ChemWiki - User contributions [en]

Rep:Mod:gaussian y u no converge??!

2013-03-15T16:59:06Z

Ajg110: /* Comparison of the Transition States */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

From 6-31G* level of theory.

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

[[FILE:Boat_TS_pic_AG.png|400px]]

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less). From the MO's that have been constructed of the HOMO's of the ENDO and EXO transition states, it can be concluded that in this case, there is no secondary orbital effects present due to the observation of a node inbetween the -(C=O)-O-(C=O)- fragment and the rest of the system. This agrees with the literature, which suggests that the formation of the endo TS is favoured over formation of the exo TS when these secondary orbital interactions are absent, implying that the endo product must have the lower energy TS<ref>M.Fox, R.Cardona, and N.Kiwiet, ''J. Org. Chem.'', '''1987''', 52, 1469-1474</ref>. Therefore, the energetics of the transition state are determined by sterics and other non-orbital effects (eg solvent).

==References==

<references/>

Rep:Mod:gaussian y u no converge??!

2013-03-15T16:57:50Z

Ajg110: /* Endo Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

From 6-31G* level of theory.

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

[[FILE:Boat_TS_pic_AG.png|400px]]

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less). From the MO's that have been constructed of the HOMO's of the ENDO and EXO transition states, it can be concluded that in this case, there is no secondary orbital effects present due to the observation of a node inbetween the two molecules of the transition state. This agrees with the literature, which suggests that the formation of the endo TS is favoured over formation of the exo TS when these secondary orbital interactions are absent, implying that the endo product must have the lower energy TS<ref>M.Fox, R.Cardona, and N.Kiwiet, ''J. Org. Chem.'', '''1987''', 52, 1469-1474</ref>. Therefore, the energetics of the transition state are determined by sterics and other non-orbital effects (eg solvent).

==References==

<references/>

Rep:Mod:gaussian y u no converge??!

2013-03-15T16:50:04Z

Ajg110: /* Comparison of the Transition States */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

From 6-31G* level of theory.

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

[[FILE:Boat_TS_pic_AG.png|400px]]

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less). From the MO's that have been constructed of the HOMO's of the ENDO and EXO transition states, it can be concluded that in this case, there is no secondary orbital effects present due to the observation of a node inbetween the two molecules of the transition state. This agrees with the literature, which suggests that the formation of the endo TS is favoured over formation of the exo TS when these secondary orbital interactions are absent, implying that the endo product must have the lower energy TS<ref>M.Fox, R.Cardona, and N.Kiwiet, ''J. Org. Chem.'', '''1987''', 52, 1469-1474</ref>. Therefore, the energetics of the transition state are determined by sterics and other non-orbital effects (eg solvent).

==References==

<references/>

Rep:Mod:gaussian y u no converge??!

2013-03-15T16:49:46Z

Ajg110: /* Comparison of the Transition States */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

From 6-31G* level of theory.

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

[[FILE:Boat_TS_pic_AG.png|400px]]

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less). From the MO's that have been constructed of the HOMO's of the ENDO and EXO transition states, it can be concluded that in this case, there is no secondary orbital effects present due to the observation of a node inbetween the two molecules of the transition state. This agrees with the literature, which suggests that the formation of the endo TS is favoured over formation of the exo TS when these secondary orbital interactions are absent, implying that the endo product must have the lower energy TS<ref>M.Fox, R.Cardona, and N.Kiwiet, ''J. Org. Chem. '', '''1987''', 52, 1469-1474</ref>. Therefore, the energetics of the transition state are determined by sterics and other non-orbital effects (eg solvent).

==References==

<references/>

Rep:Mod:gaussian y u no converge??!

2013-03-15T16:48:38Z

Ajg110: /* Comparison of the Transition States */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

From 6-31G* level of theory.

