpx| ]]||-234.611699 (-234.611710 )||[[Image:Summary_of_anti_2_dft.JPG|thumb|150px|Summary table]]
|}

Change in structure: [[Image:Comparison_2.JPG|right|200px|Comparison]]
The two structure are very similar, the small differences is found after comparing their total energies and geometric parameters such as bond angle, dihedral angle and bone length data obtained for the identical molecule but with different level of theory. It is noted that: 1)The total energy predicted at HF/6-31G level is much lower than what was obtained at B3LYP/6-31G* level, the relative energy is 2) The bond lengths obtained at HF/3-21G level are in general slightly shorter than those obtained at B3LYP/6-31G* level; 3) The most significant differences are found in the dihedral angle between central atoms and alkene carbon atoms, e.g: H(9)-C(6)-C(2)-C(1) C(7)-C(6)-C(2)-C(1). The maximum difference in dihedral angle is around 4°.

Section 2 Frequency analysis
[[Image:IR_spectrum 2.JPG|right|250px|Infra red spectrum ]]

No imaginary frequencies are found after checking the vibration results and spectrum, this means the optimized structure is not a transition structure. The thermochemistry data below are obtained from the output file.
Sum of electronic and zero-point Energies(E=Eelec+ZPE)= -234.469231
Sum of electronic and thermal Energies(E=E+Evib+Erot+Etrans)=-234.461865
Sum of electronic and thermal Enthalpies(E=E+RT)=-234.460920
Sum of electronic and thermal Free Energies(G=H-TS)=-234.500877

2) Optimizing the "Chair" and "Boat" Transition Structures

Section 1. Single allyl fragment optimization using the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Results of single allyl fragment optimization
! Structure of allyl fragement !! Summary table!!Comparison to transition structure
|-
| [[Image:Allyl.JPG|thumb|150px|Structure of Allyl fragment]] || [[Image:Summary.JPG|thumb|150px|Summary table of allyl fragment]]|| [[Image:Chair_HF.JPG|thumb|150px| ]]
|}

The structure of single allyl fragment look like one half of the transition structures shown.

Section 2. Chair two allyl fragments optimization

{| class="wikitable" border="1"
|+ Comparison of optimized structures using different settings
! Optimization setting !! Transition Structure !! Summary table!!Bond forming /breaking distance/ Å
|-
| Method in (b) ||[[Image:Opt_b.JPG|thumb|150px|Transition structure obtained from method 1]] ||[[Image:Summary_table_opt_b.JPG|thumb|150px|Summary table]]||2.02||
|-
| Method in (c)||[[Image:Opt_c.JPG|thumb|150px|Transition structure obtained from method 2]] ||[[Image:Summary_table_opt_c.JPG|thumb|150px|Summary table]]|| 2.20||
|-
| Method in (d)|| [[Image:Opt_d.JPG|thumb|150px|Transition structure obtained from method 3]] ||[[Image:Summary_table_opt_d.JPG|thumb|150px|Summary table]]|| 2.02||
|}

[[Image:Animation_of_imaginary_freq_b.gif|right|150px|Imaginary frequency at -817.87cm-1]]
This animation of imaginary frequency at -817.87cm-1 (as shown on the right) corresponds to the Cope rearrangement as it shows both bond forming and breaking at different ends of two allyl fragments in the transition structure .

Section 3 Optimization of the boat transition structure using QST2 method

The reactant and product were firstly numbered using ''atom list'' under edit menu, the first QST2 trial failed. After modification by changing the central C-C-C-C (C2-C3-C4-C5) dihedral angle to 0o, followed by reduce the inside angle (C2-C3-C4 and C3-C4-C5) to 100o, a more reasonable boat transition structure was obtained.

{| class="wikitable" border="1"
|+ Table showing labeling of atoms in reactants and products
! Component !! Picture of component!!Picture of component (modified)
|-
| Reactant || [[Image:Labeling_of_reactant.JPG|thumb|widthpx|cLabeling in reatant]] ||[[Image:Labeling_of_modified_reactant.JPG|thumb|widthpx|Labeling in modified reactant]] ||
|-
| Product || [[Image:Labeling_of_product.JPG|thumb|widthpx|cLabeling in product]] ||[[Image:Labeling_of_modified_product.JPG|thumb|widthpx|cLabeling in modified product]] ||
|-
| Transition structure || -- ||[[Image:Transition_state_1.JPG|thumb|widthpx| ]] ||
|}

The imaginary frequency was found at -840.01 cm-1. The corresponding motion is shown on the right. [[Image:Imaginary_frequency.JPG|right|150px|Motion corresponding to the imaginary frequency]]

f) Optimization of chair transition structure using IRC method

IRC method is used here to predict which conformer the reaction paths from the transitions structures will lead to.

{| class="wikitable" border="1"
|+ Table showing conformations and energies of IRC methods
! Method !!Description of method!! Conformations !! Energy / a.u.
|-
| Initial Method ||minimization with 50 points along IRC ||[[Image:Chair_IRC_initial_stucture.JPG|thumb|150px| ]]||-231.68321543
|-
| Method 1 ||Normal minimization using the last point on IRC after initial method || [[Image:Method_1.JPG|thumb|150px| ]]||-231.69166702
|-
| Method 2 ||Minimization with 200 points along IRC|| [[Image:Method_2.JPG|thumb|150px| ]]||-231.61932195
|-
| Method 3 ||IRC with force constant specified at every step || [[Image:Method_3.JPG|thumb|150px| ]]||-231.69165600
|}
Method 1: take the last point on the IRC and run a normal minimization;
Method 2: restart the IRC and specify a larger number of points until it reaches a minimum;
Method 3: redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches.

Similar conformers are obtained from method 1 and 3, which indicates the transition structures connect to the Gauche 2 conformer.

Activation energy analysis.

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from HF/3-21G
! !! Electronic energy (literature)/a.u.!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-231.619322 (-231.619322 )||-231.466696 (-231.466705)|| -231.477029(-234.461346)||[[Image:Chair_HF.JPG|thumb|100px| ]]|| [[Image:Chair_HF_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-231.602802 (-231.602802 )||-231.450929 (-231.450929 )|| -231.445301(-234.445300)||[[Image:Boat_HF.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 ||-231.692535 (-231.692535 )||-231.539541 (-231.539539|| -231.532569 -234.532566)||[[Image:Structrue_anti_2.jpg|thumb|100px| ]]|| [[Image:Summary_of_anti_2.jpg|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from B3LYP/6-31G*
! !! Electronic energy /a.u.(literature)!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-234.556983 (-234.556983 )||-234.414919 (-234.414919 )||-234.409010 (-234.408998)||[[Image:Chair_dft.JPG|thumb|100px| ]]|| [[Image:Chair_dft_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-234.543093 (-234.543093 )||-234.402340(-234.402340 )||(-234.396006)||[[Image:Boat_dft.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 || -234.611699 (-234.611710 )||-231.469242(-234.469203 )||-234.461865(-234.461856)||[[Image:DFT_method_anti_2.JPG|thumb|100px| ]]|| [[Image:Summary_of_anti_2_dft.JPG|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary table of activation energy obtained at different theory level and temperature
! Transition structure !! HF/3-21G at 0K /(kcal/mol)!!HF/3-21G at 298.15K/(kcal/mol)!!B3LYP/6-31G* at 0K/(kcal/mol)!!B3LYP/6-31G* at 298.15K/(kcal/mol)!!Expt. /(kcal/mol)
|-
| Chair ||45.71 (45.70) ||44.69(44.69)||34.09(34.06)||33.23(33.17)||33.5±0.5
|-
| Boat ||55.60 (55.60) ||55.12(54.76)||41.98(41.96)||(41.32)||44.7±2.0
|}
The numbers in bracket are literature values in appendix 2.

Comment on the results: The electronic energy and the sum of electronic and zero point energies both match the literature values very well, but the actual calculated values of the sum of electronic and thermal energies show a small difference with data given in appendix 2. This could only due to errors introduced during the calculation, as overall activation energies still match the literature value very well.

Part 2 Exercise AM1 semi empirical orbital method is used here for initial calculation, followed by calculation at HF/3-21G theory level for further transition structure optimization.

Section 1 Optimization of cis butadiene and determination of the symmetry of corresponding HOMO and LUMO [[Image:Am_1.JPG|right|150px|Summary table ]]

{| class="wikitable" border="1"
|+ Table of cis-butadiene's HOMO and LUMO and their symmetries
! Orbital !! Plot of orbital!!Symmetry with respect to the plane
|-
| HOMO || [[Image:HOMO.jpg|thumb|100px|HOMO]]|| [[Image:HOMO_symmetry_plane.jpg|thumb|100px|anti-symmetric with respect to the plane]] ||
|-
| LUMO || [[Image:LUMO.jpg|thumb|100px|LUMO]]|| [[Image:LUMO_symmetry_plane.jpg|thumb|100px|symmetric with respect to the plane]]||
|}

Section 2 Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path.

{| class="wikitable" border="1"
|+ Table of HOMO and LUMO to illustrate symmetry in the transition structure
! MO !! Picture of MO!!Symmetry of MO!!Interacting orbitals
|-
| HOMO ||[[Image:HOMO 1 .jpg |thumb|100px| ]]||Anti-symmetric with respect to the symmetry plane|| [[Image:Homo_of_diene.JPG|thumb|widthpx| ]]
|-
| LUMO || [[Image:LUMO 2 .jpg |thumb|100px| ]]||Symmetric with respect to the symmetry plane||[[Image:Lumo_of_diene.JPG|thumb|widthpx| ]]
|}

The Diels Alder reaction here, which involves two new α bonds forming due to the interaction between the diene's HOMO/LUMO and dienophile's LUMO/HOMO interaction, is a class of pericyclic reactions. Such reaction can only proceed if the π/π* orbitals involved have correct symmetry. According to the selection rules in pericyclic reaction, such 6 electrons system can interact if the stereochemistry of two interacting orbitals are supra facial or two anti-facial. The HOMO and LUMO obtained from the transition structures both are consistent with the stereochemistry in the selection rules, as the HOMO show suprafacial interaction between diene and dienophile's interacting orbitals (HOMO of diene and LUMO of dieneophile), and LUMO show suprafacial interaction between diene and dienophile's interacting orbitals (LUMO of diene and HOMO of dieneophile).

[[Image:Transition_structure 1.JPG|thumb|200px|Labeling of transition structure]]

{| class="wikitable" border="1"
|+ Table comparing bond length in transition structure and typical sp3 and sp2 C-C bond lengths
! Level of theory!!Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !!Bonding between (n)C and (n')C !! Bond length/Å
|-
| Semi-empirical AM1||(2)C --(12)C and (3)C --(9)C || 2.12||(2)C --(1)C and (3)C --(4)C||1.38||(1)C and (4)C||1.40||(1)C and (4)C||1.38
|-
| HF/3-21G||(2)C --(12)C and (3)C --(9)C || 2.21||(2)C --(1)C and (3)C --(4)C||1.37||(1)C and (4)C||1.39||(1)C and (4)C||1.38
|}

n and n' here are used to indicate the bonding carbon atoms. The 6 electrons system can interact when stereochemistry of two interacting orbitals are supra facial or two anti-facial.

[[Image:Positive_frequency.JPG|left|200px| ]] Similar structures were obtained for AM1 and HF/3-21G method, the only difference is the distance between diene and dienophile. According to the literature, the typical bond lengths of sp3 and sp2 C-C bond are 1.54Å and 1.34Å respectively, the van der waal's radius of carbon is 1.70Å. The newly form α bonds origin from 1) breaking of C-C double, 2) two partly formed α bonds between diene and dienophile. The first cases can be proven as the double bonds in dienophile and diene are longer than the typical carbon carbon double bond length, but shorter than the typical C-C α bond;[[Image:Animation 2.JPG|thumb|200px| Animation of imaginary frequency]] and the α bond length in the cie-butadiene has shortened significantly. As the diene and dienophile are two separate components before the Diels Alder reaction, a typical carbon van der waal's radius can be used here to approximate the distance between these carbons before the reaction, which is around 3.40Å (=2*1.70Å). While in the transition structure, this distance has been shortened significantly to 2.12Å. This can be further proven by looking at the animation of imaginary frequency at -955.87cm-1, the ends of dienophile and diene are getting closer to each other. This also proves the fact that two new α bonds are partly forming in the transition structure. The diene and dienophile do not approach to each other to form α bonds between them in the animation of the lowest positive frequency(as shown in the left).

Section 3 Diels Alder reaction between cyclohexa-1,3-diene reaction with maleic anhydride:

This reaction can proceed as the π/π* orbitals involved have correct symmetry.
{| class="wikitable" border="1"
|+ Table showing structure, energies and summary table of endo and exo transition structure
! Type of transition structure!!Transition structure by AM1!! Energy / a.u.!!Summary table!!Transition structure by HF/3-21G!! Energy / a.u.!!Summary table
|-
| Endo || [[Image:Endo.JPG|thumb|150px|Endo structure]]||-0.05150440||[[Image:Summary_table_endo.JPG|thumb|150px|Summary table of Endo]]||[[Image:Hf.jpg|thumb|150px| ]]||-605.61036805||[[Image:Hf_summary.JPG|thumb|150px| ]]
|-
| Exo || [[Image:Exo.JPG|thumb|150px|Exo structure]]||-0.05041965||[[Image:Summary_table_exo.JPG|thumb|150px|Summary table of Exo]]||[[Image:Exo_hf.JPG|150px| ]]||-605.60359120||[[Image:Exo_hf_summary.JPG|thumb|150px| ]]
|}

[[Image:Electronic_repulsion.JPG|right|200px|Electronic repulsion between C-H α orbital and C=O π orbital]]The endo transition structure is lower in energy than the exo structure by 0.71kcal/mol if calculation is done with semi-empirical AM1 method, but opposite results were obtained for HF/3-21G method. The structural different between the endo and exo is due to the different orientations of maleic anhydride. A possible reason for exo form is more strained is due to the electronic repulsion between electrons in C-H α orbital (atom 1 and 2) and C=O π orbital (atom 3 and 4) in the exo form (as shown on the right). This results in an increase in energy of the transition structure. Such interaction does not happen in the endo form as the C-H α orbitals are now very far apart from each other.

{| class="wikitable" border="1"
|+ Table showing HOMO and their nodal properties in endo and exo form
! Transition structure !! Picture of HOMO!!Nodal property!!Illustration of secondary orbital interactions!!
|-
| Endo || [[Image:Homo_endo.jpg|thumb|150px| ]]||Two nodal points between the -(C=O)-O-(C=O)- fragment and the remainder of the system||[[Image:Orbital_interaction.JPG|thumb|150px| ]]
|-
| Exo || [[Image:Homo_exo.jpg|thumb|150px| ]]||One nodal points between the -(C=O)-O-(C=O)- fragment and the remainder of the system||[[Image:No_Orbital_interaction.JPG|thumb|150px| ]]
|}

[[Image:Stabilization.JPG|right|150px| ]]The secondary orbital interaction is a class of electronic effect which can be rationalized here as the interactions between C=C π orbital and the C=O π* orbital as they have both correct symmetry and orientation. The resultant effect can stabilize the system by trading off the weakening the C=O double bond.

The secondary orbital overlap effect had been neglected in the AM1 calculation because the endo transition structure is higher in energy than than of exo transition structure, which contradicts with the experimental observations. As in reality, the endo product predominate over hermodynamically more stable exo productthe as it is the kinetically favorable product unless thermodynamical condition is applied. This is due to the secondary orbital overlap effect in the endo form transition state, such effect can stabilize the endo transition structure and provide a lower energy pathway for the reaction to proceed despite the fact that the exo product is thermodynamically more stable as it has less strain compare the to the endo product.

Reference:
#Yi Li, K. N. Houk J. Am. Chem. Soc., 1993, 115 (16), pp 7478–7485
#Shogo SakaiJ. Phys. Chem. A, 2000, 104 (5), pp 922–927
#Fleming, Ian Pericyclic reactions : Oxford University Press 1998

File:No Orbital interaction.JPG

2011-11-11T12:38:07Z

Fs1309:

File:Orbital interaction.JPG

2011-11-11T12:38:07Z

Fs1309:

Rep:Mod:fs1309module 3

2011-11-11T12:31:51Z

Fs1309:

3rd year computational lab Module 3 Transition states and reactivity.

Abstract:

This module aims to characterize transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions. This can be achieved by applying molecular orbital-based methods, solving the Schrodinger equation numerically, and locating transition structures based on the local shape of a potential energy surface. Together with showing what transition structures look like, reaction paths and barrier heights can also be calculated.

Part 1:

The Cope Rearrangement Tutorial [[Image:pic1.jpg|right|150px|Cope rearrangement]]

1)Optimizing the Reactants at HF/3-21G level theory. The energy of different conformers can be found in the summary table after optimization, and the symmetry is determined using '''Symmetrize''' under Edit menu. The table below shows the structures of optimized conformers and their energies.

{| class="wikitable" border="1"
|+ Table showing different conformers and their energy and comparisons to contents in appendix 1
! Conformer !! Structure !!point group!!Energy (Comparison to literature value) / a.u.!!Relative energy /kcalmol-1!!Summary Table
|-
| gauche1 ||[[Image:Structure_gauche_1.JPG|thumb|widthpx| ]]||C2||-231.68771613 (-231.68772 )||3.10 || [[Image:Summary_of_gauche_1.JPG|thumb|150px|Summary table for gauche 1]]
|-
| gauche2 ||[[Image:Structure_gauche_2.JPG|thumb|widthpx| ]]||C2||-231.69166702 (-231.69167 )||0.62 || [[Image:Summary_of_gauche_2.JPG|thumb|150px|Summary table for gauche 2]]
|-
| gauche3 ||[[Image:Structure_gauche_3.JPG|thumb|widthpx| ]]||C1||-231.69266120 (-231.69266 )||0.00 || [[Image:Summary_of_gauche_3.JPG|thumb|150px|Summary table for gauche 3]]
|-
| gauche4 ||[[Image:Structure_gauche_4.JPG|thumb|widthpx| ]]||C2||-231.69153032 (-231.69153 )||0.71 || [[Image:Summary_of_gauche_4.JPG|thumb|150px|Summary table for gauche 4]]
|-
| gauche5 ||[[Image:Structure_gauche_5.JPG|thumb|widthpx| ]]||C1||-231.68961572 (-231.68962 )||1.91 || [[Image:Summary_of_gauche_5.JPG|thumb|150px|Summary table for gauche 5]]
|-
| gauche6 ||[[Image:Structure_gauche_6.JPG|thumb|widthpx| ]]||C1||-231.68916017 (-231.68916 )||2.20|| [[Image:Summary_of_gauche_6.JPG|thumb|150px|Summary table for gauche 6]]
|-
| anti1 ||[[Image:Structrue_anti_1.jpg|thumb|widthpx| ]]||C2||-231.69260220 (-231.69260 )||0.04 || [[Image:Summary_of_anti_1.jpg|thumb|150px|Summary table for anti 1]]
|-
| anti2 ||[[Image:Structrue_anti_2.jpg|thumb|widthpx| ]]||Ci||-231.69253494 (-231.69254 )||0.08 || [[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table for anti 2]]
|-
| anti3 ||[[Image:Structrue_anti_3.jpg|thumb|widthpx| ]]||C2h||-231.68907066 (-231.68907 )||2.25 || [[Image:Summary_of_anti_3.jpg|thumb|150px|Summary table for anti 3]]||
|-
| anti4 ||[[Image:Structrue_anti_4.jpg|thumb|widthpx| ]]||C1||-231.69097054 (-231.69097 )||1.06|| [[Image:Summary_of_anti_4.jpg|thumb|150px|Summary table for anti 4]]
|}

Reoptimization and frequency analysis of Anti 2 conformer at B3LYP/6-31G* level after optimization at HF/6-31G level of theory.

