The Cope Rearrangement

Optimising the reactants and products

Optimisation of six conformers at the HF/3-21G level

Click on the name of the conformer to be taken to the log file for its optimisation.


Conformer	Item table
Anti 1	Item Value Threshold Converged? Maximum Force 0.000056 0.000450 YES RMS Force 0.000010 0.000300 YES Maximum Displacement 0.001374 0.001800 YES RMS Displacement 0.000459 0.001200 YES Predicted change in Energy=-2.090824D-08 Optimization completed. -- Stationary point found.
Anti 2	Item Value Threshold Converged? Maximum Force 0.000060 0.000450 YES RMS Force 0.000010 0.000300 YES Maximum Displacement 0.000509 0.001800 YES RMS Displacement 0.000171 0.001200 YES Predicted change in Energy=-2.037403D-08 Optimization completed. -- Stationary point found.
Anti 4	Item Value Threshold Converged? Maximum Force 0.000021 0.000450 YES RMS Force 0.000008 0.000300 YES Maximum Displacement 0.000616 0.001800 YES RMS Displacement 0.000167 0.001200 YES Predicted change in Energy=-3.114554D-08 Optimization completed. -- Stationary point found.
Gauche 2	Item Value Threshold Converged? Maximum Force 0.000018 0.000450 YES RMS Force 0.000006 0.000300 YES Maximum Displacement 0.000937 0.001800 YES RMS Displacement 0.000330 0.001200 YES Predicted change in Energy=-1.008444D-08 Optimization completed. -- Stationary point found.
Gauche 3	Item Value Threshold Converged? Maximum Force 0.000016 0.000450 YES RMS Force 0.000003 0.000300 YES Maximum Displacement 0.000430 0.001800 YES RMS Displacement 0.000130 0.001200 YES Predicted change in Energy=-1.902911D-09 Optimization completed. -- Stationary point found.
Gauche 5	Item Value Threshold Converged? Maximum Force 0.000027 0.000450 YES RMS Force 0.000008 0.000300 YES Maximum Displacement 0.001487 0.001800 YES RMS Displacement 0.000288 0.001200 YES Predicted change in Energy=-2.507751D-08 Optimization completed. -- Stationary point found.

Optimisation of the anti 2 and gauche 5 conformers at the B3LYP/6-31G* level

Anti 2

Log file

        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=-1.588997D-08
Optimization completed.
   -- Stationary point found.

Gauche 5

Log file

        Item               Value     Threshold  Converged?
Maximum Force            0.000011     0.000450     YES
RMS     Force            0.000004     0.000300     YES
Maximum Displacement     0.001359     0.001800     YES
RMS     Displacement     0.000292     0.001200     YES
Predicted change in Energy=-6.737597D-09
Optimization completed.
   -- Stationary point found.

Frequency analysis of the Anti 2 conformer at the B3LYP/6-31G* level

Log file

Low frequencies ---  -18.6393  -11.7160   -0.0003    0.0007    0.0009    1.8395
Low frequencies ---   72.7305   80.1447  120.0232

Optimising the transition structures

HF/3-21G allyl fragment optimisation

Log file

        Item               Value     Threshold  Converged?
Maximum Force            0.000006     0.000450     YES
RMS     Force            0.000003     0.000300     YES
Maximum Displacement     0.000742     0.001800     YES
RMS     Displacement     0.000314     0.001200     YES
Predicted change in Energy=-1.078416D-08
Optimization completed.
   -- Stationary point found.

HF/3-21G optimisation of the chair transition state

Log file

        Item               Value     Threshold  Converged?
Maximum Force            0.000025     0.000450     YES
RMS     Force            0.000005     0.000300     YES
Maximum Displacement     0.000855     0.001800     YES
RMS     Displacement     0.000149     0.001200     YES
Predicted change in Energy=-3.247458D-08
Optimization completed.
   -- Stationary point found.