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

[[FILE:Boat_TS_pic_AG.png|400px]]

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less). From the MO's that have been constructed of the HOMO's of the ENDO and EXO transition states, it can be concluded that in this case, there is no secondary orbital effects present due to the observation of a node inbetween the two molecules of the transition state. This agrees with the literature, which suggests that the endo product is favoured when these secondary orbital interactions are absent, suggesting that the endo product must have the lower energy TS<ref>M.Fox, R.Cardona, and N.Kiwiet, ''J. Org. Chem. '', '''1987''', 52, 1469-1474</ref>. Therefore, the energetics of the transition state are determined by sterics and other non-orbital effects (eg solvent).

==References==

<references/>

Rep:Mod:gaussian y u no converge??!

2013-03-15T16:48:29Z

Ajg110: /* Comparison of the Transition States */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

From 6-31G* level of theory.

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

[[FILE:Boat_TS_pic_AG.png|400px]]

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less). From the MO's that have been constructed of the HOMO's of the ENDO and EXO transition states, it can be concluded that in this case, there is no secondary orbital effects present due to the observation of a node inbetween the two molecules of the transition state. This agrees with the literature, which suggests that the endo product is favoured when these secondary orbital interactions are absent, suggesting that the endo product must have the lower energy TS<ref>M.Fox, R.Cardona, and N.Kiwiet, ''J. Org. Chem. '', '''1987''', 52 , 1469-1474</ref>. Therefore, the energetics of the transition state are determined by sterics and other non-orbital effects (eg solvent).

==References==

<references/>

Rep:Mod:gaussian y u no converge??!

2013-03-15T16:48:05Z

Ajg110: /* Comparison of the Transition States */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

From 6-31G* level of theory.

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

[[FILE:Boat_TS_pic_AG.png|400px]]

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less). From the MO's that have been constructed of the HOMO's of the ENDO and EXO transition states, it can be concluded that in this case, there is no secondary orbital effects present due to the observation of a node inbetween the two molecules of the transition state. This agrees with the literature, which suggests that the endo product is favoured when these secondary orbital interactions are absent, suggesting that the endo product must have the lower energy TS<ref>M.Fox, R.Cardona, and N.Kiwiet, ''J. Org. Chem. '', '''1987''',52, 1469-1474</ref>. Therefore, the energetics of the transition state are determined by sterics and other non-orbital effects (eg solvent).

==References==

<references/>

Rep:Mod:gaussian y u no converge??!

2013-03-15T16:47:27Z

Ajg110: /* Comparison of the Transition States */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

From 6-31G* level of theory.

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

[[FILE:Boat_TS_pic_AG.png|400px]]

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less). From the MO's that have been constructed of the HOMO's of the ENDO and EXO transition states, it can be concluded that in this case, there is no secondary orbital effects present due to the observation of a node inbetween the two molecules of the transition state. This agrees with the literature, which suggests that the endo product is favoured when these secondary orbital interactions are absent, suggesting that the endo product must have the lower energy TS<ref>M.Fox, R.Cardona, and N.Kiwiet, J. Org. Chem. 1987,52, 1469-1474</ref>. Therefore, the energetics of the transition state are determined by sterics and other non-orbital effects (eg solvent).

==References==

<references/>

Rep:Mod:gaussian y u no converge??!

2013-03-15T16:40:02Z

Ajg110: /* Comparison of the Transition States */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

From 6-31G* level of theory.

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

[[FILE:Boat_TS_pic_AG.png|400px]]

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less). From the MO's that have been constructed of the HOMO's of the ENDO and EXO transition states, it can be concluded that in this case, there is no secondary orbital effects present due to the observation of a node inbetween the two molecules of the transition state. Therefore, the energetics of the transition state are determined by sterics and other non-orbital effects (eg solvent).

Rep:Mod:gaussian y u no converge??!

2013-03-15T16:06:53Z

Ajg110: /* Boat Transition State Optimisation: QST2 Method */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

From 6-31G* level of theory.