Section 1 Optimization
{| class="wikitable" border="1"
|+ Comparison of results between HF/3-21G and B3LYP/6-31G*
! Method !! Structure!! Energy / a.u. (literature value)!!Summary table
|-
| HF/3-21G ||[[Image:Structrue_anti_2_HF.JPG|thumb|widthpx| ]] ||-231.692535 (-231.692535 )||[[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table]]
|-
| B3LYP/6-31G* || [[Image:Structrue_anti_2_DFT.JPG|thumb|widthpx| ]]||-234.611699 (-234.611710 )||[[Image:Summary_of_anti_2_dft.JPG|thumb|150px|Summary table]]
|}

Change in structure: [[Image:Comparison_2.JPG|right|200px|Comparison]]
The two structure are very similar, the small differences is found after comparing their total energies and geometric parameters such as bond angle, dihedral angle and bone length data obtained for the identical molecule but with different level of theory. It is noted that: 1)The total energy predicted at HF/6-31G level is much lower than what was obtained at B3LYP/6-31G* level, the relative energy is 2) The bond lengths obtained at HF/3-21G level are in general slightly shorter than those obtained at B3LYP/6-31G* level; 3) The most significant differences are found in the dihedral angle between central atoms and alkene carbon atoms, e.g: H(9)-C(6)-C(2)-C(1) C(7)-C(6)-C(2)-C(1). The maximum difference in dihedral angle is around 4°.

Section 2 Frequency analysis
[[Image:IR_spectrum 2.JPG|right|250px|Infra red spectrum ]]

No imaginary frequencies are found after checking the vibration results and spectrum, this means the optimized structure is not a transition structure. The thermochemistry data below are obtained from the output file.
Sum of electronic and zero-point Energies(E=Eelec+ZPE)= -234.469231
Sum of electronic and thermal Energies(E=E+Evib+Erot+Etrans)=-234.461865
Sum of electronic and thermal Enthalpies(E=E+RT)=-234.460920
Sum of electronic and thermal Free Energies(G=H-TS)=-234.500877

2) Optimizing the "Chair" and "Boat" Transition Structures

Section 1. Single allyl fragment optimization using the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Results of single allyl fragment optimization
! Structure of allyl fragement !! Summary table!!Comparison to transition structure
|-
| [[Image:Allyl.JPG|thumb|150px|Structure of Allyl fragment]] || [[Image:Summary.JPG|thumb|150px|Summary table of allyl fragment]]|| [[Image:Chair_HF.JPG|thumb|150px| ]]
|}

The structure of single allyl fragment look like one half of the transition structures shown.

Section 2. Chair two allyl fragments optimization

{| class="wikitable" border="1"
|+ Comparison of optimized structures using different settings
! Optimization setting !! Transition Structure !! Summary table!!Bond forming /breaking distance/ Å
|-
| Method in (b) ||[[Image:Opt_b.JPG|thumb|150px|Transition structure obtained from method 1]] ||[[Image:Summary_table_opt_b.JPG|thumb|150px|Summary table]]||2.02||
|-
| Method in (c)||[[Image:Opt_c.JPG|thumb|150px|Transition structure obtained from method 2]] ||[[Image:Summary_table_opt_c.JPG|thumb|150px|Summary table]]|| 2.20||
|-
| Method in (d)|| [[Image:Opt_d.JPG|thumb|150px|Transition structure obtained from method 3]] ||[[Image:Summary_table_opt_d.JPG|thumb|150px|Summary table]]|| 2.02||
|}

[[Image:Animation_of_imaginary_freq_b.gif|right|150px|Imaginary frequency at -817.87cm-1]]
This animation of imaginary frequency at -817.87cm-1 (as shown on the right) corresponds to the Cope rearrangement as it shows both bond forming and breaking at different ends of two allyl fragments in the transition structure .

Section 3 Optimization of the boat transition structure using QST2 method

The reactant and product were firstly numbered using ''atom list'' under edit menu, the first QST2 trial failed. After modification by changing the central C-C-C-C (C2-C3-C4-C5) dihedral angle to 0o, followed by reduce the inside angle (C2-C3-C4 and C3-C4-C5) to 100o, a more reasonable boat transition structure was obtained.

{| class="wikitable" border="1"
|+ Table showing labeling of atoms in reactants and products
! Component !! Picture of component!!Picture of component (modified)
|-
| Reactant || [[Image:Labeling_of_reactant.JPG|thumb|widthpx|cLabeling in reatant]] ||[[Image:Labeling_of_modified_reactant.JPG|thumb|widthpx|Labeling in modified reactant]] ||
|-
| Product || [[Image:Labeling_of_product.JPG|thumb|widthpx|cLabeling in product]] ||[[Image:Labeling_of_modified_product.JPG|thumb|widthpx|cLabeling in modified product]] ||
|-
| Transition structure || -- ||[[Image:Transition_state_1.JPG|thumb|widthpx| ]] ||
|}

The imaginary frequency was found at -840.01 cm-1. The corresponding motion is shown on the right. [[Image:Imaginary_frequency.JPG|right|150px|Motion corresponding to the imaginary frequency]]

f) Optimization of chair transition structure using IRC method

IRC method is used here to predict which conformer the reaction paths from the transitions structures will lead to.

{| class="wikitable" border="1"
|+ Table showing conformations and energies of IRC methods
! Method !!Description of method!! Conformations !! Energy / a.u.
|-
| Initial Method ||minimization with 50 points along IRC ||[[Image:Chair_IRC_initial_stucture.JPG|thumb|150px| ]]||-231.68321543
|-
| Method 1 ||Normal minimization using the last point on IRC after initial method || [[Image:Method_1.JPG|thumb|150px| ]]||-231.69166702
|-
| Method 2 ||Minimization with 200 points along IRC|| [[Image:Method_2.JPG|thumb|150px| ]]||-231.61932195
|-
| Method 3 ||IRC with force constant specified at every step || [[Image:Method_3.JPG|thumb|150px| ]]||-231.69165600
|}
Method 1: take the last point on the IRC and run a normal minimization;
Method 2: restart the IRC and specify a larger number of points until it reaches a minimum;
Method 3: redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches.

Similar conformers are obtained from method 1 and 3, which indicates the transition structures connect to the Gauche 2 conformer.

Activation energy analysis.

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from HF/3-21G
! !! Electronic energy (literature)/a.u.!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-231.619322 (-231.619322 )||-231.466696 (-231.466705)|| -231.477029(-234.461346)||[[Image:Chair_HF.JPG|thumb|100px| ]]|| [[Image:Chair_HF_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-231.602802 (-231.602802 )||-231.450929 (-231.450929 )|| -231.445301(-234.445300)||[[Image:Boat_HF.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 ||-231.692535 (-231.692535 )||-231.539541 (-231.539539|| -231.532569 -234.532566)||[[Image:Structrue_anti_2.jpg|thumb|100px| ]]|| [[Image:Summary_of_anti_2.jpg|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from B3LYP/6-31G*
! !! Electronic energy /a.u.(literature)!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-234.556983 (-234.556983 )||-234.414919 (-234.414919 )||-234.409010 (-234.408998)||[[Image:Chair_dft.JPG|thumb|100px| ]]|| [[Image:Chair_dft_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-234.543093 (-234.543093 )||-234.402340(-234.402340 )||(-234.396006)||[[Image:Boat_dft.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 || -234.611699 (-234.611710 )||-231.469242(-234.469203 )||-234.461865(-234.461856)||[[Image:DFT_method_anti_2.JPG|thumb|100px| ]]|| [[Image:Summary_of_anti_2_dft.JPG|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary table of activation energy obtained at different theory level and temperature
! Transition structure !! HF/3-21G at 0K /(kcal/mol)!!HF/3-21G at 298.15K/(kcal/mol)!!B3LYP/6-31G* at 0K/(kcal/mol)!!B3LYP/6-31G* at 298.15K/(kcal/mol)!!Expt. /(kcal/mol)
|-
| Chair ||45.71 (45.70) ||44.69(44.69)||34.09(34.06)||33.23(33.17)||33.5±0.5
|-
| Boat ||55.60 (55.60) ||55.12(54.76)||41.98(41.96)||(41.32)||44.7±2.0
|}
The numbers in bracket are literature values in appendix 2.

Comment on the results: The electronic energy and the sum of electronic and zero point energies both match the literature values very well, but the actual calculated values of the sum of electronic and thermal energies show a small difference with data given in appendix 2. This could only due to errors introduced during the calculation, as overall activation energies still match the literature value very well.

Part 2 Exercise AM1 semi empirical orbital method is used here for initial calculation, followed by calculation at HF/3-21G theory level for further transition structure optimization.

Section 1 Optimization of cis butadiene and determination of the symmetry of corresponding HOMO and LUMO [[Image:Am_1.JPG|right|150px|Summary table ]]

{| class="wikitable" border="1"
|+ Table of cis-butadiene's HOMO and LUMO and their symmetries
! Orbital !! Plot of orbital!!Symmetry with respect to the plane
|-
| HOMO || [[Image:HOMO.jpg|thumb|100px|HOMO]]|| [[Image:HOMO_symmetry_plane.jpg|thumb|100px|anti-symmetric with respect to the plane]] ||
|-
| LUMO || [[Image:LUMO.jpg|thumb|100px|LUMO]]|| [[Image:LUMO_symmetry_plane.jpg|thumb|100px|symmetric with respect to the plane]]||
|}

Section 2 Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path.

{| class="wikitable" border="1"
|+ Table of HOMO and LUMO to illustrate symmetry in the transition structure
! MO !! Picture of MO!!Symmetry of MO!!Interacting orbitals
|-
| HOMO ||[[Image:HOMO 1 .jpg |thumb|100px| ]]||Anti-symmetric with respect to the symmetry plane|| [[Image:Homo_of_diene.JPG|thumb|widthpx| ]]
|-
| LUMO || [[Image:LUMO 2 .jpg |thumb|100px| ]]||Symmetric with respect to the symmetry plane||[[Image:Lumo_of_diene.JPG|thumb|widthpx| ]]
|}

The Diels Alder reaction here, which involves two new α bonds forming due to the interaction between the diene's HOMO/LUMO and dienophile's LUMO/HOMO interaction, is a class of pericyclic reactions. Such reaction can only proceed if the π/π* orbitals involved have correct symmetry. According to the selection rules in pericyclic reaction, such 6 electrons system can interact if the stereochemistry of two interacting orbitals are supra facial or two anti-facial. The HOMO and LUMO obtained from the transition structures both are consistent with the stereochemistry in the selection rules, as the HOMO show suprafacial interaction between diene and dienophile's interacting orbitals (HOMO of diene and LUMO of dieneophile), and LUMO show suprafacial interaction between diene and dienophile's interacting orbitals (LUMO of diene and HOMO of dieneophile).

[[Image:Transition_structure 1.JPG|thumb|200px|Labeling of transition structure]]

{| class="wikitable" border="1"
|+ Table comparing bond length in transition structure and typical sp3 and sp2 C-C bond lengths
! Level of theory!!Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !!Bonding between (n)C and (n')C !! Bond length/Å
|-
| Semi-empirical AM1||(2)C --(12)C and (3)C --(9)C || 2.12||(2)C --(1)C and (3)C --(4)C||1.38||(1)C and (4)C||1.40||(1)C and (4)C||1.38
|-
| HF/3-21G||(2)C --(12)C and (3)C --(9)C || 2.21||(2)C --(1)C and (3)C --(4)C||1.37||(1)C and (4)C||1.39||(1)C and (4)C||1.38
|}

n and n' here are used to indicate the bonding carbon atoms. The 6 electrons system can interact when stereochemistry of two interacting orbitals are supra facial or two anti-facial.

[[Image:Positive_frequency.JPG|left|200px| ]] Similar structures were obtained for AM1 and HF/3-21G method, the only difference is the distance between diene and dienophile. According to the literature, the typical bond lengths of sp3 and sp2 C-C bond are 1.54Å and 1.34Å respectively, the van der waal's radius of carbon is 1.70Å. The newly form α bonds origin from 1) breaking of C-C double, 2) two partly formed α bonds between diene and dienophile. The first cases can be proven as the double bonds in dienophile and diene are longer than the typical carbon carbon double bond length, but shorter than the typical C-C α bond;[[Image:Animation 2.JPG|thumb|200px| Animation of imaginary frequency]] and the α bond length in the cie-butadiene has shortened significantly. As the diene and dienophile are two separate components before the Diels Alder reaction, a typical carbon van der waal's radius can be used here to approximate the distance between these carbons before the reaction, which is around 3.40Å (=2*1.70Å). While in the transition structure, this distance has been shortened significantly to 2.12Å. This can be further proven by looking at the animation of imaginary frequency at -955.87cm-1, the ends of dienophile and diene are getting closer to each other. This also proves the fact that two new α bonds are partly forming in the transition structure. The diene and dienophile do not approach to each other to form α bonds between them in the animation of the lowest positive frequency(as shown in the left).

Section 3 Diels Alder reaction between cyclohexa-1,3-diene reaction with maleic anhydride:

This reaction can proceed as the π/π* orbitals involved have correct symmetry.
{| class="wikitable" border="1"
|+ Table showing structure, energies and summary table of endo and exo transition structure
! Type of transition structure!!Transition structure by AM1!! Energy / a.u.!!Summary table!!Transition structure by HF/3-21G!! Energy / a.u.!!Summary table
|-
| Endo || [[Image:Endo.JPG|thumb|150px|Endo structure]]||-0.05150440||[[Image:Summary_table_endo.JPG|thumb|150px|Summary table of Endo]]||[[Image:Hf.jpg|thumb|150px| ]]||-605.61036805||[[Image:Hf_summary.JPG|thumb|150px| ]]
|-
| Exo || [[Image:Exo.JPG|thumb|150px|Exo structure]]||-0.05041965||[[Image:Summary_table_exo.JPG|thumb|150px|Summary table of Exo]]||[[Image:Exo_hf.JPG|150px| ]]||-605.60359120||[[Image:Exo_hf_summary.JPG|thumb|150px| ]]
|}

[[Image:Electronic_repulsion.JPG|right|200px|Electronic repulsion between C-H α orbital and C=O π orbital]]The endo transition structure is lower in energy than the exo structure by 0.71kcal/mol if calculation is done with semi-empirical AM1 method, but opposite results were obtained for HF/3-21G method. The structural different between the endo and exo is due to the different orientations of maleic anhydride. A possible reason for exo form is more strained is due to the electronic repulsion between electrons in C-H α orbital (atom 1 and 2) and C=O π orbital (atom 3 and 4) in the exo form (as shown on the right). This results in an increase in energy of the transition structure. Such interaction does not happen in the endo form as the C-H α orbitals are now very far apart from each other.

{| class="wikitable" border="1"
|+ Table showing HOMO and their nodal properties in endo and exo form
! Transition structure !! Picture of HOMO!!Nodal property
|-
| Endo || [[Image:Homo_endo.jpg|thumb|150px| ]]||Two nodal points between the -(C=O)-O-(C=O)- fragment and the remainder of the system
|-
| Exo || [[Image:Homo_exo.jpg|thumb|150px| ]]||One nodal points between the -(C=O)-O-(C=O)- fragment and the remainder of the system
|}

[[Image:Stabilization.JPG|right|150px| ]]The secondary orbital interaction is a class of electronic effect which can be rationalized here as the interactions between C=C π orbital and the C=O π* orbital as they have both correct symmetry and orientation. The resultant effect can stabilize the system by trading off the weakening the C=O double bond.

The secondary orbital overlap effect had been neglected in the AM1 calculation because the endo transition structure is higher in energy than than of exo transition structure, which contradicts with the experimental observations. As in reality, the endo product predominate over hermodynamically more stable exo productthe as it is the kinetically favorable product unless thermodynamical condition is applied. This is due to the secondary orbital overlap effect in the endo form transition state, such effect can stabilize the endo transition structure and provide a lower energy pathway for the reaction to proceed despite the fact that the exo product is thermodynamically more stable as it has less strain compare the to the endo product.

Reference:
#Yi Li, K. N. Houk J. Am. Chem. Soc., 1993, 115 (16), pp 7478–7485
#Shogo SakaiJ. Phys. Chem. A, 2000, 104 (5), pp 922–927
#Fleming, Ian Pericyclic reactions : Oxford University Press 1998

2011-11-11T12:23:55Z

Fs1309:

File:Exo hf summary.JPG

2011-11-11T12:23:55Z

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File:Hf.jpg

2011-11-11T12:23:54Z

Fs1309:

2011-11-11T11:15:17Z

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Rep:Mod:fs1309module 3

2011-11-11T11:09:46Z

Fs1309:

3rd year computational lab Module 3 Transition states and reactivity.

Abstract:

This module aims to characterize transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions. This can be achieved by applying molecular orbital-based methods, solving the Schrodinger equation numerically, and locating transition structures based on the local shape of a potential energy surface. Together with showing what transition structures look like, reaction paths and barrier heights can also be calculated.

Part 1:

The Cope Rearrangement Tutorial [[Image:pic1.jpg|right|150px|Cope rearrangement]]

1)Optimizing the Reactants at HF/3-21G level theory. The energy of different conformers can be found in the summary table after optimization, and the symmetry is determined using '''Symmetrize''' under Edit menu. The table below shows the structures of optimized conformers and their energies.

{| class="wikitable" border="1"
|+ Table showing different conformers and their energy and comparisons to contents in appendix 1
! Conformer !! Structure !!point group!!Energy (Comparison to literature value) / a.u.!!Relative energy /kcalmol-1!!Summary Table
|-
| gauche1 ||[[Image:Structure_gauche_1.JPG|thumb|widthpx| ]]||C2||-231.68771613 (-231.68772 )||3.10 || [[Image:Summary_of_gauche_1.JPG|thumb|150px|Summary table for gauche 1]]
|-
| gauche2 ||[[Image:Structure_gauche_2.JPG|thumb|widthpx| ]]||C2||-231.69166702 (-231.69167 )||0.62 || [[Image:Summary_of_gauche_2.JPG|thumb|150px|Summary table for gauche 2]]
|-
| gauche3 ||[[Image:Structure_gauche_3.JPG|thumb|widthpx| ]]||C1||-231.69266120 (-231.69266 )||0.00 || [[Image:Summary_of_gauche_3.JPG|thumb|150px|Summary table for gauche 3]]
|-
| gauche4 ||[[Image:Structure_gauche_4.JPG|thumb|widthpx| ]]||C2||-231.69153032 (-231.69153 )||0.71 || [[Image:Summary_of_gauche_4.JPG|thumb|150px|Summary table for gauche 4]]
|-
| gauche5 ||[[Image:Structure_gauche_5.JPG|thumb|widthpx| ]]||C1||-231.68961572 (-231.68962 )||1.91 || [[Image:Summary_of_gauche_5.JPG|thumb|150px|Summary table for gauche 5]]
|-
| gauche6 ||[[Image:Structure_gauche_6.JPG|thumb|widthpx| ]]||C1||-231.68916017 (-231.68916 )||2.20|| [[Image:Summary_of_gauche_6.JPG|thumb|150px|Summary table for gauche 6]]
|-
| anti1 ||[[Image:Structrue_anti_1.jpg|thumb|widthpx| ]]||C2||-231.69260220 (-231.69260 )||0.04 || [[Image:Summary_of_anti_1.jpg|thumb|150px|Summary table for anti 1]]
|-
| anti2 ||[[Image:Structrue_anti_2.jpg|thumb|widthpx| ]]||Ci||-231.69253494 (-231.69254 )||0.08 || [[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table for anti 2]]
|-
| anti3 ||[[Image:Structrue_anti_3.jpg|thumb|widthpx| ]]||C2h||-231.68907066 (-231.68907 )||2.25 || [[Image:Summary_of_anti_3.jpg|thumb|150px|Summary table for anti 3]]||
|-
| anti4 ||[[Image:Structrue_anti_4.jpg|thumb|widthpx| ]]||C1||-231.69097054 (-231.69097 )||1.06|| [[Image:Summary_of_anti_4.jpg|thumb|150px|Summary table for anti 4]]
|}

Reoptimization and frequency analysis of Anti 2 conformer at B3LYP/6-31G* level after optimization at HF/6-31G level of theory.