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

[[FILE:Boat_TS_pic_AG.png|400px]]

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less). From the MO's that have been constructed of the HOMO's of the ENDO and EXO transition states, it can be concluded that there is no secondary orbital effects present due to the observation of a node inbetween the two molecules of the transition state. Therefore, the energetics of the transition state are determined by sterics and other non-orbital effects (eg solvent) alone in this case.

File:Boat TS pic AG.png

2013-03-15T16:06:21Z

Ajg110:

Rep:Mod:gaussian y u no converge??!

2013-03-15T15:58:24Z

Ajg110: /* Thermochemistry */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

From 6-31G* level of theory.

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less). From the MO's that have been constructed of the HOMO's of the ENDO and EXO transition states, it can be concluded that there is no secondary orbital effects present due to the observation of a node inbetween the two molecules of the transition state. Therefore, the energetics of the transition state are determined by sterics and other non-orbital effects (eg solvent) alone in this case.

Rep:Mod:gaussian y u no converge??!

2013-03-15T15:14:20Z

Ajg110: /* Comparison of the Transition States */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less). From the MO's that have been constructed of the HOMO's of the ENDO and EXO transition states, it can be concluded that there is no secondary orbital effects present due to the observation of a node inbetween the two molecules of the transition state. Therefore, the energetics of the transition state are determined by sterics and other non-orbital effects (eg solvent) alone in this case.

Rep:Mod:gaussian y u no converge??!

2013-03-15T15:05:37Z

Ajg110: /* Comparison of the Transition States */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less).

Rep:Mod:gaussian y u no converge??!

2013-03-15T15:05:21Z

Ajg110: /* Comparison of the Transition States */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is as we would expect, because there is increased steric repulsions in the exo form (as the sp3 section of the molecule is residing over the maleic anhydride, which leads to steric clashing between the hydrogens bonded to these sp3 carbons and the maleic anhydride itself. The endo form has the planar part of the molecule residing over the maleic anhydride instead, which clashes less), which would lead to the prediction of the exo form having a slightly lower energy. However, to rationalise the apparent endo-preference, we must consider secondary orbit interactions.

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:54:43Z

Ajg110: /* Comparison of the Transition States */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is surprising at first, because there is increased steric repulsions in the endo form (as the planar, sp2 section of the molecule is residing over the maleic anhydride, which is less flexible and can't bend upwards to minimise the steric repulsion, as the sp3 section can in the exo form), which would lead to the prediction of the exo form having a slightly lower energy. However, to rationalise the apparent endo-preference, we must consider secondary orbit interactions.

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:52:00Z

Ajg110: /* Comparison of the Transition States */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is surprising at first, because there is increased steric repulsions in the endo form, which would lead to the prediction of the exo form having a slightly lower energy. However, to rationalise the apparent endo-preference, we must consider secondary orbit interactions.

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:47:32Z

Ajg110:

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

===Comparison of the Transition States===

As seen above, the transition state for the exo form has a slightly higher energy than the endo form (18.29 kcal/mol vs. 15.72 kcal/mol). This is likely due to increased steric repulsion in the exo form, likely originating from

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:38:08Z

Ajg110: /* Transition State HOMO */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:37:54Z

Ajg110: /* Transition State HOMO */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

The HOMO is anti-symmetric with respect to the plane.

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:28:27Z

Ajg110: /* Endo Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

File:Endo TS AG.png

2013-03-15T14:28:13Z

Ajg110:

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:27:00Z

Ajg110: /* Exo Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS_AG.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

File:Exo TS AG.png

2013-03-15T14:26:48Z

Ajg110:

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:26:03Z

Ajg110: /* Exo Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:Exo_TS.png|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:23:23Z

Ajg110: /* Exo Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:23:08Z

Ajg110: /* Endo Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

The energy of the transition state is:

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

'''The energy of the transition state is:'''

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:22:38Z

Ajg110: /* Optimisation of the Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

The energy of the transition state is:

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

The energy of the transition state is:

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.68339677 +612.708455 = 0.02505823 a.u. = 15.724280085 kcal/mol

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:20:23Z

Ajg110: /* Optimisation of the Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

The energy of the transition state is:

-233.41891076 - 379.28954427 = -612.708455 a.u. (The energy of the reactant molecules combined)/

-612.67931096 +612.708455 = 0.02914404 a.u. = 18.288165117 kcal/mol

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:13:38Z

Ajg110: /* Optimisation of Cyclohexadiene */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -233.41891076 a.u.

RMS Gradient Norm = 0.00003542 a.u.

Dipole Moment = 0.3782 Debye

Point Group = C2

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T14:00:58Z

Ajg110: /* HOMO of the Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's. The reaction is allowed because the orbitals have the same symmetry properties, making orbital overal possible.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T13:55:39Z

Ajg110: /* HOMO of the Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the ''cis-''butadiene to give 2 new symmetric MO's.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T13:54:37Z

Ajg110: /* HOMO of the Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO. This predicts that the reaction will be allowed as 2 symmetric orbits overlap: the filled HOMO of the ethene and the unfilled LUMO of the 'cis-''butadiene.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T13:41:35Z

Ajg110: /* HOMO of the Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO.

HOMO of ethene:

[[FILE:HOMO_ethene.png|200px]]

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T13:40:02Z

Ajg110: /* Optimisation of ethene */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png|400px]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png|400px]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO.

HOMO of ethene:

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T13:39:41Z

Ajg110: /* The Diels Alder Cycloaddition */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===Optimisation of ethene===
File Type = .log

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -77.60098811 a.u.

RMS Gradient Norm = 0.00009216 a.u.

Dipole Moment = 0.0000 Debye

LOG File: [[FILE:ETHENE_OPT.LOG]]

====Ethene HOMO====

[[FILE:HOMO_ethene.png]]

This MO is symmetric with respect to the plane.

====Ethene LUMO====

[[FILE:LUMO_ethene.png]]

This MO is antisymmetric with respect to the plane.

===Optimisation of ''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This MO is antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This MO is symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO.

HOMO of ethene:

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

File:LUMO ethene.png

2013-03-15T13:37:33Z

Ajg110:

File:HOMO ethene.png

2013-03-15T13:37:33Z

Ajg110:

File:ETHENE OPT.LOG

2013-03-15T13:37:32Z

Ajg110:

Rep:Mod:gaussian y u no converge??!

2013-03-15T13:21:14Z

Ajg110: /* HOMO of the Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This is MO antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This is MO symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO.

HOMO of ethene:

LUMO of ''cis-''butadiene:

[[FILE:Butadiene_LUMO.png|200px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T13:19:33Z

Ajg110: /* HOMO of the Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This is MO antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This is MO symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

We can see that the HOMO of ethene and the LUMO of ''cis-''butadiene have been used to form this MO.

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T13:16:06Z

Ajg110: /* Vibration of Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This is MO antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This is MO symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

The formation of the 2 bonds in the vibration corresponding to the reaction pathway is synchronous as the vibration is symmetrical, leading to both bonds being formed at the same time. In the lowest positive vibration, the motion of the atoms is asynchronous, with the molecules twisting in opposite directions.

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T13:13:35Z

Ajg110: /* LUMO of the Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This is MO antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This is MO symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

The LUMO is symmetric to the plane.

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T13:13:11Z

Ajg110: /* HOMO of the Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This is MO antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This is MO symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

The HOMO is symmetric to the plane.

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T13:12:24Z

Ajg110: /* Transition State Geometry for the Prototype Reaction */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This is MO antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This is MO symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is slightly larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T13:08:57Z

Ajg110: /* Transition State Geometry for the Prototype Reaction */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This is MO antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This is MO symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

'''Bond Lengths:'''

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å. The partially formed C-C bond is much larger than what would be expected from typical C-C bonds, as would be expected as the bond hasn't been completely formed yet, which will make it weaker and therefore longer than its formed counterpart. The fact that the partially formed bond is larger than the VdW radii for carbon suggests that the atoms are at a separation where there are weak attractive forces pulling the atoms together, which is consistent with the situation where the bonds are just beginning to form.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T12:50:55Z

Ajg110: /* Transition State Geometry for the Prototype Reaction */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This is MO antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This is MO symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and the carbon VdW radii of 1.70Å.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T12:50:00Z

Ajg110: /* Transition State Geometry for the Prototype Reaction */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This is MO antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This is MO symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

The partially formed C-C bond is 2.21Å long. This can be compared to the standard sp3 bond length of about 1.54Å, the standard sp2 bond length of around 1.47Å and Carbon VdW radii of 1.70Å.