Section 1 Optimization
{| class="wikitable" border="1"
|+ Comparison of results between HF/3-21G and B3LYP/6-31G*
! Method !! Structure!! Energy / a.u. (literature value)!!Summary table
|-
| HF/3-21G ||[[Image:Structrue_anti_2_HF.JPG|thumb|widthpx| ]] ||-231.692535 (-231.692535 )||[[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table]]
|-
| B3LYP/6-31G* || [[Image:Structrue_anti_2_DFT.JPG|thumb|widthpx| ]]||-234.611699 (-234.611710 )||[[Image:Summary_of_anti_2_dft.JPG|thumb|150px|Summary table]]
|}

Change in structure: [[Image:Comparison_2.JPG|right|200px|Comparison]]
The two structure are very similar, the small differences is found after comparing their total energies and geometric parameters such as bond angle, dihedral angle and bone length data obtained for the identical molecule but with different level of theory. It is noted that: 1)The total energy predicted at HF/6-31G level is much lower than what was obtained at B3LYP/6-31G* level, the relative energy is 2) The bond lengths obtained at HF/3-21G level are in general slightly shorter than those obtained at B3LYP/6-31G* level; 3) The most significant differences are found in the dihedral angle between central atoms and alkene carbon atoms, e.g: H(9)-C(6)-C(2)-C(1) C(7)-C(6)-C(2)-C(1). The maximum difference in dihedral angle is around 4°.

Section 2 Frequency analysis
[[Image:IR_spectrum 2.JPG|right|250px|Infra red spectrum ]]

No imaginary frequencies are found after checking the vibration results and spectrum, this means the optimized structure is not a transition structure. The thermochemistry data below are obtained from the output file.
Sum of electronic and zero-point Energies(E=Eelec+ZPE)= -234.469231
Sum of electronic and thermal Energies(E=E+Evib+Erot+Etrans)=-234.461865
Sum of electronic and thermal Enthalpies(E=E+RT)=-234.460920
Sum of electronic and thermal Free Energies(G=H-TS)=-234.500877

2) Optimizing the "Chair" and "Boat" Transition Structures

Section 1. Single allyl fragment optimization using the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Results of single allyl fragment optimization
! Structure of allyl fragement !! Summary table!!Comparison to transition structure
|-
| [[Image:Allyl.JPG|thumb|150px|Structure of Allyl fragment]] || [[Image:Summary.JPG|thumb|150px|Summary table of allyl fragment]]|| [[Image:Chair_HF.JPG|thumb|150px| ]]
|}

The structure of single allyl fragment look like one half of the transition structures shown.

Section 2. Chair two allyl fragments optimization

{| class="wikitable" border="1"
|+ Comparison of optimized structures using different settings
! Optimization setting !! Transition Structure !! Summary table!!Bond forming /breaking distance/ Å
|-
| Method in (b) ||[[Image:Opt_b.JPG|thumb|150px|Transition structure obtained from method 1]] ||[[Image:Summary_table_opt_b.JPG|thumb|150px|Summary table]]||2.02||
|-
| Method in (c)||[[Image:Opt_c.JPG|thumb|150px|Transition structure obtained from method 2]] ||[[Image:Summary_table_opt_c.JPG|thumb|150px|Summary table]]|| 2.20||
|-
| Method in (d)|| [[Image:Opt_d.JPG|thumb|150px|Transition structure obtained from method 3]] ||[[Image:Summary_table_opt_d.JPG|thumb|150px|Summary table]]|| 2.02||
|}

[[Image:Animation_of_imaginary_freq_b.gif|right|150px|Imaginary frequency at -817.87cm-1]]
This animation of imaginary frequency at -817.87cm-1 (as shown on the right) corresponds to the Cope rearrangement as it shows both bond forming and breaking at different ends of two allyl fragments in the transition structure .

Section 3 Optimization of the boat transition structure using QST2 method

The reactant and product were firstly numbered using ''atom list'' under edit menu, the first QST2 trial failed. After modification by changing the central C-C-C-C (C2-C3-C4-C5) dihedral angle to 0o, followed by reduce the inside angle (C2-C3-C4 and C3-C4-C5) to 100o, a more reasonable boat transition structure was obtained.

{| class="wikitable" border="1"
|+ Table showing labeling of atoms in reactants and products
! Component !! Picture of component!!Picture of component (modified)
|-
| Reactant || [[Image:Labeling_of_reactant.JPG|thumb|widthpx|cLabeling in reatant]] ||[[Image:Labeling_of_modified_reactant.JPG|thumb|widthpx|Labeling in modified reactant]] ||
|-
| Product || [[Image:Labeling_of_product.JPG|thumb|widthpx|cLabeling in product]] ||[[Image:Labeling_of_modified_product.JPG|thumb|widthpx|cLabeling in modified product]] ||
|-
| Transition structure || -- ||[[Image:Transition_state_1.JPG|thumb|widthpx| ]] ||
|}

The imaginary frequency was found at -840.01 cm-1. The corresponding motion is shown on the right. [[Image:Imaginary_frequency.JPG|right|150px|Motion corresponding to the imaginary frequency]]

f) Optimization of chair transition structure using IRC method

IRC method is used here to predict which conformer the reaction paths from the transitions structures will lead to.

{| class="wikitable" border="1"
|+ Table showing conformations and energies of IRC methods
! Method !!Description of method!! Conformations !! Energy / a.u.
|-
| Initial Method ||minimization with 50 points along IRC ||[[Image:Chair_IRC_initial_stucture.JPG|thumb|150px| ]]||-231.68321543
|-
| Method 1 ||Normal minimization using the last point on IRC after initial method || [[Image:Method_1.JPG|thumb|150px| ]]||-231.69166702
|-
| Method 2 ||Minimization with 200 points along IRC|| [[Image:Method_2.JPG|thumb|150px| ]]||-231.61932195
|-
| Method 3 ||IRC with force constant specified at every step || [[Image:Method_3.JPG|thumb|150px| ]]||-231.69165600
|}
Method 1: take the last point on the IRC and run a normal minimization;
Method 2: restart the IRC and specify a larger number of points until it reaches a minimum;
Method 3: redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches.

Similar conformers are obtained from method 1 and 3, which indicates the transition structures connect to the Gauche 2 conformer.

Activation energy analysis.

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from HF/3-21G
! !! Electronic energy (literature)/a.u.!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-231.619322 (-231.619322 )||-231.466696 (-231.466705)|| -231.477029(-234.461346)||[[Image:Chair_HF.JPG|thumb|100px| ]]|| [[Image:Chair_HF_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-231.602802 (-231.602802 )||-231.450929 (-231.450929 )|| -231.445301(-234.445300)||[[Image:Boat_HF.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 ||-231.692535 (-231.692535 )||-231.539541 (-231.539539|| -231.532569 -234.532566)||[[Image:Structrue_anti_2.jpg|thumb|100px| ]]|| [[Image:Summary_of_anti_2.jpg|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from B3LYP/6-31G*
! !! Electronic energy /a.u.(literature)!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-234.556983 (-234.556983 )||-234.414919 (-234.414919 )||-234.409010 (-234.408998)||[[Image:Chair_dft.JPG|thumb|100px| ]]|| [[Image:Chair_dft_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-234.543093 (-234.543093 )||-234.402340(-234.402340 )||(-234.396006)||[[Image:Boat_dft.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 || -234.611699 (-234.611710 )||-231.469242(-234.469203 )||-234.461865(-234.461856)||[[Image:DFT_method_anti_2.JPG|thumb|100px| ]]|| [[Image:Summary_of_anti_2_dft.JPG|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary table of activation energy obtained at different theory level and temperature
! Transition structure !! HF/3-21G at 0K /(kcal/mol)!!HF/3-21G at 298.15K/(kcal/mol)!!B3LYP/6-31G* at 0K/(kcal/mol)!!B3LYP/6-31G* at 298.15K/(kcal/mol)!!Expt. /(kcal/mol)
|-
| Chair ||45.71 (45.70) ||44.69(44.69)||34.09(34.06)||33.23(33.17)||33.5±0.5
|-
| Boat ||55.60 (55.60) ||55.12(54.76)||41.98(41.96)||(41.32)||44.7±2.0
|}
The numbers in bracket are literature values in appendix 2.

Comment on the results: The electronic energy and the sum of electronic and zero point energies both match the literature values very well, but the actual calculated values of the sum of electronic and thermal energies show a small difference with data given in appendix 2. This could only due to errors introduced during the calculation, as overall activation energies still match the literature value very well.

Part 2 Exercise

Section 1 Optimization of cis butadiene and determination of the symmetry of corresponding HOMO and LUMO [[Image:Summary_table.JPG|right|150px|Summary table]]

{| class="wikitable" border="1"
|+ Table of cis-butadiene's HOMO and LUMO and their symmetries
! Orbital !! Plot of orbital!!Symmetry with respect to the plane
|-
| HOMO || [[Image:HOMO.jpg|thumb|100px|HOMO]]|| [[Image:HOMO_symmetry_plane.jpg|thumb|100px|anti-symmetric with respect to the plane]] ||
|-
| LUMO || [[Image:LUMO.jpg|thumb|100px|LUMO]]|| [[Image:LUMO_symmetry_plane.jpg|thumb|100px|symmetric with respect to the plane]]||
|}

Section 2 Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path.

{| class="wikitable" border="1"
|+ Table of HOMO and LUMO to illustrate symmetry in the transition structure
! MO !! Picture of MO!!Symmetry of MO!!Interacting orbitals
|-
| HOMO ||[[Image:HOMO 1 .jpg |thumb|100px| ]]||Anti-symmetric with respect to the symmetry plane|| [[Image:Homo_of_diene.JPG|thumb|widthpx| ]]
|-
| LUMO || [[Image:LUMO 2 .jpg |thumb|100px| ]]||Symmetric with respect to the symmetry plane||[[Image:Lumo_of_diene.JPG|thumb|widthpx| ]]
|}

The Diels Alder reaction here, which involves two new α bonds forming due to the interaction between the diene's HOMO/LUMO and dienophile's LUMO/HOMO interaction, is a class of pericyclic reactions. Such reaction can only proceed if the π orbitals involved have correct symmetry. According to the selection rules in pericyclic reaction, such 6 electrons system can interact if the stereochemistry of two interacting orbitals are supra facial or two anti-facial. The HOMO and LUMO obtained from the transition structures both are consistent with the stereochemistry in the selection rules, as the HOMO show suprafacial interaction between diene and dienophile's interacting orbitals (HOMO of diene and LUMO of dieneophile), and LUMO show suprafacial interaction between diene and dienophile's interacting orbitals (LUMO of diene and HOMO of dieneophile).

[[Image:Transition_structure 1.JPG|thumb|200px|Labeling of transition structure]]

{| class="wikitable" border="1"
|+ Table comparing bond length in transition structure and typical sp3 and sp2 C-C bond lengths
! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !!Bonding between (n)C and (n')C !! Bond length/Å
|-
| (2)C --(12)C and (3)C --(9)C || 2.12||(2)C --(1)C and (3)C --(4)C||1.38||(1)C and (4)C||1.40||(1)C and (4)C||1.38
|}

n and n' here are used to indicate the bonding carbon atoms.

[[Image:Positive_frequency.JPG|left|200px| ]]The typical bond lengths of sp3 and sp2 C-C bond are 1.54Å and 1.34Å respectively, the van der waal's radius of carbon is 1.70Å. The newly form α bonds origin from 1) breaking of C-C double, 2) two partly formed α bonds between diene and dienophile. The first cases can be proven as the double bonds in dienophile and diene are longer than the typical carbon carbon double bond length, but shorter than the typical C-C α bond;[[Image:Animation 2.JPG|thumb|200px| Animation of imaginary frequency]] and the α bond length in the cie-butadiene has shortened significantly. As the diene and dienophile are two separate components before the Diels Alder reaction, a typical carbon van der waal's radius can be used here to approximate the distance between these carbons before the reaction, which is around 3.40Å (=2*1.70Å). While in the transition structure, this distance has been shortened significantly to 2.12Å. This can be further proven by looking at the animation of imaginary frequency at -955.87cm-1, the ends of dienophile and diene are getting closer to each other. This also proves the fact that two new α bonds are partly forming in the transition structure. The diene and dienophile do not approach to each other to form α bonds between them in the animation of the lowest positive frequency(as shown in the left).

Reference:
#Yi Li, K. N. Houk J. Am. Chem. Soc., 1993, 115 (16), pp 7478–7485
#Shogo SakaiJ. Phys. Chem. A, 2000, 104 (5), pp 922–927
#Fleming, Ian Pericyclic reactions : Oxford University Press 1998

Section 3 Diels Alder reaction between cyclohexa-1,3-diene reaction with maleic anhydride:

{| class="wikitable" border="1"
|+ Table showing structure, energies and summary table of endo and exo transition structure
! Type of transition structure!!Transition structure!! Energy / a.u.!!Summary table
|-
| Endo || [[Image:Endo.JPG|thumb|150px|Endo structure]]||-0.05150440||[[Image:Summary_table_endo.JPG|thumb|150px|Summary table of Endo]]
|-
| Exo || [[Image:Exo.JPG|thumb|150px|Exo structure]]||-0.05041965||[[Image:Summary_table_exo.JPG|thumb|150px|Summary table of Exo]]
|}

[[Image:Electronic_repulsion.JPG|right|200px|Electronic repulsion between C-H α orbital and C=O π orbital]]The endo transition structure is lower in energy than the exo structure by 0.71kcal/mol. The structural different between the endo and exo is due to the different orientations of maleic anhydride. A possible reason for exo form is more strained is due to the electronic repulsion between electrons in C-H α orbital (atom 1 and 2) and C=O π orbital (atom 3 and 4) in the exo form (as shown on the right). This results in an increase in energy of the transition structure. Such interaction does not happen in the endo form as the C-H α orbitals are now very far apart from each other.

{| class="wikitable" border="1"
|+ Table showing HOMO and their nodal properties in endo and exo form
! Transition structure !! Picture of HOMO!!Nodal property
|-
| Endo || [[Image:Homo_endo.jpg|thumb|150px| ]]||Two nodal points between the -(C=O)-O-(C=O)- fragment and the remainder of the system
|-
| Exo || [[Image:Homo_exo.jpg|thumb|150px| ]]||One nodal points between the -(C=O)-O-(C=O)- fragment and the remainder of the system
|}

The secondary orbital interaction is a class of electronic effect which can be rationalized here as the interactions between C=C π orbital and the C=O π* orbital as they have both correct symmetry and orientation. The resultant effect can stabilize the system by weakening the C=O double bond.

Rep:Mod:fs1309module 3

2011-11-11T11:09:11Z

Fs1309:

3rd year computational lab Module 3 Transition states and reactivity.

Abstract:

This module aims to characterize transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions. This can be achieved by applying molecular orbital-based methods, solving the Schrodinger equation numerically, and locating transition structures based on the local shape of a potential energy surface. Together with showing what transition structures look like, reaction paths and barrier heights can also be calculated.

Part 1:

The Cope Rearrangement Tutorial [[Image:pic1.jpg|right|150px|Cope rearrangement]]

1)Optimizing the Reactants at HF/3-21G level theory. The energy of different conformers can be found in the summary table after optimization, and the symmetry is determined using '''Symmetrize''' under Edit menu. The table below shows the structures of optimized conformers and their energies.

{| class="wikitable" border="1"
|+ Table showing different conformers and their energy and comparisons to contents in appendix 1
! Conformer !! Structure !!point group!!Energy (Comparison to literature value) / a.u.!!Relative energy /kcalmol-1!!Summary Table
|-
| gauche1 ||[[Image:Structure_gauche_1.JPG|thumb|widthpx| ]]||C2||-231.68771613 (-231.68772 )||3.10 || [[Image:Summary_of_gauche_1.JPG|thumb|150px|Summary table for gauche 1]]
|-
| gauche2 ||[[Image:Structure_gauche_2.JPG|thumb|widthpx| ]]||C2||-231.69166702 (-231.69167 )||0.62 || [[Image:Summary_of_gauche_2.JPG|thumb|150px|Summary table for gauche 2]]
|-
| gauche3 ||[[Image:Structure_gauche_3.JPG|thumb|widthpx| ]]||C1||-231.69266120 (-231.69266 )||0.00 || [[Image:Summary_of_gauche_3.JPG|thumb|150px|Summary table for gauche 3]]
|-
| gauche4 ||[[Image:Structure_gauche_4.JPG|thumb|widthpx| ]]||C2||-231.69153032 (-231.69153 )||0.71 || [[Image:Summary_of_gauche_4.JPG|thumb|150px|Summary table for gauche 4]]
|-
| gauche5 ||[[Image:Structure_gauche_5.JPG|thumb|widthpx| ]]||C1||-231.68961572 (-231.68962 )||1.91 || [[Image:Summary_of_gauche_5.JPG|thumb|150px|Summary table for gauche 5]]
|-
| gauche6 ||[[Image:Structure_gauche_6.JPG|thumb|widthpx| ]]||C1||-231.68916017 (-231.68916 )||2.20|| [[Image:Summary_of_gauche_6.JPG|thumb|150px|Summary table for gauche 6]]
|-
| anti1 ||[[Image:Structrue_anti_1.jpg|thumb|widthpx| ]]||C2||-231.69260220 (-231.69260 )||0.04 || [[Image:Summary_of_anti_1.jpg|thumb|150px|Summary table for anti 1]]
|-
| anti2 ||[[Image:Structrue_anti_2.jpg|thumb|widthpx| ]]||Ci||-231.69253494 (-231.69254 )||0.08 || [[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table for anti 2]]
|-
| anti3 ||[[Image:Structrue_anti_3.jpg|thumb|widthpx| ]]||C2h||-231.68907066 (-231.68907 )||2.25 || [[Image:Summary_of_anti_3.jpg|thumb|150px|Summary table for anti 3]]||
|-
| anti4 ||[[Image:Structrue_anti_4.jpg|thumb|widthpx| ]]||C1||-231.69097054 (-231.69097 )||1.06|| [[Image:Summary_of_anti_4.jpg|thumb|150px|Summary table for anti 4]]
|}

Reoptimization and frequency analysis of Anti 2 conformer at B3LYP/6-31G* level after optimization at HF/6-31G level of theory.

Section 1 Optimization
{| class="wikitable" border="1"
|+ Comparison of results between HF/3-21G and B3LYP/6-31G*
! Method !! Structure!! Energy / a.u. (literature value)!!Summary table
|-
| HF/3-21G ||[[Image:Structrue_anti_2_HF.JPG|thumb|widthpx| ]] ||-231.692535 (-231.692535 )||[[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table]]
|-
| B3LYP/6-31G* || [[Image:Structrue_anti_2_DFT.JPG|thumb|widthpx| ]]||-234.611699 (-234.611710 )||[[Image:Summary_of_anti_2_dft.JPG|thumb|150px|Summary table]]
|}

Change in structure: [[Image:Comparison_2.JPG|right|200px|Comparison]]
The two structure are very similar, the small differences is found after comparing their total energies and geometric parameters such as bond angle, dihedral angle and bone length data obtained for the identical molecule but with different level of theory. It is noted that: 1)The total energy predicted at HF/6-31G level is much lower than what was obtained at B3LYP/6-31G* level, the relative energy is 2) The bond lengths obtained at HF/3-21G level are in general slightly shorter than those obtained at B3LYP/6-31G* level; 3) The most significant differences are found in the dihedral angle between central atoms and alkene carbon atoms, e.g: H(9)-C(6)-C(2)-C(1) C(7)-C(6)-C(2)-C(1). The maximum difference in dihedral angle is around 4°.