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T12:35:21Z

Ajg110: /* Vibration of Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This is MO antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This is MO symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

'''Lowest positive frequency:'''

[[FILE:DA_lowest_freq_vibration.gif|400px]]

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]

Rep:Mod:gaussian y u no converge??!

2013-03-15T12:35:12Z

Ajg110: /* Vibration of Transition State */

==Optimisation of 1,5-hexadiene==

===Anti Conformer===

====Optimisation With HF/3-21G Basis Set====

The Anti linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Diene_anti_pic.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69253528 a.u.

RMS Gradient Norm = 0.00001891 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

<pre>
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000463 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037380D-08
Optimization completed.
-- Stationary point found.</pre>

LOG file: [[FILE:DIENE_ANTI_321G_Ci_symm.LOG]]

''anti-2'' energy: -231.69254 a.u.

My ''anti-2'' energy: -231.69253528 a.u.

====Optimisation With B3LYP/6-31G* Basis Set====

[[FILE:Anti_631G_pic.png|400px]]

This was then re-optimised using the B3LYP/6-31G* level of theory:

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001326 a.u.

Dipole Moment = 0.0000 Debye

Point Group = Ci

Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.

<pre>Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.589030D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:DIENE_ANTI_631G.LOG]]

In terms of the overall geometry, there is very little difference between the 3-21G and 6-31G* optimised forms (as can be seen from the pictures), with both forms having virtually identical structures. The most obvious difference is in the energy of the 2 forms, with the 6-31G* form having a significantly lower energy, which is to be expected as it has been optimised using a much more accurate basis set.

====Frequency Analysis====

A frequency analysis was then carried out to ensure a minimum had been found and IR spectrum simulated:

[[FILE:Anti_diene_IR.png|500px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61170280 a.u.

RMS Gradient Norm = 0.00001310 a.u.

Dipole Moment = 0.0000 Debye

Point Group = CI

Job cpu time: 0 days 0 hours 2 minutes 31.0 seconds.

<pre>Low frequencies --- -18.6412 -11.7204 -0.0006 0.0007 0.0011 1.8205
Low frequencies --- 72.7270 80.1433 120.0219</pre>

Frequency Analysis File: [[FILE:DIENE_ANTI_631G_FREQ.LOG]]

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212 a.u.

Sum of electronic and thermal Energies= -234.461856 a.u.

Sum of electronic and thermal Enthalpies= -234.460912 a.u.

Sum of electronic and thermal Free Energies= -234.500821 a.u.

===Gauche Conformer===

====Optimisation With HF/3-21G Basis Set====

The Gauche linkage conformer was optimised using the HF/3-21G level of theory:

[[FILE:Gauche_image_hexa.png|400px]]

File Type = .chk

Calculation Type = FOPT

Calculation Method = RHF

Basis Set = 3-21G

Total Energy = -231.69266122 a.u.

RMS Gradient Norm = 0.00000702 a.u.

Dipole Moment = 0.3405 Debye

Point Group = C1

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001043 0.001800 YES
RMS Displacement 0.000297 0.001200 YES
Predicted change in Energy=-8.759674D-09
Optimization completed.
-- Stationary point found.</pre>

The lowest energy ''gauche-3'' structure was calculated.

LOG File: [[FILE:DIENE_GAUCHE_321G_C1_symm.LOG]]

====Optimisation with 6-31G* Basis Set====

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.61132934 a.u.