Section 2 Frequency analysis
[[Image:IR_spectrum 2.JPG|right|250px|Infra red spectrum ]]

No imaginary frequencies are found after checking the vibration results and spectrum, this means the optimized structure is not a transition structure. The thermochemistry data below are obtained from the output file.
Sum of electronic and zero-point Energies(E=Eelec+ZPE)= -234.469231
Sum of electronic and thermal Energies(E=E+Evib+Erot+Etrans)=-234.461865
Sum of electronic and thermal Enthalpies(E=E+RT)=-234.460920
Sum of electronic and thermal Free Energies(G=H-TS)=-234.500877

2) Optimizing the "Chair" and "Boat" Transition Structures

Section 1. Single allyl fragment optimization using the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Results of single allyl fragment optimization
! Structure of allyl fragement !! Summary table!!Comparison to transition structure
|-
| [[Image:Allyl.JPG|thumb|150px|Structure of Allyl fragment]] || [[Image:Summary.JPG|thumb|150px|Summary table of allyl fragment]]|| [[Image:Chair_HF.JPG|thumb|150px| ]]
|}

The structure of single allyl fragment look like one half of the transition structures shown.

Section 2. Chair two allyl fragments optimization

{| class="wikitable" border="1"
|+ Comparison of optimized structures using different settings
! Optimization setting !! Transition Structure !! Summary table!!Bond forming /breaking distance/ Å
|-
| Method in (b) ||[[Image:Opt_b.JPG|thumb|150px|Transition structure obtained from method 1]] ||[[Image:Summary_table_opt_b.JPG|thumb|150px|Summary table]]||2.02||
|-
| Method in (c)||[[Image:Opt_c.JPG|thumb|150px|Transition structure obtained from method 2]] ||[[Image:Summary_table_opt_c.JPG|thumb|150px|Summary table]]|| 2.20||
|-
| Method in (d)|| [[Image:Opt_d.JPG|thumb|150px|Transition structure obtained from method 3]] ||[[Image:Summary_table_opt_d.JPG|thumb|150px|Summary table]]|| 2.02||
|}

[[Image:Animation_of_imaginary_freq_b.gif|right|150px|Imaginary frequency at -817.87cm-1]]
This animation of imaginary frequency at -817.87cm-1 (as shown on the right) corresponds to the Cope rearrangement as it shows both bond forming and breaking at different ends of two allyl fragments in the transition structure .

Section 3 Optimization of the boat transition structure using QST2 method

The reactant and product were firstly numbered using ''atom list'' under edit menu, the first QST2 trial failed. After modification by changing the central C-C-C-C (C2-C3-C4-C5) dihedral angle to 0o, followed by reduce the inside angle (C2-C3-C4 and C3-C4-C5) to 100o, a more reasonable boat transition structure was obtained.

{| class="wikitable" border="1"
|+ Table showing labeling of atoms in reactants and products
! Component !! Picture of component!!Picture of component (modified)
|-
| Reactant || [[Image:Labeling_of_reactant.JPG|thumb|widthpx|cLabeling in reatant]] ||[[Image:Labeling_of_modified_reactant.JPG|thumb|widthpx|Labeling in modified reactant]] ||
|-
| Product || [[Image:Labeling_of_product.JPG|thumb|widthpx|cLabeling in product]] ||[[Image:Labeling_of_modified_product.JPG|thumb|widthpx|cLabeling in modified product]] ||
|-
| Transition structure || -- ||[[Image:Transition_state_1.JPG|thumb|widthpx| ]] ||
|}

The imaginary frequency was found at -840.01 cm-1. The corresponding motion is shown on the right. [[Image:Imaginary_frequency.JPG|right|150px|Motion corresponding to the imaginary frequency]]

f) Optimization of chair transition structure using IRC method

IRC method is used here to predict which conformer the reaction paths from the transitions structures will lead to.

{| class="wikitable" border="1"
|+ Table showing conformations and energies of IRC methods
! Method !!Description of method!! Conformations !! Energy / a.u.
|-
| Initial Method ||minimization with 50 points along IRC ||[[Image:Chair_IRC_initial_stucture.JPG|thumb|150px| ]]||-231.68321543
|-
| Method 1 ||Normal minimization using the last point on IRC after initial method || [[Image:Method_1.JPG|thumb|150px| ]]||-231.69166702
|-
| Method 2 ||Minimization with 200 points along IRC|| [[Image:Method_2.JPG|thumb|150px| ]]||-231.61932195
|-
| Method 3 ||IRC with force constant specified at every step || [[Image:Method_3.JPG|thumb|150px| ]]||-231.69165600
|}
Method 1: take the last point on the IRC and run a normal minimization;
Method 2: restart the IRC and specify a larger number of points until it reaches a minimum;
Method 3: redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches.

Similar conformers are obtained from method 1 and 3, which indicates the transition structures connect to the Gauche 2 conformer.

Activation energy analysis.

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from HF/3-21G
! !! Electronic energy (literature)/a.u.!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-231.619322 (-231.619322 )||-231.466696 (-231.466705)|| -231.477029(-234.461346)||[[Image:Chair_HF.JPG|thumb|100px| ]]|| [[Image:Chair_HF_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-231.602802 (-231.602802 )||-231.450929 (-231.450929 )|| -231.445301(-234.445300)||[[Image:Boat_HF.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 ||-231.692535 (-231.692535 )||-231.539541 (-231.539539|| -231.532569 -234.532566)||[[Image:Structrue_anti_2.jpg|thumb|100px| ]]|| [[Image:Summary_of_anti_2.jpg|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from B3LYP/6-31G*
! !! Electronic energy /a.u.(literature)!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-234.556983 (-234.556983 )||-234.414919 (-234.414919 )||-234.409010 (-234.408998)||[[Image:Chair_dft.JPG|thumb|100px| ]]|| [[Image:Chair_dft_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-234.543093 (-234.543093 )||-234.402340(-234.402340 )||(-234.396006)||[[Image:Boat_dft.JPG|thumb|100px| ]]|| [[Image:filename|thumb|100px| ]]||
|-
| Reactant Anti 2 || -234.611699 (-234.611710 )||-231.469242(-234.469203 )||-234.461865(-234.461856)||[[Image:DFT_method_anti_2.JPG|thumb|100px| ]]|| [[Image:Summary_of_anti_2_dft.JPG|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary table of activation energy obtained at different theory level and temperature
! Transition structure !! HF/3-21G at 0K /(kcal/mol)!!HF/3-21G at 298.15K/(kcal/mol)!!B3LYP/6-31G* at 0K/(kcal/mol)!!B3LYP/6-31G* at 298.15K/(kcal/mol)!!Expt. /(kcal/mol)
|-
| Chair ||45.71 (45.70) ||44.69(44.69)||34.09(34.06)||33.23(33.17)||33.5±0.5
|-
| Boat ||55.60 (55.60) ||55.12(54.76)||41.98(41.96)||(41.32)||44.7±2.0
|}
The numbers in bracket are literature values in appendix 2.

Comment on the results: The electronic energy and the sum of electronic and zero point energies both match the literature values very well, but the actual calculated values of the sum of electronic and thermal energies show a small difference with data given in appendix 2. This could only due to errors introduced during the calculation, as overall activation energies still match the literature value very well.

Part 2 Exercise

Section 1 Optimization of cis butadiene and determination of the symmetry of corresponding HOMO and LUMO [[Image:Summary_table.JPG|right|150px|Summary table]]

{| class="wikitable" border="1"
|+ Table of cis-butadiene's HOMO and LUMO and their symmetries
! Orbital !! Plot of orbital!!Symmetry with respect to the plane
|-
| HOMO || [[Image:HOMO.jpg|thumb|100px|HOMO]]|| [[Image:HOMO_symmetry_plane.jpg|thumb|100px|anti-symmetric with respect to the plane]] ||
|-
| LUMO || [[Image:LUMO.jpg|thumb|100px|LUMO]]|| [[Image:LUMO_symmetry_plane.jpg|thumb|100px|symmetric with respect to the plane]]||
|}

Section 2 Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path.

{| class="wikitable" border="1"
|+ Table of HOMO and LUMO to illustrate symmetry in the transition structure
! MO !! Picture of MO!!Symmetry of MO!!Interacting orbitals
|-
| HOMO ||[[Image:HOMO 1 .jpg |thumb|100px| ]]||Anti-symmetric with respect to the symmetry plane|| [[Image:Homo_of_diene.JPG|thumb|widthpx| ]]
|-
| LUMO || [[Image:LUMO 2 .jpg |thumb|100px| ]]||Symmetric with respect to the symmetry plane||[[Image:Lumo_of_diene.JPG|thumb|widthpx| ]]
|}

The Diels Alder reaction here, which involves two new α bonds forming due to the interaction between the diene's HOMO/LUMO and dienophile's LUMO/HOMO interaction, is a class of pericyclic reactions. Such reaction can only proceed if the π orbitals involved have correct symmetry. According to the selection rules in pericyclic reaction, such 6 electrons system can interact if the stereochemistry of two interacting orbitals are supra facial or two anti-facial. The HOMO and LUMO obtained from the transition structures both are consistent with the stereochemistry in the selection rules, as the HOMO show suprafacial interaction between diene and dienophile's interacting orbitals (HOMO of diene and LUMO of dieneophile), and LUMO show suprafacial interaction between diene and dienophile's interacting orbitals (LUMO of diene and HOMO of dieneophile).

[[Image:Transition_structure 1.JPG|thumb|200px|Labeling of transition structure]]

{| class="wikitable" border="1"
|+ Table comparing bond length in transition structure and typical sp3 and sp2 C-C bond lengths
! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !!Bonding between (n)C and (n')C !! Bond length/Å
|-
| (2)C --(12)C and (3)C --(9)C || 2.12||(2)C --(1)C and (3)C --(4)C||1.38||(1)C and (4)C||1.40||(1)C and (4)C||1.38
|}

n and n' here are used to indicate the bonding carbon atoms.

[[Image:Positive_frequency.JPG|left|200px| ]]The typical bond lengths of sp3 and sp2 C-C bond are 1.54Å and 1.34Å respectively, the van der waal's radius of carbon is 1.70Å. The newly form α bonds origin from 1) breaking of C-C double, 2) two partly formed α bonds between diene and dienophile. The first cases can be proven as the double bonds in dienophile and diene are longer than the typical carbon carbon double bond length, but shorter than the typical C-C α bond;[[Image:Animation 2.JPG|thumb|200px| Animation of imaginary frequency]] and the α bond length in the cie-butadiene has shortened significantly. As the diene and dienophile are two separate components before the Diels Alder reaction, a typical carbon van der waal's radius can be used here to approximate the distance between these carbons before the reaction, which is around 3.40Å (=2*1.70Å). While in the transition structure, this distance has been shortened significantly to 2.12Å. This can be further proven by looking at the animation of imaginary frequency at -955.87cm-1, the ends of dienophile and diene are getting closer to each other. This also proves the fact that two new α bonds are partly forming in the transition structure. The diene and dienophile do not approach to each other to form α bonds between them in the animation of the lowest positive frequency(as shown in the left).

Reference:
#Yi Li, K. N. Houk J. Am. Chem. Soc., 1993, 115 (16), pp 7478–7485
#Shogo SakaiJ. Phys. Chem. A, 2000, 104 (5), pp 922–927
#Fleming, Ian Pericyclic reactions : Oxford University Press 1998

Section 3 Diels Alder reaction between cyclohexa-1,3-diene reaction with maleic anhydride:

{| class="wikitable" border="1"
|+ Table showing structure, energies and summary table of endo and exo transition structure
! Type of transition structure!!Transition structure!! Energy / a.u.!!Summary table
|-
| Endo || [[Image:Endo.JPG|thumb|150px|Endo structure]]||-0.05150440||[[Image:Summary_table_endo.JPG|thumb|150px|Summary table of Endo]]
|-
| Exo || [[Image:Exo.JPG|thumb|150px|Exo structure]]||-0.05041965||[[Image:Summary_table_exo.JPG|thumb|150px|Summary table of Exo]]
|}

[[Image:Electronic_repulsion.JPG|right|200px|Electronic repulsion between C-H α orbital and C=O π orbital]]The endo transition structure is lower in energy than the exo structure by 0.71kcal/mol. The structural different between the endo and exo is due to the different orientations of maleic anhydride. A possible reason for exo form is more strained is due to the electronic repulsion between electrons in C-H α orbital (atom 1 and 2) and C=O π orbital (atom 3 and 4) in the exo form (as shown on the right). This results in an increase in energy of the transition structure. Such interaction does not happen in the endo form as the C-H α orbitals are now very far apart from each other.

{| class="wikitable" border="1"
|+ Table showing HOMO and their nodal properties in endo and exo form
! Transition structure !! Picture of HOMO!!Nodal property
|-
| Endo || [[Image:Homo_endo.jpg|thumb|150px| ]]||Two nodal points between the -(C=O)-O-(C=O)- fragment and the remainder of the system
|-
| Exo || [[Image:Homo_exo.jpg|thumb|150px| ]]||One nodal points between the -(C=O)-O-(C=O)- fragment and the remainder of the system
|}

The secondary orbital interaction is a class of electronic effect which can be rationalized here as the interactions between C=C π orbital and the C=O π* orbital as they have both correct symmetry and orientation. The resultant effect can stabilize the system by weakening the C=O double bond.

2011-11-11T10:57:12Z

Fs1309:

File:Animation.gif

2011-11-11T10:57:12Z

Fs1309:

Rep:Mod:fs1309module 3

2011-11-11T10:37:57Z

Fs1309:

3rd year computational lab Module 3 Transition states and reactivity.

Abstract:

This module aims to characterize transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions. This can be achieved by applying molecular orbital-based methods, solving the Schrodinger equation numerically, and locating transition structures based on the local shape of a potential energy surface. Together with showing what transition structures look like, reaction paths and barrier heights can also be calculated.

Part 1:

The Cope Rearrangement Tutorial [[Image:pic1.jpg|right|150px|Cope rearrangement]]

1)Optimizing the Reactants at HF/3-21G level theory. The energy of different conformers can be found in the summary table after optimization, and the symmetry is determined using '''Symmetrize''' under Edit menu. The table below shows the structures of optimized conformers and their energies.

{| class="wikitable" border="1"
|+ Table showing different conformers and their energy and comparisons to contents in appendix 1
! Conformer !! Structure !!point group!!Energy (Comparison to literature value) / a.u.!!Relative energy /kcalmol-1!!Summary Table
|-
| gauche1 ||[[Image:Structure_gauche_1.JPG|thumb|widthpx| ]]||C2||-231.68771613 (-231.68772 )||3.10 || [[Image:Summary_of_gauche_1.JPG|thumb|150px|Summary table for gauche 1]]
|-
| gauche2 ||[[Image:Structure_gauche_2.JPG|thumb|widthpx| ]]||C2||-231.69166702 (-231.69167 )||0.62 || [[Image:Summary_of_gauche_2.JPG|thumb|150px|Summary table for gauche 2]]
|-
| gauche3 ||[[Image:Structure_gauche_3.JPG|thumb|widthpx| ]]||C1||-231.69266120 (-231.69266 )||0.00 || [[Image:Summary_of_gauche_3.JPG|thumb|150px|Summary table for gauche 3]]
|-
| gauche4 ||[[Image:Structure_gauche_4.JPG|thumb|widthpx| ]]||C2||-231.69153032 (-231.69153 )||0.71 || [[Image:Summary_of_gauche_4.JPG|thumb|150px|Summary table for gauche 4]]
|-
| gauche5 ||[[Image:Structure_gauche_5.JPG|thumb|widthpx| ]]||C1||-231.68961572 (-231.68962 )||1.91 || [[Image:Summary_of_gauche_5.JPG|thumb|150px|Summary table for gauche 5]]
|-
| gauche6 ||[[Image:Structure_gauche_6.JPG|thumb|widthpx| ]]||C1||-231.68916017 (-231.68916 )||2.20|| [[Image:Summary_of_gauche_6.JPG|thumb|150px|Summary table for gauche 6]]
|-
| anti1 ||[[Image:Structrue_anti_1.jpg|thumb|widthpx| ]]||C2||-231.69260220 (-231.69260 )||0.04 || [[Image:Summary_of_anti_1.jpg|thumb|150px|Summary table for anti 1]]
|-
| anti2 ||[[Image:Structrue_anti_2.jpg|thumb|widthpx| ]]||Ci||-231.69253494 (-231.69254 )||0.08 || [[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table for anti 2]]
|-
| anti3 ||[[Image:Structrue_anti_3.jpg|thumb|widthpx| ]]||C2h||-231.68907066 (-231.68907 )||2.25 || [[Image:Summary_of_anti_3.jpg|thumb|150px|Summary table for anti 3]]||
|-
| anti4 ||[[Image:Structrue_anti_4.jpg|thumb|widthpx| ]]||C1||-231.69097054 (-231.69097 )||1.06|| [[Image:Summary_of_anti_4.jpg|thumb|150px|Summary table for anti 4]]
|}

Reoptimization and frequency analysis of Anti 2 conformer at B3LYP/6-31G* level after optimization at HF/6-31G level of theory.

Section 1 Optimization
{| class="wikitable" border="1"
|+ Comparison of results between HF/3-21G and B3LYP/6-31G*
! Method !! Structure!! Energy / a.u. (literature value)!!Summary table
|-
| HF/3-21G ||[[Image:Structrue_anti_2_HF.JPG|thumb|widthpx| ]] ||-231.692535 (-231.692535 )||[[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table]]
|-
| B3LYP/6-31G* || [[Image:Structrue_anti_2_DFT.JPG|thumb|widthpx| ]]||-234.611699 (-234.611710 )||[[Image:Summary_of_anti_2_dft.JPG|thumb|150px|Summary table]]
|}

Change in structure: [[Image:Comparison_2.JPG|right|200px|Comparison]]
The two structure are very similar, the small differences is found after comparing their total energies and geometric parameters such as bond angle, dihedral angle and bone length data obtained for the identical molecule but with different level of theory. It is noted that: 1)The total energy predicted at HF/6-31G level is much lower than what was obtained at B3LYP/6-31G* level, the relative energy is 2) The bond lengths obtained at HF/3-21G level are generally shorter than those at B3LYP/6-31G* level; 3) The most significant differences are found in the dihedral angle between central atoms and alkene carbon atoms, e.g: H(9)-C(6)-C(2)-C(1) C(7)-C(6)-C(2)-C(1). The maximum difference in dihedral angle is around 4°.

Section 2 Frequency analysis
[[Image:IR_spectrum 2.JPG|right|250px|Infra red spectrum ]]

No imaginary frequencies are found after checking the vibration results and spectrum, this means the optimized structure is not a transition structure. The thermochemistry data below are obtained from the output file.
Sum of electronic and zero-point Energies(E=Eelec+ZPE)= -234.469231
Sum of electronic and thermal Energies(E=E+Evib+Erot+Etrans)=-234.461865
Sum of electronic and thermal Enthalpies(E=E+RT)=-234.460920
Sum of electronic and thermal Free Energies(G=H-TS)=-234.500877

2) Optimizing the "Chair" and "Boat" Transition Structures

Section 1. Single allyl fragment optimization using the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Results of single allyl fragment optimization
! Structure of allyl fragement !! Summary table!!Comparison to transition structure
|-
| [[Image:Allyl.JPG|thumb|150px|Structure of Allyl fragment]] || [[Image:Summary.JPG|thumb|150px|Summary table of allyl fragment]]|| [[Image:Chair_HF.JPG|thumb|150px| ]]
|}

The structure of single allyl fragment look like one half of the transition structures shown.