RMS Gradient Norm = 0.00000382 a.u.

Dipole Moment = 0.3959 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 1 minutes 22.0 seconds.

LOG File:[[FILE:DIENE_GAUCHE_631G.LOG]]

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

===Optimisation of the allyl C3H5 fragment===

File Type = .log

Calculation Type = FOPT

Calculation Method = UHF

Basis Set = 3-21G

E(UHF) = -115.82304010 a.u.

RMS Gradient Norm = 0.00003049 a.u.

Dipole Moment = 0.0292 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

<pre> Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277266D-08
Optimization completed.
-- Stationary point found.</pre>

LOG File: [[FILE:ALLYL_FRAGMENT_321G.LOG]]

===Chair Transition State Optimisation Method 1===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932248 a.u.

RMS Gradient Norm = 0.00000290 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.

====Transition State:====

[[FILE:Chair_TS_pic.png|400px]]

Bond breaking/making length = 2.02045Å

====Transition State Vibration:====

[[FILE:TS_animation_chair_AG.gif|500px]]

Imaginary Frequency: -817.93 cm-1

Symmetry: C2h

LOG File: [[FILE:CHAIR_TS_OPT_AG_321G_ACTUAL_V3.LOG]]

===Chair Transition State Optimisation Method 2: Frozen Co-ordinates===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FTS

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.61932006 a.u.

RMS Gradient Norm = 0.00010842 a.u.

Dipole Moment = 0.0022 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 26.0 seconds.

Part 1 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_1.LOG]]

Part 2 LOG File: [[FILE:FREEZE_COORDINATE_METHOD_PART_2_NEWEST.LOG]]

Bond breaking/making length: 2.01807Å

The structure of the TS calculated in this way is virtually identical in terms of the relative orientations of the atoms. However, a small distance in the bond breaking/making length can be seen. This difference is of the order of 0.002Å, which is such a small difference that we can say the structures are identical for all intensive purposes.

===Chair Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.55698295 a.u.

RMS Gradient Norm = 0.00002998 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0000 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 4 minutes 25.0 seconds.

LOG File: [[FILE:CHAIR_TS_OPT_AG_631G.LOG]]

====Activation energy for the Chair TS====

-234.55698295 + 234.61132934 = 0.05434639 a.u.

Convert to kcal/mol: 34.102881887 kcal/mol

The activation energy for the Chair TS, calculated from the lowest energy ''gauche-3'' product is: 34.102881887 kcal/mol, which is in very good agreement with the experimental value of 33.5 ± 0.5 kcal/mol.

===Boat Transition State Optimisation: QST2 Method===

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60280199 a.u.

RMS Gradient Norm = 0.00008337 a.u.

Imaginary Freq = 1

Dipole Moment = 0.1578 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 0 minutes 8.0 seconds.

LOG File: [[FILE:ANTI_TS_OPT_WIN.LOG]]

====Transition State Vibration:====

[[FILE:Boat_TS_annimation_1.gif|500px]]

===Boat Transition State Optimisation with 6-31G* Basis Set===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -234.54309304 a.u.

RMS Gradient Norm = 0.00000724 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0614 Debye

Point Group = CS

Job cpu time: 0 days 0 hours 9 minutes 13.0 seconds.

LOG File: [[FILE:BOAT_TS_OPT_631G.LOG]]

====Activation energy for the Boat TS====

-234.54309304 + 234.61132934 = 0.0682363 a.u.

Convert to kcal/mol: 42.81893387 kcal/mol

This is in good agreement with the literature value of 44.7 ± 2.0 kcal/mol, calculated from the lowest energy ''gauche-3'' conformer.

===Intrinsic Reaction Coordinate===

It is found that the Chair TS corresponds to the ''gauche-2'' conformer of 1,5-hexadiene.

LOG File: [[FILE:Log_73795.log]]

{{DOI|10042/24088}}

==The Diels Alder Cycloaddition==

===''cis''-Butadiene===

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -155.98594955 a.u.