Section 2. Chair two allyl fragments optimization

{| class="wikitable" border="1"
|+ Comparison of optimized structures using different settings
! Optimization setting !! Transition Structure !! Summary table!! Animation of imaginary frequency!!Bond forming /breaking distance/ Å
|-
| Method in (b) ||[[Image:Opt_b.JPG|thumb|150px|Transition structure obtained from method 1]] ||[[Image:Summary_table_opt_b.JPG|thumb|150px|Summary table]]||[[Image:Animation_of_imaginary_freq_b.JPG|thumb|150px|Imaginary frequency at -817.87cm-1]] ||2.02||
|-
| Method in (c)||[[Image:Opt_c.JPG|thumb|150px|Transition structure obtained from method 2]] ||[[Image:Summary_table_opt_c.JPG|thumb|150px|Summary table]]|| -||2.20||
|-
| Method in (d)|| [[Image:Opt_d.JPG|thumb|150px|Transition structure obtained from method 3]] ||[[Image:Summary_table_opt_d.JPG|thumb|150px|Summary table]]|| -||2.02||
|}

This animation of imaginary frequency at -817.87cm-1 corresponds to the Cope rearrangement as it shows both bond forming and breaking at different ends of two allyl fragments in the transition structure .

Section 3 Optimization of the boat transition structure using QST2 method

The reactant and product were firstly numbered using ''atom list'' under edit menu, the first QST2 trial failed. After modification by changing the central C-C-C-C (C2-C3-C4-C5) dihedral angle to 0o, followed by reduce the inside angle (C2-C3-C4 and C3-C4-C5) to 100o, a more reasonable boat transition structure was obtained.

{| class="wikitable" border="1"
|+ Table showing labeling of atoms in reactants and products
! Component !! Picture of component!!Picture of component (modified)
|-
| Reactant || [[Image:Labeling_of_reactant.JPG|thumb|widthpx|cLabeling in reatant]] ||[[Image:Labeling_of_modified_reactant.JPG|thumb|widthpx|Labeling in modified reactant]] ||
|-
| Product || [[Image:Labeling_of_product.JPG|thumb|widthpx|cLabeling in product]] ||[[Image:Labeling_of_modified_product.JPG|thumb|widthpx|cLabeling in modified product]] ||
|-
| Transition structure || -- ||[[Image:Transition_state_1.JPG|thumb|widthpx| ]] ||
|}

The imaginary frequency was found at -840.01 cm-1. The corresponding motion is shown on the right. [[Image:Imaginary_frequency.JPG|right|150px|Motion corresponding to the imaginary frequency]]

f) Optimization of chair transition structure using IRC method

IRC method is used here to predict which conformer the reaction paths from the transitions structures will lead to.

{| class="wikitable" border="1"
|+ Table showing conformations and energies of IRC methods
! Method !!Description of method!! Conformations !! Energy / a.u.
|-
| Initial Method ||minimization with 50 points along IRC ||[[Image:Chair_IRC_initial_stucture.JPG|thumb|150px| ]]||-231.68321543
|-
| Method 1 ||Normal minimization using the last point on IRC after initial method || [[Image:Method_1.JPG|thumb|150px| ]]||-231.69166702
|-
| Method 2 ||Minimization with 200 points along IRC|| [[Image:Method_2.JPG|thumb|150px| ]]||-231.61932195
|-
| Method 3 ||IRC with force constant specified at every step || [[Image:Method_3.JPG|thumb|150px| ]]||-231.69165600
|}
Method 1: take the last point on the IRC and run a normal minimization;
Method 2: restart the IRC and specify a larger number of points until it reaches a minimum;
Method 3: redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches.

Similar conformers are obtained from method 1 and 3, which indicates the transition structures connect to the Gauche 2 conformer.

Activation energy analysis.

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from HF/3-21G
! !! Electronic energy (literature)/a.u.!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-231.619322 (-231.619322 )||-231.466696 (-231.466705)|| -231.477029(-234.461346)||[[Image:Chair_HF.JPG|thumb|100px| ]]|| [[Image:Chair_HF_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-231.602802 (-231.602802 )||-231.450929 (-231.450929 )|| -231.445301(-234.445300)||[[Image:Boat_HF.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 ||-231.692535 (-231.692535 )||-231.539541 (-231.539539)||-231.532569
-234.532566)||[[Image:Structrue_anti_2.jpg|thumb|100px| ]]|| [[Image:Summary_of_anti_2.jpg|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from B3LYP/6-31G*
! !! Electronic energy /a.u.(literature)!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-234.556983 (-234.556983 )||-234.414919 (-234.414919 )||-234.409010 (-234.408998)||[[Image:Chair_dft.JPG|thumb|100px| ]]|| [[Image:Chair_dft_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-234.543093 (-234.543093 )||-234.402340(-234.402340 )||(-234.396006)||[[Image:filename|thumb|100px| ]]|| [[Image:filename|thumb|100px| ]]||
|-
| Reactant Anti 2 || -234.611699 (-234.611710 )||-231.469242(-234.469203 )||-234.461865(-234.461856)||[[Image:DFT_method_anti_2.JPG|thumb|100px| ]]|| [[Image:Summary_of_anti_2_dft.JPG|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary table of activation energy obtained at different theory level and temperature
! Transition structure !! HF/3-21G at 0K /(kcal/mol)!!HF/3-21G at 298.15K/(kcal/mol)!!B3LYP/6-31G* at 0K/(kcal/mol)!!B3LYP/6-31G* at 298.15K/(kcal/mol)!!Expt. /(kcal/mol)
|-
| Chair ||45.71 (45.70) ||44.69(44.69)||34.09(34.06)||33.23(33.17)||33.5±0.5
|-
| Boat ||55.60 (55.60) ||55.12(54.76)||41.98(41.96)||(41.32)||44.7±2.0
|}
The numbers in bracket are literature values in appendix 2.

Comment on the results: The electronic energy and the sum of electronic and zero point energies both match the literature values very well, but the actual calculated values of the sum of electronic and thermal energies show a small difference with data given in appendix 2. This could only due to errors introduced during the calculation, as overall activation energies still match the literature value very well.

Part 2 Exercise

Section 1 Optimization of cis butadiene and determination of the symmetry of corresponding HOMO and LUMO [[Image:Summary_table.JPG|right|150px|Summary table]]

{| class="wikitable" border="1"
|+ Table of cis-butadiene's HOMO and LUMO and their symmetries
! Orbital !! Plot of orbital!!Symmetry with respect to the plane
|-
| HOMO || [[Image:HOMO.jpg|thumb|100px|HOMO]]|| [[Image:HOMO_symmetry_plane.jpg|thumb|100px|anti-symmetric with respect to the plane]] ||
|-
| LUMO || [[Image:LUMO.jpg|thumb|100px|LUMO]]|| [[Image:LUMO_symmetry_plane.jpg|thumb|100px|symmetric with respect to the plane]]||
|}

Section 2 Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path.

{| class="wikitable" border="1"
|+ Table of HOMO and LUMO to illustrate symmetry in the transition structure
! MO !! Picture of MO!!Symmetry of MO!!Interacting orbitals
|-
| HOMO ||[[Image:HOMO 1 .jpg |thumb|100px| ]]||Anti-symmetric with respect to the symmetry plane|| [[Image:Homo_of_diene.JPG|thumb|widthpx| ]]
|-
| LUMO || [[Image:LUMO 2 .jpg |thumb|100px| ]]||Symmetric with respect to the symmetry plane||[[Image:Lumo_of_diene.JPG|thumb|widthpx| ]]
|}

The Diels Alder reaction here, which involves two new α bonds forming due to the interaction between the diene's HOMO/LUMO and dienophile's LUMO/HOMO interaction, is a class of pericyclic reactions. Such reaction can only proceed if the π orbitals involved have correct symmetry. According to the selection rules in pericyclic reaction, such 6 electrons system can interact if the stereochemistry of two interacting orbitals are supra facial or two anti-facial. The HOMO and LUMO obtained from the transition structures both are consistent with the stereochemistry in the selection rules, as the HOMO show suprafacial interaction between diene and dienophile's interacting orbitals (HOMO of diene and LUMO of dieneophile), and LUMO show suprafacial interaction between diene and dienophile's interacting orbitals (LUMO of diene and HOMO of dieneophile).

[[Image:Transition_structure 1.JPG|thumb|200px|Labeling of transition structure]]

{| class="wikitable" border="1"
|+ Table comparing bond length in transition structure and typical sp3 and sp2 C-C bond lengths
! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !!Bonding between (n)C and (n')C !! Bond length/Å
|-
| (2)C --(12)C and (3)C --(9)C || 2.12||(2)C --(1)C and (3)C --(4)C||1.38||(1)C and (4)C||1.40||(1)C and (4)C||1.38
|}

n and n' here are used to indicate the bonding carbon atoms.

[[Image:Positive_frequency.JPG|left|200px| ]]The typical bond lengths of sp3 and sp2 C-C bond are 1.54Å and 1.34Å respectively, the van der waal's radius of carbon is 1.70Å. The newly form α bonds origin from 1) breaking of C-C double, 2) two partly formed α bonds between diene and dienophile. The first cases can be proven as the double bonds in dienophile and diene are longer than the typical carbon carbon double bond length, but shorter than the typical C-C α bond;[[Image:Animation 2.JPG|thumb|200px| Animation of imaginary frequency]] and the α bond length in the cie-butadiene has shortened significantly. As the diene and dienophile are two separate components before the Diels Alder reaction, a typical carbon van der waal's radius can be used here to approximate the distance between these carbons before the reaction, which is around 3.40Å (=2*1.70Å). While in the transition structure, this distance has been shortened significantly to 2.12Å. This can be further proven by looking at the animation of imaginary frequency at -955.87cm-1, the ends of dienophile and diene are getting closer to each other. This also proves the fact that two new α bonds are partly forming in the transition structure. The diene and dienophile do not approach to each other to form α bonds between them in the animation of the lowest positive frequency(as shown in the left).

Reference:
#Yi Li, K. N. Houk J. Am. Chem. Soc., 1993, 115 (16), pp 7478–7485
#Shogo SakaiJ. Phys. Chem. A, 2000, 104 (5), pp 922–927
#Fleming, Ian Pericyclic reactions : Oxford University Press 1998

Section 3 Diels Alder reaction between cyclohexa-1,3-diene reaction with maleic anhydride:

{| class="wikitable" border="1"
|+ Table showing structure, energies and summary table of endo and exo transition structure
! Type of transition structure!!Transition structure!! Energy / a.u.!!Summary table
|-
| Endo || [[Image:Endo.JPG|thumb|150px|Endo structure]]||-0.05150440||[[Image:Summary_table_endo.JPG|thumb|150px|Summary table of Endo]]
|-
| Exo || [[Image:Exo.JPG|thumb|150px|Exo structure]]||-0.05041965||[[Image:Summary_table_exo.JPG|thumb|150px|Summary table of Exo]]
|}

[[Image:Electronic_repulsion.JPG|right|200px|Electronic repulsion between C-H α orbital and C=O π orbital]]The endo transition structure is lower in energy than the exo structure by 0.71kcal/mol. The structural different between the endo and exo is due to the different orientations of maleic anhydride. A possible reason for exo form is more strained is due to the electronic repulsion between electrons in C-H α orbital (atom 1 and 2) and C=O π orbital (atom 3 and 4) in the exo form (as shown on the right). This results in an increase in energy of the transition structure. Such interaction does not happen in the endo form as the C-H α orbitals are now very far apart from each other.

{| class="wikitable" border="1"
|+ Table showing HOMO and their nodal properties in endo and exo form
! Transition structure !! Picture of HOMO!!Nodal property
|-
| Endo || [[Image:Homo_endo.jpg|thumb|150px| ]]||Two nodal points between the -(C=O)-O-(C=O)- fragment and the remainder of the system
|-
| Exo || [[Image:Homo_exo.jpg|thumb|150px| ]]||One nodal points between the -(C=O)-O-(C=O)- fragment and the remainder of the system
|}

The secondary orbital interaction is a class of electronic effect which can be rationalized here as the interactions between C=C π orbital and the C=O π* orbital as they have both correct symmetry and orientation. The resultant effect can stabilize the system by weakening the C=O double bond.

Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

2011-11-10T15:30:29Z

Fs1309:

2011-11-10T15:10:47Z

Fs1309:

2011-11-10T14:24:57Z

Fs1309:

Rep:Mod:fs1309module 3

2011-11-10T14:24:43Z

Fs1309:

3rd year computational lab Module 3 Transition states and reactivity.

Abstract:

This module aims to characterize transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions. This can be achieved by applying molecular orbital-based methods, solving the Schrodinger equation numerically, and locating transition structures based on the local shape of a potential energy surface. Together with showing what transition structures look like, reaction paths and barrier heights can also be calculated.

Part 1:

The Cope Rearrangement Tutorial [[Image:pic1.jpg|right|150px|Cope rearrangement]]

1)Optimizing the Reactants at HF/3-21G level theory. The energy of different conformers can be found in the summary table after optimization, and the symmetry is determined using '''Symmetrize''' under Edit menu.

{| class="wikitable" border="1"
|+ Table showing different conformers and their energy and comparisons to contents in appendix 1
! Conformer !! Structure !!point group!!Energy (Comparison to literature value) / a.u.!!Relative energy /kcalmol-1!!Summary Table
|-
| gauche1 ||[[Image:Structure_gauche_1.JPG|thumb|widthpx| ]]||C2||-231.68771613 (-231.68772 )||3.10 || [[Image:Summary_of_gauche_1.JPG|thumb|150px|Summary table for gauche 1]]
|-
| gauche2 ||[[Image:Structure_gauche_2.JPG|thumb|widthpx| ]]||C2||-231.69166702 (-231.69167 )||0.62 || [[Image:Summary_of_gauche_2.JPG|thumb|150px|Summary table for gauche 2]]
|-
| gauche3 ||[[Image:Structure_gauche_3.JPG|thumb|widthpx| ]]||C1||-231.69266120 (-231.69266 )||0.00 || [[Image:Summary_of_gauche_3.JPG|thumb|150px|Summary table for gauche 3]]
|-
| gauche4 ||[[Image:Structure_gauche_4.JPG|thumb|widthpx| ]]||C2||-231.69153032 (-231.69153 )||0.71 || [[Image:Summary_of_gauche_4.JPG|thumb|150px|Summary table for gauche 4]]
|-
| gauche5 ||[[Image:Structure_gauche_5.JPG|thumb|widthpx| ]]||C1||-231.68961572 (-231.68962 )||1.91 || [[Image:Summary_of_gauche_5.JPG|thumb|150px|Summary table for gauche 5]]
|-
| gauche6 ||[[Image:Structure_gauche_6.JPG|thumb|widthpx| ]]||C1||-231.68916017 (-231.68916 )||2.20|| [[Image:Summary_of_gauche_6.JPG|thumb|150px|Summary table for gauche 6]]
|-
| anti1 ||[[Image:Structrue_anti_1.jpg|thumb|widthpx| ]]||C2||-231.69260220 (-231.69260 )||0.04 || [[Image:Summary_of_anti_1.jpg|thumb|150px|Summary table for anti 1]]
|-
| anti2 ||[[Image:Structrue_anti_2.jpg|thumb|widthpx| ]]||Ci||-231.69253494 (-231.69254 )||0.08 || [[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table for anti 2]]
|-
| anti3 ||[[Image:Structrue_anti_3.jpg|thumb|widthpx| ]]||C2h||-231.68907066 (-231.68907 )||2.25 || [[Image:Summary_of_anti_3.jpg|thumb|150px|Summary table for anti 3]]||
|-
| anti4 ||[[Image:Structrue_anti_4.jpg|thumb|widthpx| ]]||C1||-231.69097054 (-231.69097 )||1.06|| [[Image:Summary_of_anti_4.jpg|thumb|150px|Summary table for anti 4]]
|}

Reoptimization and frequency analysis of Anti 2 conformer at B3LYP/6-31G* level after optimization at HF/6-31G level of theory.

Section 1 Optimization
{| class="wikitable" border="1"
|+ Comparison of results between HF/3-21G and B3LYP/6-31G*
! Method !! Structure!! Energy / a.u. (literature value)!!Summary table
|-
| HF/3-21G ||[[Image:Structrue_anti_2_HF.JPG|thumb|widthpx| ]] ||-231.69253494 (-231.692535 )||[[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table]]
|-
| B3LYP/6-31G* || [[Image:Structrue_anti_2_DFT.JPG|thumb|widthpx| ]]||-234.61169891 (-234.611710 )||[[Image:Summary_of_anti_2_dft.JPG|thumb|150px|Summary table]]
|}

Change in structure: [[Image:Comparison anti.jpg|right|200px|Comparison]]
The two structure are very similar, the small differences is found after comparing their total energies and geometric parameters such as bond angle, dihedral angle and bone length data obtained for the identical molecule but with different level of theory. It is noted that: 1)The total energy predicted at HF/6-31G level is much lower than what was obtained at B3LYP/6-31G* level, the relative energy is 2) The bond lengths obtained at HF/3-21G level are generally shorter than those at B3LYP/6-31G* level; 3) The most significant differences are found in the dihedral angle between central atoms and alkene carbon atoms, e.g: H(9)-C(6)-C(2)-C(1) C(7)-C(6)-C(2)-C(1). The maximum difference in dihedral angle is around 4°.

Section 2 Frequency analysis
[[Image:IR_spectrum 2.JPG|right|250px|Infra red spectrum ]]

No imaginary frequencies are found after checking the vibration results and spectrum, this means the optimized structure is not a transition structure. The thermochemistry data below are obtained from the output file.
Sum of electronic and zero-point Energies(E=Eelec+ZPE)= -234.469231
Sum of electronic and thermal Energies(E=E+Evib+Erot+Etrans)=-234.461865
Sum of electronic and thermal Enthalpies(E=E+RT)=-234.460920
Sum of electronic and thermal Free Energies(G=H-TS)=-234.500877

2) Optimizing the "Chair" and "Boat" Transition Structures

Section 1. Single allyl fragment optimization using the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Results of single allyl fragment optimization
! Structure of allyl fragement !! Summary table!!Comparison to transition structure
|-
| [[Image:Allyl.JPG|thumb|150px|Structure of Allyl fragment]] || [[Image:Summary.JPG|thumb|150px|Summary table of allyl fragment]]|| [[Image:Chair_HF.JPG|thumb|150px| ]]
|}

The structure of single allyl fragment look like one half of the transition structures shown.

Section 2. Chair two allyl fragments optimization

{| class="wikitable" border="1"
|+ Comparison of optimized structures using different settings
! Optimization setting !! Transition Structure !! Summary table!! Animation of imaginary frequency!!Bond forming /breaking distance/ Å
|-
| Method in (b) ||[[Image:Opt_b.JPG|thumb|150px|Transition structure obtained from method 1]] ||[[Image:Summary_table_opt_b.JPG|thumb|150px|Summary table]]||[[Image:Animation_of_imaginary_freq_b.JPG|thumb|150px|Imaginary frequency at -817.87cm-1]] ||2.02||
|-
| Method in (c)||[[Image:Opt_c.JPG|thumb|150px|Transition structure obtained from method 2]] ||[[Image:Summary_table_opt_c.JPG|thumb|150px|Summary table]]|| -||2.20||
|-
| Method in (d)|| [[Image:Opt_d.JPG|thumb|150px|Transition structure obtained from method 3]] ||[[Image:Summary_table_opt_d.JPG|thumb|150px|Summary table]]|| -||2.02||
|}

This animation of imaginary frequency at -817.87cm-1 corresponds to the Cope rearrangement as it shows both bond forming and breaking at different ends of two allyl fragments in the transition structure .

Section 3 Optimization of the boat transition structure using QST2 method

The modification refer to changing the central C-C-C-C (C2-C3-C4-C5) dihedral angle to 0o, followed by reduce the inside angle (C2-C3-C4 and C3-C4-C5) to 100o.

{| class="wikitable" border="1"
|+ Table showing labeling of atoms in reactants and products
! Component !! Picture of component!!Picture of component (modified)
|-
| Reactant || [[Image:Labeling_of_reactant.JPG|thumb|widthpx|cLabeling in reatant]] ||[[Image:|thumb|widthpx|Labeling in modified reactant]] ||
|-
| Product || [[Image:Labeling_of_product.JPG|thumb|widthpx|cLabeling in product]] ||[[Image:|thumb|widthpx|cLabeling in modified product]] ||
|-
| Transition structure || -- ||[[Image:Transition_state_1.JPG|thumb|widthpx| ]] ||
|}

The imaginary frequency was found at -840.01 cm-1. The corresponding motion is shown on the right. [[Image:Imaginary_frequency.JPG|right|150px|Motion corresponding to the imaginary frequency]]

f) Optimization of chair transition structure using IRC method

{| class="wikitable" border="1"
|+ Table showing conformations and energies of IRC methods
! Method !!Description of method!! Conformations !! Energy / a.u.
|-
| Initial Method ||minimization with 50 points along IRC ||[[Image:Chair_IRC_initial_stucture.JPG|thumb|150px| ]]||-231.68321543
|-
| Method 1 ||Normal minimization using the last point on IRC after initial method || [[Image:Method_1.JPG|thumb|150px| ]]||-231.69166702
|-
| Method 2 ||Minimization with 200 points along IRC|| [[Image:Method_2.JPG|thumb|150px| ]]||-231.61932195
|-
| Method 3 ||IRC with force constant specified at every step || [[Image:Method_3.JPG|thumb|150px| ]]||-231.69165600
|}

Similar conformers are obtained from method 1 and 3, which indicates the transition structures connect to the Gauche 2 conformer.

Activation energy analysis.

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from HF/3-21G
! !! Electronic energy (literature)/a.u.!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-231.619322 (-231.619322 )||-231.466696 (-231.466705)|| -231.477029(-234.461346)||[[Image:Chair_HF.JPG|thumb|100px| ]]|| [[Image:Chair_HF_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-231.602802 (-231.602802 )||-231.450929 (-231.450929 )|| -231.460610(-234.445300)||[[Image:Boat_HF.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 ||-231.692535 (-231.692535 )||-231.539541 (-231.539539)||-231.548453(-234.532566)||[[Image:Structrue_anti_2.jpg|thumb|100px| ]]|| [[Image:Summary_of_anti_2.jpg|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from B3LYP/6-31G*
! !! Electronic energy /a.u.(literature)!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-234.556983 (-234.556983 )||-234.414919 (-234.414919 )||-234.423600 (-234.408998)||[[Image:Chair_dft.JPG|thumb|100px| ]]|| [[Image:Chair_dft_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-234.543093 (-234.543093 )||-234.402340(-234.402340 )||(-234.396006)||[[Image:filename|thumb|100px| ]]|| [[Image:filename|thumb|100px| ]]||
|-
| Reactant Anti 2 || -234.611699 (-234.611710 )||-231.469242(-234.469203 )||-234.476549(-234.461856)||[[Image:DFT_method_anti_2.JPG|thumb|100px| ]]|| [[Image:Summary_of_anti_2_dft.JPG|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary table of activation energy obtained at different theory level and temperature
! Transition structure !! HF/3-21G at 0K /(kcal/mol)!!HF/3-21G at 298.15K/(kcal/mol)!!B3LYP/6-31G* at 0K/(kcal/mol)!!B3LYP/6-31G* at 298.15K/(kcal/mol)!!Expt. /(kcal/mol)
|-
| Chair ||45.71 (45.70) ||44.69(44.69)||34.09(34.06)||33.23(33.17)||33.5±0.5
|-
| Boat ||55.60 (55.60) ||55.12(54.76)||41.98(41.96)||(41.32)||44.7±2.0
|}
The numbers in bracket are literature values in appendix 2.

Comment on the results: The electronic energy and the sum of electronic and zero point energies both match the literature values very well, but the actual calculated values of the sum of electronic and thermal energies show a small difference with data given in appendix 2. This could only due to errors introduced during the calculation, as overall activation energies still match the literature value very well.

Part 2 Exercise

Section 1 Optimization of cis butadiene and determination of the symmetry of corresponding HOMO and LUMO [[Image:Summary_table.JPG|right|150px|Summary table]]

{| class="wikitable" border="1"
|+ Table of cis-butadiene's HOMO and LUMO and their symmetries
! Orbital !! Plot of orbital!!Symmetry with respect to the plane
|-
| HOMO || [[Image:HOMO.jpg|thumb|100px|HOMO]]|| [[Image:HOMO_symmetry_plane.jpg|thumb|100px|anti-symmetric with respect to the plane]] ||
|-
| LUMO || [[Image:LUMO.jpg|thumb|100px|LUMO]]|| [[Image:LUMO_symmetry_plane.jpg|thumb|100px|symmetric with respect to the plane]]||
|}

Section 2 Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path.

{| class="wikitable" border="1"
|+ Table of HOMO and LUMO to illustrate symmetry in the transition structure
! MO !! Picture of MO!!Symmetry of MO!!Interacting orbitals
|-
| HOMO ||[[Image:HOMO 1 .jpg |thumb|100px| ]]||Anti-symmetric with respect to the symmetry plane|| [[Image:Homo_of_diene.JPG|thumb|widthpx| ]]
|-
| LUMO || [[Image:LUMO 2 .jpg |thumb|100px| ]]||Symmetric with respect to the symmetry plane||[[Image:Lumo_of_diene.JPG|thumb|widthpx| ]]
|}

The Diels Alder reaction here, which involves two new α bonds forming due to the interaction between the diene's HOMO/LUMO and dienophile's LUMO/HOMO interaction, is a class of pericyclic reactions. Such reaction can only proceed if the π orbitals involved have correct symmetry. According to the selection rules in pericyclic reaction, such 6 electrons system can interact if the stereochemistry of two interacting orbitals are supra facial or two anti-facial. The HOMO and LUMO obtained from the transition structures both are consistent with the stereochemistry in the selection rules, as the HOMO show suprafacial interaction between diene and dienophile's interacting orbitals (HOMO of diene and LUMO of dieneophile), and LUMO show suprafacial interaction between diene and dienophile's interacting orbitals (LUMO of diene and HOMO of dieneophile).

[[Image:Transition_structure 1.JPG|thumb|200px|Labeling of transition structure]]

{| class="wikitable" border="1"
|+ Table comparing bond length in transition structure and typical sp3 and sp2 C-C bond lengths
! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !!Bonding between (n)C and (n')C !! Bond length/Å
|-
| (2)C --(12)C and (3)C --(9)C || 2.12||(2)C --(1)C and (3)C --(4)C||1.38||(1)C and (4)C||1.40||(1)C and (4)C||1.38
|}

n and n' here are used to indicate the bonding carbon atoms.

[[Image:Positive_frequency.JPG|left|200px| ]]The typical bond lengths of sp3 and sp2 C-C bond are 1.54Å and 1.34Å respectively, the van der waal's radius of carbon is 1.70Å. The newly form α bonds origin from 1) breaking of C-C double, 2) two partly formed α bonds between diene and dienophile. The first cases can be proven as the double bonds in dienophile and diene are longer than the typical carbon carbon double bond length, but shorter than the typical C-C α bond;[[Image:Animation 2.JPG|thumb|200px| Animation of imaginary frequency]] and the α bond length in the cie-butadiene has shortened significantly. As the diene and dienophile are two separate components before the Diels Alder reaction, a typical carbon van der waal's radius can be used here to approximate the distance between these carbons before the reaction, which is around 3.40Å (=2*1.70Å). While in the transition structure, this distance has been shortened significantly to 2.12Å. This can be further proven by looking at the animation of imaginary frequency at -955.87cm-1, the ends of dienophile and diene are getting closer to each other. This also proves the fact that two new α bonds are partly forming in the transition structure. The diene and dienophile do not approach to each other to form α bonds between them in the animation of the lowest positive frequency(as shown in the left).

Reference:
#Yi Li, K. N. Houk J. Am. Chem. Soc., 1993, 115 (16), pp 7478–7485
#Shogo SakaiJ. Phys. Chem. A, 2000, 104 (5), pp 922–927

Section 3 Diels Alder reaction between cyclohexa-1,3-diene reaction with maleic anhydride:

{| class="wikitable" border="1"
|+ Table showing structure, energies and summary table of endo and exo transition structure
! Type of transition structure!!Transition structure!! Energy / a.u.!!Summary table
|-
| Endo || [[Image:Endo.JPG|thumb|150px|Endo structure]]||-0.05150440||[[Image:Summary_table_endo.JPG|thumb|150px|Summary table of Endo]]
|-
| Exo || [[Image:Exo.JPG|thumb|150px|Exo structure]]||-0.05041965||[[Image:Summary_table_exo.JPG|thumb|150px|Summary table of Exo]]
|}

[[Image:Electronic_repulsion.JPG|thumb|200px|Electronic repulsion between C-H α orbital and C=O π orbital]]The endo transition structure is lower in energy than the exo structure by 0.71kcal/mol. The structural different between the endo and exo is due to the different orientations of maleic anhydride. A possible reason for exo form is more strained is due to the electronic repulsion between electrons in C-H α orbital and C=O π orbital in the exo form.

Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Rep:Mod:fs1309module 3

2011-11-10T13:04:46Z

Fs1309:

3rd year computational lab Module 3 Transition states and reactivity.

Abstract:

This module aims to characterize transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions. This can be achieved by applying molecular orbital-based methods, solving the Schrodinger equation numerically, and locating transition structures based on the local shape of a potential energy surface. Together with showing what transition structures look like, reaction paths and barrier heights can also be calculated.

Part 1:

The Cope Rearrangement Tutorial [[Image:pic1.jpg|right|150px|Cope rearrangement]]

1)Optimizing the Reactants at HF/3-21G level theory. The energy of different conformers can be found in the summary table after optimization, and the symmetry is determined using '''Symmetrize''' under Edit menu.

{| class="wikitable" border="1"
|+ Table showing different conformers and their energy and comparisons to contents in appendix 1
! Conformer !! Structure !!point group!!Energy (Comparison to literature value) / a.u.!!Relative energy /kcalmol-1!!Summary Table
|-
| gauche1 ||[[Image:Structure_gauche_1.JPG|thumb|widthpx| ]]||C2||-231.68771613 (-231.68772 )||3.10 || [[Image:Summary_of_gauche_1.JPG|thumb|150px|Summary table for gauche 1]]
|-
| gauche2 ||[[Image:Structure_gauche_2.JPG|thumb|widthpx| ]]||C2||-231.69166702 (-231.69167 )||0.62 || [[Image:Summary_of_gauche_2.JPG|thumb|150px|Summary table for gauche 2]]
|-
| gauche3 ||[[Image:Structure_gauche_3.JPG|thumb|widthpx| ]]||C1||-231.69266120 (-231.69266 )||0.00 || [[Image:Summary_of_gauche_3.JPG|thumb|150px|Summary table for gauche 3]]
|-
| gauche4 ||[[Image:Structure_gauche_4.JPG|thumb|widthpx| ]]||C2||-231.69153032 (-231.69153 )||0.71 || [[Image:Summary_of_gauche_4.JPG|thumb|150px|Summary table for gauche 4]]
|-
| gauche5 ||[[Image:Structure_gauche_5.JPG|thumb|widthpx| ]]||C1||-231.68961572 (-231.68962 )||1.91 || [[Image:Summary_of_gauche_5.JPG|thumb|150px|Summary table for gauche 5]]
|-
| gauche6 ||[[Image:Structure_gauche_6.JPG|thumb|widthpx| ]]||C1||-231.68916017 (-231.68916 )||2.20|| [[Image:Summary_of_gauche_6.JPG|thumb|150px|Summary table for gauche 6]]
|-
| anti1 ||[[Image:Structrue_anti_1.jpg|thumb|widthpx| ]]||C2||-231.69260220 (-231.69260 )||0.04 || [[Image:Summary_of_anti_1.jpg|thumb|150px|Summary table for anti 1]]
|-
| anti2 ||[[Image:Structrue_anti_2.jpg|thumb|widthpx| ]]||Ci||-231.69253494 (-231.69254 )||0.08 || [[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table for anti 2]]
|-
| anti3 ||[[Image:Structrue_anti_3.jpg|thumb|widthpx| ]]||C2h||-231.68907066 (-231.68907 )||2.25 || [[Image:Summary_of_anti_3.jpg|thumb|150px|Summary table for anti 3]]||
|-
| anti4 ||[[Image:Structrue_anti_4.jpg|thumb|widthpx| ]]||C1||-231.69097054 (-231.69097 )||1.06|| [[Image:Summary_of_anti_4.jpg|thumb|150px|Summary table for anti 4]]
|}

Reoptimization and frequency analysis of Anti 2 conformer at B3LYP/6-31G* level after optimization at HF/6-31G level of theory.

Section 1 Optimization
{| class="wikitable" border="1"
|+ Comparison of results between HF/3-21G and B3LYP/6-31G*
! Method !! Structure!! Energy / a.u. (literature value)!!Summary table
|-
| HF/3-21G ||[[Image:Structrue_anti_2_HF.JPG|thumb|widthpx| ]] ||-231.69253494 (-231.692535 )||[[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table]]
|-
| B3LYP/6-31G* || [[Image:Structrue_anti_2_DFT.JPG|thumb|widthpx| ]]||-234.61169891 (-234.611710 )||[[Image:Summary_of_anti_2_dft.JPG|thumb|150px|Summary table]]
|}

Change in structure: [[Image:Comparison anti.jpg|right|200px|Comparison]]
The two structure are very similar, the small differences is found after comparing their total energies and geometric parameters such as bond angle, dihedral angle and bone length data obtained for the identical molecule but with different level of theory. It is noted that: 1)The total energy predicted at HF/6-31G level is much lower than what was obtained at B3LYP/6-31G* level, the relative energy is 2) The bond lengths obtained at HF/3-21G level are generally shorter than those at B3LYP/6-31G* level; 3) The most significant differences are found in the dihedral angle between central atoms and alkene carbon atoms, e.g: H(9)-C(6)-C(2)-C(1) C(7)-C(6)-C(2)-C(1). The maximum difference in dihedral angle is around 4°.

Section 2 Frequency analysis
[[Image:IR_spectrum 2.JPG|right|250px|Infra red spectrum ]]

No imaginary frequencies are found after checking the vibration results and spectrum, this means the optimized structure is not a transition structure. The thermochemistry data below are obtained from the output file.
Sum of electronic and zero-point Energies(E=Eelec+ZPE)= -234.469231
Sum of electronic and thermal Energies(E=E+Evib+Erot+Etrans)=-234.461865
Sum of electronic and thermal Enthalpies(E=E+RT)=-234.460920
Sum of electronic and thermal Free Energies(G=H-TS)=-234.500877

2) Optimizing the "Chair" and "Boat" Transition Structures

Section 1. Single allyl fragment optimization using the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Results of single allyl fragment optimization
! Structure of allyl fragement !! Summary table!!Comparison to transition structure
|-
| [[Image:Allyl.JPG|thumb|150px|Structure of Allyl fragment]] || [[Image:Summary.JPG|thumb|150px|Summary table of allyl fragment]]|| [[Image:Chair_HF.JPG|thumb|150px| ]]
|}

The structure of single allyl fragment look like one half of the transition structures shown.

Section 2. Chair two allyl fragments optimization

{| class="wikitable" border="1"
|+ Comparison of optimized structures using different settings
! Optimization setting !! Transition Structure !! Summary table!! Animation of imaginary frequency!!Bond forming /breaking distance/ Å
|-
| Method in (b) ||[[Image:Opt_b.JPG|thumb|150px|Transition structure obtained from method 1]] ||[[Image:Summary_table_opt_b.JPG|thumb|150px|Summary table]]||[[Image:Animation_of_imaginary_freq_b.JPG|thumb|150px|Imaginary frequency at -817.87cm-1]] ||2.02||
|-
| Method in (c)||[[Image:Opt_c.JPG|thumb|150px|Transition structure obtained from method 2]] ||[[Image:Summary_table_opt_c.JPG|thumb|150px|Summary table]]|| -||2.20||
|-
| Method in (d)|| [[Image:Opt_d.JPG|thumb|150px|Transition structure obtained from method 3]] ||[[Image:Summary_table_opt_d.JPG|thumb|150px|Summary table]]|| -||2.02||
|}

This animation of imaginary frequency at -817.87cm-1 corresponds to the Cope rearrangement as it shows both bond forming and breaking at different ends of two allyl fragments in the transition structure .

Section 3 Optimization of the boat transition structure using QST2 method

The modification refer to changing the central C-C-C-C (C2-C3-C4-C5) dihedral angle to 0o, followed by reduce the inside angle (C2-C3-C4 and C3-C4-C5) to 100o.

{| class="wikitable" border="1"
|+ Table showing labeling of atoms in reactants and products
! Component !! Picture of component!!Picture of component (modified)
|-
| Reactant || [[Image:Labeling_of_reactant.JPG|thumb|widthpx|cLabeling in reatant]] ||[[Image:|thumb|widthpx|Labeling in modified reactant]] ||
|-
| Product || [[Image:Labeling_of_product.JPG|thumb|widthpx|cLabeling in product]] ||[[Image:|thumb|widthpx|cLabeling in modified product]] ||
|-
| Transition structure || -- ||[[Image:Transition_state_1.JPG|thumb|widthpx| ]] ||
|}

The imaginary frequency was found at -840.01 cm-1. The corresponding motion is shown on the right. [[Image:Imaginary_frequency.JPG|right|150px|Motion corresponding to the imaginary frequency]]

f) Optimization of chair transition structure using IRC method

{| class="wikitable" border="1"
|+ Table showing conformations and energies of IRC methods
! Method !!Description of method!! Conformations !! Energy / a.u.
|-
| Initial Method ||minimization with 50 points along IRC ||[[Image:Chair_IRC_initial_stucture.JPG|thumb|150px| ]]||-231.68321543
|-
| Method 1 ||Normal minimization using the last point on IRC after initial method || [[Image:Method_1.JPG|thumb|150px| ]]||-231.69166702
|-
| Method 2 ||Minimization with 200 points along IRC|| [[Image:Method_2.JPG|thumb|150px| ]]||-231.61932195
|-
| Method 3 ||IRC with force constant specified at every step || [[Image:Method_3.JPG|thumb|150px| ]]||-231.69165600
|}

Similar conformers are obtained from method 1 and 3, which indicates the transition structures connect to the Gauche 2 conformer.

Activation energy analysis.

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from HF/3-21G
! !! Electronic energy (literature)/a.u.!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-231.619322 (-231.619322 )||-231.466696 (-231.466705)|| -231.477029(-234.461346)||[[Image:Chair_HF.JPG|thumb|100px| ]]|| [[Image:Chair_HF_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-231.602802 (-231.602802 )||-231.450929 (-231.450929 )|| -231.460610(-234.445300)||[[Image:Boat_HF.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 ||-231.692535 (-231.692535 )||-231.539541 (-231.539539)||-231.548453(-234.532566)||[[Image:Structrue_anti_2.jpg|thumb|100px| ]]|| [[Image:Summary_of_anti_2.jpg|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from B3LYP/6-31G*
! !! Electronic energy /a.u.(literature)!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-234.556983 (-234.556983 )||-234.414919 (-234.414919 )||-234.423600 (-234.408998)||[[Image:Chair_dft.JPG|thumb|100px| ]]|| [[Image:Chair_dft_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-234.543093 (-234.543093 )||-234.402340(-234.402340 )||(-234.396006)||[[Image:filename|thumb|100px| ]]|| [[Image:filename|thumb|100px| ]]||
|-
| Reactant Anti 2 || -234.611699 (-234.611710 )||-231.469242(-234.469203 )||-234.476549(-234.461856)||[[Image:DFT_method_anti_2.JPG|thumb|100px| ]]|| [[Image:Summary_of_anti_2_dft.JPG|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary table of activation energy obtained at different theory level and temperature
! Transition structure !! HF/3-21G at 0K /(kcal/mol)!!HF/3-21G at 298.15K/(kcal/mol)!!B3LYP/6-31G* at 0K/(kcal/mol)!!B3LYP/6-31G* at 298.15K/(kcal/mol)!!Expt. /(kcal/mol)
|-
| Chair ||45.71 (45.70) ||44.69(44.69)||34.09(34.06)||33.23(33.17)||33.5±0.5
|-
| Boat ||55.60 (55.60) ||55.12(54.76)||41.98(41.96)||(41.32)||44.7±2.0
|}
The numbers in bracket are literature values in appendix 2.