RMS Gradient Norm = 0.00002286 a.u.

Imaginary Freq = 1

Dipole Moment = 0.0852 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 24.0 seconds.

LOG File: [[FILE:BUTADIENE_OPT.LOG]]

====''cis''-Butadiene HOMO====

[[FILE:Butadiene_HOMO.png|400px]]

This is MO antisymmetric with respect to the plane.

====''cis''-Butadiene LUMO====

[[FILE:Butadiene_LUMO.png|400px]]

This is MO symmetric with respect to the plane.

===Transition State Geometry for the Prototype Reaction===

The transition state for the ethene/''cis''-butadiene reaction was calculated using the frozen co-ordinate method.

The transition state was calculated using HF/3-21G level of theory:

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

Part 1 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN.LOG]]

Part 2 LOG File: [[FILE:DA_TS_OPT_TRY3_FROZEN_PART_2.LOG]]

====HOMO of the Transition State====

[[FILE:DA_TS_HOMO.png|400px]]

====LUMO of the Transition State====

[[FILE:DA_TS_LUMO.png|400px]]

====Vibration of Transition State====

[[FILE:DA_TS_HOMO_animated.gif|400px]]

Lowest positive frequency:

[[FILE:DA_lowest_freq_vibration.gif|400px]]

==Study of the Regioselectivity of the Diels Alder Reaction==

For cyclohexadiene and maleic anhydride.

===Optimisation of Cyclohexadiene===

[[FILE:CHD_image.png|400px]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RHF

Basis Set = 3-21G

E(RHF) = -231.60320781 a.u.

RMS Gradient Norm = 0.00002089 a.u.

Imaginary Freq = 1

Dipole Moment = 0.5755 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

LOG File: [[FILE:CYCLOHEXADIENE_OPT_DOUBLE_BOND.LOG]]

===Optimisation of Maleic Anhydride===

[[FILE:Mal_anyhd_image.png|400px]]

File Type = .log

Calculation Type = FOPT

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -379.28954427 a.u.

RMS Gradient Norm = 0.00011846 a.u.

Dipole Moment = 4.0754 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 0 minutes 58.0 seconds.

[[FILE:MALEIC_ANHYDRIDE_OPT.LOG]]

===Optimisation of the Transition State===

All were calculated using the frozen co-ordinate method.

====Exo Transition State====

[[FILE:|400px]]

LOG File Part 1: [[FILE:Mal_anhyd_diene_TS_freeze_opt_part_1_321G.log]]

Log File Part 2: [[FILE:MAL_ANHYD_DIENE_TS_FREEZE_OPT_PART_2_631G.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74233.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.67931096 a.u.

RMS Gradient Norm = 0.00000177 a.u.

Imaginary Freq = 1

Dipole Moment = 5.5501 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 54.4 seconds.

{{DOI|10042/24213}}

====Transition State Vibration====

[[FILE:Exo_TS_moving.gif]]

====Transition State HOMO====

[[FILE:HOMO_exo.png|400px]]

====Endo Transition State====

[[FILE:Endo_TS.png|400px]]

LOG File Part 1: [[FILE:ENDO_MAL_ANHYD_DIENE_ENDO_TS_FREEZE_OPT_PART_1_321G.LOG]]

Log File Part 2: [[FILE:ENDO_PART_2.LOG]]

'''6-31G* optimised:''' [[FILE:Log_74244.log]]

File Type = .log

Calculation Type = FREQ

Calculation Method = RB3LYP

Basis Set = 6-31G(d)

E(RB3LYP) = -612.68339677 a.u.

RMS Gradient Norm = 0.00000436 a.u.

Imaginary Freq = 1

Dipole Moment = 6.1143 Debye

Point Group = C1

Job cpu time: 0 days 0 hours 35 minutes 26.6 seconds.

{{DOI|10042/24216}}

====Transition State Vibration====

[[FILE:Endo_TS_moving.gif|400px]]

====Transition State HOMO====

[[FILE:Endo_HOMO.png|400px]]