Comment on the results: The electronic energy and the sum of electronic and zero point energies both match the literature values very well, but the actual calculated values of the sum of electronic and thermal energies show a small difference with data given in appendix 2. This could only due to errors introduced during the calculation, as overall activation energies still match the literature value very well.

Part 2 Exercise

Section 1 Optimization of cis butadiene and determination of the symmetry of corresponding HOMO and LUMO [[Image:Summary_table.JPG|right|150px|Summary table]]

{| class="wikitable" border="1"
|+ Table of cis-butadiene's HOMO and LUMO and their symmetries
! Orbital !! Plot of orbital!!Symmetry with respect to the plane
|-
| HOMO || [[Image:HOMO.jpg|thumb|100px|HOMO]]|| [[Image:HOMO_symmetry_plane.jpg|thumb|100px|anti-symmetric with respect to the plane]] ||
|-
| LUMO || [[Image:LUMO.jpg|thumb|100px|LUMO]]|| [[Image:LUMO_symmetry_plane.jpg|thumb|100px|symmetric with respect to the plane]]||
|}

Section 2 Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path.

{| class="wikitable" border="1"
|+ Table of HOMO and LUMO to illustrate symmetry in the transition structure
! MO !! Picture of MO!!Symmetry of MO!!Interacting orbitals
|-
| HOMO ||[[Image:HOMO 1 .jpg |thumb|100px| ]]||Anti-symmetric with respect to the symmetry plane|| [[Image:Homo_of_diene.JPG|thumb|widthpx| ]]
|-
| LUMO || [[Image:LUMO 2 .jpg |thumb|100px| ]]||Symmetric with respect to the symmetry plane||[[Image:Lumo_of_diene.JPG|thumb|widthpx| ]]
|}

The Diels Alder reaction here, which involves two new α bonds forming due to the interaction between the diene's HOMO/LUMO and dienophile's LUMO/HOMO interaction, is a class of pericyclic reactions. Such reaction can only proceed if the π orbitals involved have correct symmetry. According to the selection rules in pericyclic reaction, such 6 electrons system can interact if the stereochemistry of two interacting orbitals are supra facial or two anti-facial. The HOMO and LUMO obtained from the transition structures both are consistent with the stereochemistry in the selection rules, as the HOMO show suprafacial interaction between diene and dienophile's interacting orbitals (HOMO of diene and LUMO of dieneophile), and LUMO show suprafacial interaction between diene and dienophile's interacting orbitals (LUMO of diene and HOMO of dieneophile).

[[Image:Transition_structure 1.JPG|thumb|200px|Labeling of transition structure]]

{| class="wikitable" border="1"
|+ Table comparing bond length in transition structure and typical sp3 and sp2 C-C bond lengths
! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !!Bonding between (n)C and (n')C !! Bond length/Å
|-
| (2)C --(12)C and (3)C --(9)C || 2.12||(2)C --(1)C and (3)C --(4)C||1.38||(1)C and (4)C||1.40||(1)C and (4)C||1.38
|}

n and n' here are used to indicate the bonding carbon atoms.

[[Image:Positive_frequency.JPG|left|200px| ]]The typical bond lengths of sp3 and sp2 C-C bond are 1.54Å and 1.34Å respectively, the van der waal's radius of carbon is 1.70Å. The newly form α bonds origin from 1) breaking of C-C double, 2) two partly formed α bonds between diene and dienophile. The first cases can be proven as the double bonds in dienophile and diene are longer than the typical carbon carbon double bond length, but shorter than the typical C-C α bond;[[Image:Animation 2.JPG|thumb|200px| Animation of imaginary frequency]] and the α bond length in the cie-butadiene has shortened significantly. As the diene and dienophile are two separate components before the Diels Alder reaction, a typical carbon van der waal's radius can be used here to approximate the distance between these carbons before the reaction, which is around 3.40Å (=2*1.70Å). While in the transition structure, this distance has been shortened significantly to 2.12Å. This can be further proven by looking at the animation of imaginary frequency at -955.87cm-1, the ends of dienophile and diene are getting closer to each other. This also proves the fact that two new α bonds are partly forming in the transition structure. The diene and dienophile do not approach to each other to form α bonds between them in the animation of the lowest positive frequency(as shown in the left).

Reference:
#Yi Li, K. N. Houk J. Am. Chem. Soc., 1993, 115 (16), pp 7478–7485
#Shogo SakaiJ. Phys. Chem. A, 2000, 104 (5), pp 922–927

Section 3 Diels Alder reaction between cyclohexa-1,3-diene reaction with maleic anhydride:

{| class="wikitable" border="1"
|+ Table showing structure, energies and summary table of endo and exo transition structure
! Type of transition structure!!Transition structure!! Energy / a.u.!!Summary table
|-
| Endo || [[Image:Endo.JPG|thumb|150px|Endo structure]]||-0.05150440||[[Image:Summary_table_endo.JPG|thumb|150px|Summary table of Endo]]
|-
| Exo || [[Image:Exo.JPG|thumb|150px|Exo structure]]||-0.05041965||[[Image:Summary_table_exo.JPG|thumb|150px|Summary table of Exo]]
|}

Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Rep:Mod:fs1309module 3

2011-11-10T13:04:00Z

Fs1309:

3rd year computational lab Module 3 Transition states and reactivity.

Abstract:

This module aims to characterize transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions. This can be achieved by applying molecular orbital-based methods, solving the Schrodinger equation numerically, and locating transition structures based on the local shape of a potential energy surface. Together with showing what transition structures look like, reaction paths and barrier heights can also be calculated.

Part 1:

The Cope Rearrangement Tutorial [[Image:pic1.jpg|right|150px|Cope rearrangement]]

1)Optimizing the Reactants at HF/3-21G level theory. The energy of different conformers can be found in the summary table after optimization, and the symmetry is determined using '''Symmetrize''' under Edit menu.

{| class="wikitable" border="1"
|+ Table showing different conformers and their energy and comparisons to contents in appendix 1
! Conformer !! Structure !!point group!!Energy (Comparison to literature value) / a.u.!!Relative energy /kcalmol-1!!Summary Table
|-
| gauche1 ||[[Image:Structure_gauche_1.JPG|thumb|widthpx| ]]||C2||-231.68771613 (-231.68772 )||3.10 || [[Image:Summary_of_gauche_1.JPG|thumb|150px|Summary table for gauche 1]]
|-
| gauche2 ||[[Image:Structure_gauche_2.JPG|thumb|widthpx| ]]||C2||-231.69166702 (-231.69167 )||0.62 || [[Image:Summary_of_gauche_2.JPG|thumb|150px|Summary table for gauche 2]]
|-
| gauche3 ||[[Image:Structure_gauche_3.JPG|thumb|widthpx| ]]||C1||-231.69266120 (-231.69266 )||0.00 || [[Image:Summary_of_gauche_3.JPG|thumb|150px|Summary table for gauche 3]]
|-
| gauche4 ||[[Image:Structure_gauche_4.JPG|thumb|widthpx| ]]||C2||-231.69153032 (-231.69153 )||0.71 || [[Image:Summary_of_gauche_4.JPG|thumb|150px|Summary table for gauche 4]]
|-
| gauche5 ||[[Image:Structure_gauche_5.JPG|thumb|widthpx| ]]||C1||-231.68961572 (-231.68962 )||1.91 || [[Image:Summary_of_gauche_5.JPG|thumb|150px|Summary table for gauche 5]]
|-
| gauche6 ||[[Image:Structure_gauche_6.JPG|thumb|widthpx| ]]||C1||-231.68916017 (-231.68916 )||2.20|| [[Image:Summary_of_gauche_6.JPG|thumb|150px|Summary table for gauche 6]]
|-
| anti1 ||[[Image:Structrue_anti_1.jpg|thumb|widthpx| ]]||C2||-231.69260220 (-231.69260 )||0.04 || [[Image:Summary_of_anti_1.jpg|thumb|150px|Summary table for anti 1]]
|-
| anti2 ||[[Image:Structrue_anti_2.jpg|thumb|widthpx| ]]||Ci||-231.69253494 (-231.69254 )||0.08 || [[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table for anti 2]]
|-
| anti3 ||[[Image:Structrue_anti_3.jpg|thumb|widthpx| ]]||C2h||-231.68907066 (-231.68907 )||2.25 || [[Image:Summary_of_anti_3.jpg|thumb|150px|Summary table for anti 3]]||
|-
| anti4 ||[[Image:Structrue_anti_4.jpg|thumb|widthpx| ]]||C1||-231.69097054 (-231.69097 )||1.06|| [[Image:Summary_of_anti_4.jpg|thumb|150px|Summary table for anti 4]]
|}

Reoptimization and frequency analysis of Anti 2 conformer at B3LYP/6-31G* level after optimization at HF/6-31G level of theory.

Section 1 Optimization
{| class="wikitable" border="1"
|+ Comparison of results between HF/3-21G and B3LYP/6-31G*
! Method !! Structure!! Energy / a.u. (literature value)!!Summary table
|-
| HF/3-21G ||[[Image:Structrue_anti_2_HF.JPG|thumb|widthpx| ]] ||-231.69253494 (-231.692535 )||[[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table]]
|-
| B3LYP/6-31G* || [[Image:Structrue_anti_2_DFT.JPG|thumb|widthpx| ]]||-234.61169891 (-234.611710 )||[[Image:Summary_of_anti_2_dft.JPG|thumb|150px|Summary table]]
|}

Change in structure: [[Image:Comparison anti.jpg|right|200px|Comparison]]
The two structure are very similar, the small differences is found after comparing their total energies and geometric parameters such as bond angle, dihedral angle and bone length data obtained for the identical molecule but with different level of theory. It is noted that: 1)The total energy predicted at HF/6-31G level is much lower than what was obtained at B3LYP/6-31G* level, the relative energy is 2) The bond lengths obtained at HF/3-21G level are generally shorter than those at B3LYP/6-31G* level; 3) The most significant differences are found in the dihedral angle between central atoms and alkene carbon atoms, e.g: H(9)-C(6)-C(2)-C(1) C(7)-C(6)-C(2)-C(1). The maximum difference in dihedral angle is around 4°.

Section 2 Frequency analysis
[[Image:IR_spectrum 2.JPG|right|250px|Infra red spectrum ]]

No imaginary frequencies are found after checking the vibration results and spectrum, this means the optimized structure is not a transition structure. The thermochemistry data below are obtained from the output file.
Sum of electronic and zero-point Energies(E=Eelec+ZPE)= -234.469231
Sum of electronic and thermal Energies(E=E+Evib+Erot+Etrans)=-234.461865
Sum of electronic and thermal Enthalpies(E=E+RT)=-234.460920
Sum of electronic and thermal Free Energies(G=H-TS)=-234.500877

2) Optimizing the "Chair" and "Boat" Transition Structures

Section 1. Single allyl fragment optimization using the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Results of single allyl fragment optimization
! Structure of allyl fragement !! Summary table!!Comparison to transition structure
|-
| [[Image:Allyl.JPG|thumb|150px|Structure of Allyl fragment]] || [[Image:Summary.JPG|thumb|150px|Summary table of allyl fragment]]|| [[Image:Chair_HF.JPG|thumb|150px| ]]
|}

The structure of single allyl fragment look like one half of the transition structures shown.

Section 2. Chair two allyl fragments optimization

{| class="wikitable" border="1"
|+ Comparison of optimized structures using different settings
! Optimization setting !! Transition Structure !! Summary table!! Animation of imaginary frequency!!Bond forming /breaking distance/ Å
|-
| Method in (b) ||[[Image:Opt_b.JPG|thumb|150px|Transition structure obtained from method 1]] ||[[Image:Summary_table_opt_b.JPG|thumb|150px|Summary table]]||[[Image:Animation_of_imaginary_freq_b.JPG|thumb|150px|Imaginary frequency at -817.87cm-1]] ||2.02||
|-
| Method in (c)||[[Image:Opt_c.JPG|thumb|150px|Transition structure obtained from method 2]] ||[[Image:Summary_table_opt_c.JPG|thumb|150px|Summary table]]|| -||2.20||
|-
| Method in (d)|| [[Image:Opt_d.JPG|thumb|150px|Transition structure obtained from method 3]] ||[[Image:Summary_table_opt_d.JPG|thumb|150px|Summary table]]|| -||2.02||
|}

This animation of imaginary frequency at -817.87cm-1 corresponds to the Cope rearrangement as it shows both bond forming and breaking at different ends of two allyl fragments in the transition structure .

Section 3 Optimization of the boat transition structure using QST2 method

The modification refer to changing the central C-C-C-C (C2-C3-C4-C5) dihedral angle to 0o, followed by reduce the inside angle (C2-C3-C4 and C3-C4-C5) to 100o.

{| class="wikitable" border="1"
|+ Table showing labeling of atoms in reactants and products
! Component !! Picture of component!!Picture of component (modified)
|-
| Reactant || [[Image:Labeling_of_reactant.JPG|thumb|widthpx|cLabeling in reatant]] ||[[Image:|thumb|widthpx|Labeling in modified reactant]] ||
|-
| Product || [[Image:Labeling_of_product.JPG|thumb|widthpx|cLabeling in product]] ||[[Image:|thumb|widthpx|cLabeling in modified product]] ||
|-
| Transition structure || -- ||[[Image:Transition_state_1.JPG|thumb|widthpx| ]] ||
|}

The imaginary frequency was found at -840.01 cm-1. The corresponding motion is shown on the right. [[Image:Imaginary_frequency.JPG|right|150px|Motion corresponding to the imaginary frequency]]

f) Optimization of chair transition structure using IRC method

{| class="wikitable" border="1"
|+ Table showing conformations and energies of IRC methods
! Method !!Description of method!! Conformations !! Energy / a.u.
|-
| Initial Method ||minimization with 50 points along IRC ||[[Image:Chair_IRC_initial_stucture.JPG|thumb|150px| ]]||-231.68321543
|-
| Method 1 ||Normal minimization using the last point on IRC after initial method || [[Image:Method_1.JPG|thumb|150px| ]]||-231.69166702
|-
| Method 2 ||Minimization with 200 points along IRC|| [[Image:Method_2.JPG|thumb|150px| ]]||-231.61932195
|-
| Method 3 ||IRC with force constant specified at every step || [[Image:Method_3.JPG|thumb|150px| ]]||-231.69165600
|}

Similar conformers are obtained from method 1 and 3, which indicates the transition structures connect to the Gauche 2 conformer.

Activation energy analysis.

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from HF/3-21G
! !! Electronic energy (literature)/a.u.!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-231.619322 (-231.619322 )||-231.466696 (-231.466705)|| -231.477029(-234.461346)||[[Image:Chair_HF.JPG|thumb|100px| ]]|| [[Image:Chair_HF_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-231.602802 (-231.602802 )||-231.450929 (-231.450929 )|| -231.460610(-234.445300)||[[Image:Boat_HF.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 ||-231.692535 (-231.692535 )||-231.539541 (-231.539539)||-231.548453(-234.532566)||[[Image:Structrue_anti_2.jpg|thumb|100px| ]]|| [[Image:Summary_of_anti_2.jpg|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from B3LYP/6-31G*
! !! Electronic energy /a.u.(literature)!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-234.556983 (-234.556983 )||-234.414919 (-234.414919 )||-234.423600 (-234.408998)||[[Image:Chair_dft.JPG|thumb|100px| ]]|| [[Image:Chair_dft_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-234.543093 (-234.543093 )||-234.402340(-234.402340 )||(-234.396006)||[[Image:filename|thumb|100px| ]]|| [[Image:filename|thumb|100px| ]]||
|-
| Reactant Anti 2 || -234.611699 (-234.611710 )||-231.469242(-234.469203 )||-234.476549(-234.461856)||[[Image:DFT_method_anti_2.JPG|thumb|100px| ]]|| [[Image:Summary_of_anti_2_dft.JPG|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary table of activation energy obtained at different theory level and temperature
! Transition structure !! HF/3-21G at 0K /(kcal/mol)!!HF/3-21G at 298.15K/(kcal/mol)!!B3LYP/6-31G* at 0K/(kcal/mol)!!B3LYP/6-31G* at 298.15K/(kcal/mol)!!Expt. /(kcal/mol)
|-
| Chair ||45.71 (45.70) ||44.69(44.69)||34.09(34.06)||33.23(33.17)||33.5±0.5
|-
| Boat ||55.60 (55.60) ||55.12(54.76)||41.98(41.96)||(41.32)||44.7±2.0
|}
The numbers in bracket are literature values in appendix 2.

Comment on the results: The electronic energy and the sum of electronic and zero point energies both match the literature values very well, but the actual calculated values of the sum of electronic and thermal energies show a small difference with data given in appendix 2. This could only due to errors introduced during the calculation, as overall activation energies still match the literature value very well.

Part 2 Exercise

Section 1 Optimization of cis butadiene and determination of the symmetry of corresponding HOMO and LUMO [[Image:Summary_table.JPG|right|150px|Summary table]]

{| class="wikitable" border="1"
|+ Table of cis-butadiene's HOMO and LUMO and their symmetries
! Orbital !! Plot of orbital!!Symmetry with respect to the plane
|-
| HOMO || [[Image:HOMO.jpg|thumb|100px|HOMO]]|| [[Image:HOMO_symmetry_plane.jpg|thumb|100px|anti-symmetric with respect to the plane]] ||
|-
| LUMO || [[Image:LUMO.jpg|thumb|100px|LUMO]]|| [[Image:LUMO_symmetry_plane.jpg|thumb|100px|symmetric with respect to the plane]]||
|}

Section 2 Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path.

{| class="wikitable" border="1"
|+ Table of HOMO and LUMO to illustrate symmetry in the transition structure
! MO !! Picture of MO!!Symmetry of MO!!Interacting orbitals
|-
| HOMO ||[[Image:HOMO 1 .jpg |thumb|100px| ]]||Anti-symmetric with respect to the symmetry plane|| [[Image:Homo_of_diene.JPG|thumb|widthpx| ]]
|-
| LUMO || [[Image:LUMO 2 .jpg |thumb|100px| ]]||Symmetric with respect to the symmetry plane||[[Image:Lumo_of_diene.JPG|thumb|widthpx| ]]
|}

The Diels Alder reaction here, which involves two new α bonds forming due to the interaction between the diene's HOMO/LUMO and dienophile's LUMO/HOMO interaction, is a class of pericyclic reactions. Such reaction can only proceed if the π orbitals involved have correct symmetry. According to the selection rules in pericyclic reaction, such 6 electrons system can interact if the stereochemistry of two interacting orbitals are supra facial or two anti-facial. The HOMO and LUMO obtained from the transition structures both are consistent with the stereochemistry in the selection rules, as the HOMO show suprafacial interaction between diene and dienophile's interacting orbitals (HOMO of diene and LUMO of dieneophile), and LUMO show suprafacial interaction between diene and dienophile's interacting orbitals (LUMO of diene and HOMO of dieneophile).

[[Image:Transition_structure 1.JPG|thumb|200px|Labeling of transition structure]]

{| class="wikitable" border="1"
|+ Table comparing bond length in transition structure and typical sp3 and sp2 C-C bond lengths
! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !!Bonding between (n)C and (n')C !! Bond length/Å
|-
| (2)C --(12)C and (3)C --(9)C || 2.12||(2)C --(1)C and (3)C --(4)C||1.38||(1)C and (4)C||1.40||(1)C and (4)C||1.38
|}

n and n' here are used to indicate the bonding carbon atoms.

[[Image:Positive_frequency.JPG|left|200px| ]]The typical bond lengths of sp3 and sp2 C-C bond are 1.54Å and 1.34Å respectively, the van der waal's radius of carbon is 1.70Å. The newly form α bonds origin from 1) breaking of C-C double, 2) two partly formed α bonds between diene and dienophile. The first cases can be proven as the double bonds in dienophile and diene are longer than the typical carbon carbon double bond length, but shorter than the typical C-C α bond;[[Image:Animation 2.JPG|thumb|200px| Animation of imaginary frequency]] and the α bond length in the cie-butadiene has shortened significantly. As the diene and dienophile are two separate components before the Diels Alder reaction, a typical carbon van der waal's radius can be used here to approximate the distance between these carbons before the reaction, which is around 3.40Å (=2*1.70Å). While in the transition structure, this distance has been shortened significantly to 2.12Å. This can be further proven by looking at the animation of imaginary frequency at -955.87cm-1, the ends of dienophile and diene are getting closer to each other. This also proves the fact that two new α bonds are partly forming in the transition structure. The diene and dienophile do not approach to each other to form α bonds between them in the animation of the lowest positive frequency(as shown in the left).

Reference:
#Yi Li, K. N. Houk J. Am. Chem. Soc., 1993, 115 (16), pp 7478–7485
#Shogo SakaiJ. Phys. Chem. A, 2000, 104 (5), pp 922–927

Section 3 Diels Alder reaction between cyclohexa-1,3-diene reaction with maleic anhydride:

{| class="wikitable" border="1"
|+ Table showing structure, energies and summary table of endo and exo transition structure
! Transition structure !! Energy / a.u.!!Summary table
|-
| Endo || [[Image:Endo.JPG|thumb|150px|Endo structure]]||-0.05150440||[[Image:Summary_table_endo.JPG|thumb|150px|Summary table of Endo]]
|-
| Exo || [[Image:Exo.JPG|thumb|150px|Exo structure]]||-0.05041965||[[Image:Summary_table_exo.JPG|thumb|150px|Summary table of Exo]]
|}

Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

Rep:Mod:fs1309module 3

2011-11-10T13:02:39Z

Fs1309:

3rd year computational lab Module 3 Transition states and reactivity.

Abstract:

This module aims to characterize transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions. This can be achieved by applying molecular orbital-based methods, solving the Schrodinger equation numerically, and locating transition structures based on the local shape of a potential energy surface. Together with showing what transition structures look like, reaction paths and barrier heights can also be calculated.

Part 1:

The Cope Rearrangement Tutorial [[Image:pic1.jpg|right|150px|Cope rearrangement]]

1)Optimizing the Reactants at HF/3-21G level theory. The energy of different conformers can be found in the summary table after optimization, and the symmetry is determined using '''Symmetrize''' under Edit menu.

{| class="wikitable" border="1"
|+ Table showing different conformers and their energy and comparisons to contents in appendix 1
! Conformer !! Structure !!point group!!Energy (Comparison to literature value) / a.u.!!Relative energy /kcalmol-1!!Summary Table
|-
| gauche1 ||[[Image:Structure_gauche_1.JPG|thumb|widthpx| ]]||C2||-231.68771613 (-231.68772 )||3.10 || [[Image:Summary_of_gauche_1.JPG|thumb|150px|Summary table for gauche 1]]
|-
| gauche2 ||[[Image:Structure_gauche_2.JPG|thumb|widthpx| ]]||C2||-231.69166702 (-231.69167 )||0.62 || [[Image:Summary_of_gauche_2.JPG|thumb|150px|Summary table for gauche 2]]
|-
| gauche3 ||[[Image:Structure_gauche_3.JPG|thumb|widthpx| ]]||C1||-231.69266120 (-231.69266 )||0.00 || [[Image:Summary_of_gauche_3.JPG|thumb|150px|Summary table for gauche 3]]
|-
| gauche4 ||[[Image:Structure_gauche_4.JPG|thumb|widthpx| ]]||C2||-231.69153032 (-231.69153 )||0.71 || [[Image:Summary_of_gauche_4.JPG|thumb|150px|Summary table for gauche 4]]
|-
| gauche5 ||[[Image:Structure_gauche_5.JPG|thumb|widthpx| ]]||C1||-231.68961572 (-231.68962 )||1.91 || [[Image:Summary_of_gauche_5.JPG|thumb|150px|Summary table for gauche 5]]
|-
| gauche6 ||[[Image:Structure_gauche_6.JPG|thumb|widthpx| ]]||C1||-231.68916017 (-231.68916 )||2.20|| [[Image:Summary_of_gauche_6.JPG|thumb|150px|Summary table for gauche 6]]
|-
| anti1 ||[[Image:Structrue_anti_1.jpg|thumb|widthpx| ]]||C2||-231.69260220 (-231.69260 )||0.04 || [[Image:Summary_of_anti_1.jpg|thumb|150px|Summary table for anti 1]]
|-
| anti2 ||[[Image:Structrue_anti_2.jpg|thumb|widthpx| ]]||Ci||-231.69253494 (-231.69254 )||0.08 || [[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table for anti 2]]
|-
| anti3 ||[[Image:Structrue_anti_3.jpg|thumb|widthpx| ]]||C2h||-231.68907066 (-231.68907 )||2.25 || [[Image:Summary_of_anti_3.jpg|thumb|150px|Summary table for anti 3]]||
|-
| anti4 ||[[Image:Structrue_anti_4.jpg|thumb|widthpx| ]]||C1||-231.69097054 (-231.69097 )||1.06|| [[Image:Summary_of_anti_4.jpg|thumb|150px|Summary table for anti 4]]
|}

Reoptimization and frequency analysis of Anti 2 conformer at B3LYP/6-31G* level after optimization at HF/6-31G level of theory.

Section 1 Optimization
{| class="wikitable" border="1"
|+ Comparison of results between HF/3-21G and B3LYP/6-31G*
! Method !! Structure!! Energy / a.u. (literature value)!!Summary table
|-
| HF/3-21G ||[[Image:Structrue_anti_2_HF.JPG|thumb|widthpx| ]] ||-231.69253494 (-231.692535 )||[[Image:Summary_of_anti_2.jpg|thumb|150px|Summary table]]
|-
| B3LYP/6-31G* || [[Image:Structrue_anti_2_DFT.JPG|thumb|widthpx| ]]||-234.61169891 (-234.611710 )||[[Image:Summary_of_anti_2_dft.JPG|thumb|150px|Summary table]]
|}

Change in structure: [[Image:Comparison anti.jpg|right|200px|Comparison]]
The two structure are very similar, the small differences is found after comparing their total energies and geometric parameters such as bond angle, dihedral angle and bone length data obtained for the identical molecule but with different level of theory. It is noted that: 1)The total energy predicted at HF/6-31G level is much lower than what was obtained at B3LYP/6-31G* level, the relative energy is 2) The bond lengths obtained at HF/3-21G level are generally shorter than those at B3LYP/6-31G* level; 3) The most significant differences are found in the dihedral angle between central atoms and alkene carbon atoms, e.g: H(9)-C(6)-C(2)-C(1) C(7)-C(6)-C(2)-C(1). The maximum difference in dihedral angle is around 4°.

Section 2 Frequency analysis
[[Image:IR_spectrum 2.JPG|right|250px|Infra red spectrum ]]

No imaginary frequencies are found after checking the vibration results and spectrum, this means the optimized structure is not a transition structure. The thermochemistry data below are obtained from the output file.
Sum of electronic and zero-point Energies(E=Eelec+ZPE)= -234.469231
Sum of electronic and thermal Energies(E=E+Evib+Erot+Etrans)=-234.461865
Sum of electronic and thermal Enthalpies(E=E+RT)=-234.460920
Sum of electronic and thermal Free Energies(G=H-TS)=-234.500877

2) Optimizing the "Chair" and "Boat" Transition Structures

Section 1. Single allyl fragment optimization using the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Results of single allyl fragment optimization
! Structure of allyl fragement !! Summary table!!Comparison to transition structure
|-
| [[Image:Allyl.JPG|thumb|150px|Structure of Allyl fragment]] || [[Image:Summary.JPG|thumb|150px|Summary table of allyl fragment]]|| [[Image:Chair_HF.JPG|thumb|150px| ]]
|}

The structure of single allyl fragment look like one half of the transition structures shown.

Section 2. Chair two allyl fragments optimization

{| class="wikitable" border="1"
|+ Comparison of optimized structures using different settings
! Optimization setting !! Transition Structure !! Summary table!! Animation of imaginary frequency!!Bond forming /breaking distance/ Å
|-
| Method in (b) ||[[Image:Opt_b.JPG|thumb|150px|Transition structure obtained from method 1]] ||[[Image:Summary_table_opt_b.JPG|thumb|150px|Summary table]]||[[Image:Animation_of_imaginary_freq_b.JPG|thumb|150px|Imaginary frequency at -817.87cm-1]] ||2.02||
|-
| Method in (c)||[[Image:Opt_c.JPG|thumb|150px|Transition structure obtained from method 2]] ||[[Image:Summary_table_opt_c.JPG|thumb|150px|Summary table]]|| -||2.20||
|-
| Method in (d)|| [[Image:Opt_d.JPG|thumb|150px|Transition structure obtained from method 3]] ||[[Image:Summary_table_opt_d.JPG|thumb|150px|Summary table]]|| -||2.02||
|}

This animation of imaginary frequency at -817.87cm-1 corresponds to the Cope rearrangement as it shows both bond forming and breaking at different ends of two allyl fragments in the transition structure .

Section 3 Optimization of the boat transition structure using QST2 method

The modification refer to changing the central C-C-C-C (C2-C3-C4-C5) dihedral angle to 0o, followed by reduce the inside angle (C2-C3-C4 and C3-C4-C5) to 100o.

{| class="wikitable" border="1"
|+ Table showing labeling of atoms in reactants and products
! Component !! Picture of component!!Picture of component (modified)
|-
| Reactant || [[Image:Labeling_of_reactant.JPG|thumb|widthpx|cLabeling in reatant]] ||[[Image:|thumb|widthpx|Labeling in modified reactant]] ||
|-
| Product || [[Image:Labeling_of_product.JPG|thumb|widthpx|cLabeling in product]] ||[[Image:|thumb|widthpx|cLabeling in modified product]] ||
|-
| Transition structure || -- ||[[Image:Transition_state_1.JPG|thumb|widthpx| ]] ||
|}

The imaginary frequency was found at -840.01 cm-1. The corresponding motion is shown on the right. [[Image:Imaginary_frequency.JPG|right|150px|Motion corresponding to the imaginary frequency]]

f) Optimization of chair transition structure using IRC method

{| class="wikitable" border="1"
|+ Table showing conformations and energies of IRC methods
! Method !!Description of method!! Conformations !! Energy / a.u.
|-
| Initial Method ||minimization with 50 points along IRC ||[[Image:Chair_IRC_initial_stucture.JPG|thumb|150px| ]]||-231.68321543
|-
| Method 1 ||Normal minimization using the last point on IRC after initial method || [[Image:Method_1.JPG|thumb|150px| ]]||-231.69166702
|-
| Method 2 ||Minimization with 200 points along IRC|| [[Image:Method_2.JPG|thumb|150px| ]]||-231.61932195
|-
| Method 3 ||IRC with force constant specified at every step || [[Image:Method_3.JPG|thumb|150px| ]]||-231.69165600
|}

Similar conformers are obtained from method 1 and 3, which indicates the transition structures connect to the Gauche 2 conformer.

Activation energy analysis.

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from HF/3-21G
! !! Electronic energy (literature)/a.u.!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-231.619322 (-231.619322 )||-231.466696 (-231.466705)|| -231.477029(-234.461346)||[[Image:Chair_HF.JPG|thumb|100px| ]]|| [[Image:Chair_HF_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-231.602802 (-231.602802 )||-231.450929 (-231.450929 )|| -231.460610(-234.445300)||[[Image:Boat_HF.JPG|thumb|100px| ]]|| [[Image:Boat_hf_summary.JPG|thumb|100px| ]]||
|-
| Reactant Anti 2 ||-231.692535 (-231.692535 )||-231.539541 (-231.539539)||-231.548453(-234.532566)||[[Image:Structrue_anti_2.jpg|thumb|100px| ]]|| [[Image:Summary_of_anti_2.jpg|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary of energies and transition structure obtained from B3LYP/6-31G*
! !! Electronic energy /a.u.(literature)!!Sum of electronic and zero-point energies at 0K(literature)/a.u.!!Sum of electronic and zero-point energies at 298.15K(literature)/a.u.!!Structure !! Summary tables
|-
| Chair TS ||-234.556983 (-234.556983 )||-234.414919 (-234.414919 )||-234.423600 (-234.408998)||[[Image:Chair_dft.JPG|thumb|100px| ]]|| [[Image:Chair_dft_table.JPG|thumb|100px| ]]||
|-
| Boat TS ||-234.543093 (-234.543093 )||-234.402340(-234.402340 )||(-234.396006)||[[Image:filename|thumb|100px| ]]|| [[Image:filename|thumb|100px| ]]||
|-
| Reactant Anti 2 || -234.611699 (-234.611710 )||-231.469242(-234.469203 )||-234.476549(-234.461856)||[[Image:DFT_method_anti_2.JPG|thumb|100px| ]]|| [[Image:Summary_of_anti_2_dft.JPG|thumb|100px| ]]||
|}

{| class="wikitable" border="1"
|+ Summary table of activation energy obtained at different theory level and temperature
! Transition structure !! HF/3-21G at 0K /(kcal/mol)!!HF/3-21G at 298.15K/(kcal/mol)!!B3LYP/6-31G* at 0K/(kcal/mol)!!B3LYP/6-31G* at 298.15K/(kcal/mol)!!Expt. /(kcal/mol)
|-
| Chair ||45.71 (45.70) ||44.69(44.69)||34.09(34.06)||33.23(33.17)||33.5±0.5
|-
| Boat ||55.60 (55.60) ||55.12(54.76)||41.98(41.96)||(41.32)||44.7±2.0
|}
The numbers in bracket are literature values in appendix 2.

Comment on the results: The electronic energy and the sum of electronic and zero point energies both match the literature values very well, but the actual calculated values of the sum of electronic and thermal energies show a small difference with data given in appendix 2. This could only due to errors introduced during the calculation, as overall activation energies still match the literature value very well.

Part 2 Exercise

Section 1 Optimization of cis butadiene and determination of the symmetry of corresponding HOMO and LUMO [[Image:Summary_table.JPG|right|150px|Summary table]]

{| class="wikitable" border="1"
|+ Table of cis-butadiene's HOMO and LUMO and their symmetries
! Orbital !! Plot of orbital!!Symmetry with respect to the plane
|-
| HOMO || [[Image:HOMO.jpg|thumb|100px|HOMO]]|| [[Image:HOMO_symmetry_plane.jpg|thumb|100px|anti-symmetric with respect to the plane]] ||
|-
| LUMO || [[Image:LUMO.jpg|thumb|100px|LUMO]]|| [[Image:LUMO_symmetry_plane.jpg|thumb|100px|symmetric with respect to the plane]]||
|}

Section 2 Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path.

{| class="wikitable" border="1"
|+ Table of HOMO and LUMO to illustrate symmetry in the transition structure
! MO !! Picture of MO!!Symmetry of MO!!Interacting orbitals
|-
| HOMO ||[[Image:HOMO 1 .jpg |thumb|100px| ]]||Anti-symmetric with respect to the symmetry plane|| [[Image:Homo_of_diene.JPG|thumb|widthpx| ]]
|-
| LUMO || [[Image:LUMO 2 .jpg |thumb|100px| ]]||Symmetric with respect to the symmetry plane||[[Image:Lumo_of_diene.JPG|thumb|widthpx| ]]
|}

The Diels Alder reaction here, which involves two new α bonds forming due to the interaction between the diene's HOMO/LUMO and dienophile's LUMO/HOMO interaction, is a class of pericyclic reactions. Such reaction can only proceed if the π orbitals involved have correct symmetry. According to the selection rules in pericyclic reaction, such 6 electrons system can interact if the stereochemistry of two interacting orbitals are supra facial or two anti-facial. The HOMO and LUMO obtained from the transition structures both are consistent with the stereochemistry in the selection rules, as the HOMO show suprafacial interaction between diene and dienophile's interacting orbitals (HOMO of diene and LUMO of dieneophile), and LUMO show suprafacial interaction between diene and dienophile's interacting orbitals (LUMO of diene and HOMO of dieneophile).

[[Image:Transition_structure 1.JPG|thumb|200px|Labeling of transition structure]]

{| class="wikitable" border="1"
|+ Table comparing bond length in transition structure and typical sp3 and sp2 C-C bond lengths
! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !! Bonding between (n)C and (n')C !! Bond length/Å !!Bonding between (n)C and (n')C !! Bond length/Å
|-
| (2)C --(12)C and (3)C --(9)C || 2.12||(2)C --(1)C and (3)C --(4)C||1.38||(1)C and (4)C||1.40||(1)C and (4)C||1.38
|}

n and n' here are used to indicate the bonding carbon atoms.

[[Image:Positive_frequency.JPG|left|200px| ]]The typical bond lengths of sp3 and sp2 C-C bond are 1.54Å and 1.34Å respectively, the van der waal's radius of carbon is 1.70Å. The newly form α bonds origin from 1) breaking of C-C double, 2) two partly formed α bonds between diene and dienophile. The first cases can be proven as the double bonds in dienophile and diene are longer than the typical carbon carbon double bond length, but shorter than the typical C-C α bond;[[Image:Animation 2.JPG|thumb|200px| Animation of imaginary frequency]] and the α bond length in the cie-butadiene has shortened significantly. As the diene and dienophile are two separate components before the Diels Alder reaction, a typical carbon van der waal's radius can be used here to approximate the distance between these carbons before the reaction, which is around 3.40Å (=2*1.70Å). While in the transition structure, this distance has been shortened significantly to 2.12Å. This can be further proven by looking at the animation of imaginary frequency at -955.87cm-1, the ends of dienophile and diene are getting closer to each other. This also proves the fact that two new α bonds are partly forming in the transition structure. The diene and dienophile do not approach to each other to form α bonds between them in the animation of the lowest positive frequency(as shown in the left).

Reference:
#Yi Li, K. N. Houk J. Am. Chem. Soc., 1993, 115 (16), pp 7478–7485
#Shogo SakaiJ. Phys. Chem. A, 2000, 104 (5), pp 922–927

Section 3 Diels Alder reaction between cyclohexa-1,3-diene reaction with maleic anhydride:

{| class="wikitable" border="1"
|+ Table showing structure, energies and summary table of endo and exo transition structure
! Transition structure !! heading
|-
| Endo || [[Image:Endo.JPG|thumb|widthpx|Endo structure]]||||[[Image:Summary_table_endo.JPG|thumb|widthpx|Summary table of Endo]]
|-
| Exo || [[Image:Exo.JPG|thumb|widthpx|Exo structure]]||||[[Image:Summary_table_exo.JPG|thumb|widthpx|Summary table of Exo]]
|}

Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

File:Summary table exo.JPG

2011-11-10T13:02:32Z

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