Frequency analysis

Log file

Low frequencies --- -817.9006   -3.2174    0.0002    0.0005    0.0008    1.4799
Low frequencies ---    2.2968  209.5418  395.8705
******    1 imaginary frequencies (negative Signs) ******

Note: The imaginary frequency is inserted into the top line because Gaussian puts the frequencies in ascending order. The job has converged, and you can see on the second line the first frequency is small.

Frozen coordinate optimisation of the chair transition state

Optimisation to a minimum

Log file

        Item               Value     Threshold  Converged?
Maximum Force            0.000017     0.000450     YES
RMS     Force            0.000005     0.000300     YES
Maximum Displacement     0.001213     0.001800     YES
RMS     Displacement     0.000185     0.001200     YES
Predicted change in Energy=-3.681256D-10
Optimization completed.
   -- Stationary point found.

Optimisation to a transition state

Log file

        Item               Value     Threshold  Converged?
Maximum Force            0.000062     0.000450     YES
RMS     Force            0.000016     0.000300     YES
Maximum Displacement     0.000499     0.001800     YES
RMS     Displacement     0.000143     0.001200     YES
Predicted change in Energy=-1.228026D-07
Optimization completed.
   -- Stationary point found.

QST2 Boat transition state optimisation

Optimisation 1

Log file

        Item               Value     Threshold  Converged?
Maximum Force            0.000200     0.000450     YES
RMS     Force            0.000057     0.000300     YES
Maximum Displacement     0.001435     0.001800     YES
RMS     Displacement     0.000592     0.001200     YES
Predicted change in Energy=-8.523055D-07
Optimization completed.
   -- Stationary point found.

Low frequencies --- -818.2840   -0.0052   -0.0009   -0.0002    1.4378    7.1590
Low frequencies ---   10.7944  209.9053  396.6623
******    1 imaginary frequencies (negative Signs) ******

Optimisation 2

Log file

        Item               Value     Threshold  Converged?
Maximum Force            0.000035     0.000450     YES
RMS     Force            0.000016     0.000300     YES
Maximum Displacement     0.000874     0.001800     YES
RMS     Displacement     0.000272     0.001200     YES
Predicted change in Energy=-1.381500D-07
Optimization completed.
   -- Stationary point found.

Low frequencies --- -839.8287   -1.9649   -0.0015    0.0003    0.0013    3.0033
Low frequencies ---    3.7533  155.2805  381.9453
******    1 imaginary frequencies (negative Signs) ******

IRC calculation

Log file

DFT optimisations and frequency calculations

Click the name of the structure to see the log file.

Name

Item table

Low frequencies

Chair TS

        Item               Value     Threshold  Converged?
Maximum Force            0.000027     0.000450     YES
RMS     Force            0.000005     0.000300     YES
Maximum Displacement     0.000111     0.001800     YES
RMS     Displacement     0.000035     0.001200     YES
Predicted change in Energy=-4.956844D-09
Optimization completed.
   -- Stationary point found.

Low frequencies --- -565.5338   -0.0003   -0.0001    0.0005   21.8425   27.2463
Low frequencies ---   39.6905  194.4985  267.9729
******    1 imaginary frequencies (negative Signs) ******

Boat TS

        Item               Value     Threshold  Converged?
Maximum Force            0.000017     0.000450     YES
RMS     Force            0.000004     0.000300     YES
Maximum Displacement     0.000686     0.001800     YES
RMS     Displacement     0.000155     0.001200     YES
Predicted change in Energy=-2.910921D-08
Optimization completed.
   -- Stationary point found.

Low frequencies --- -530.5366   -8.1194   -0.0008    0.0004    0.0004   15.1718
Low frequencies ---   17.3858  135.5715  261.8356
******    1 imaginary frequencies (negative Signs) ******

The Diels-Alder Cycloaddition

The prototype reaction

Optimising cis butadiene

Log file

         Item               Value     Threshold  Converged?
 Maximum Force            0.000075     0.000450     YES
 RMS     Force            0.000028     0.000300     YES
 Maximum Displacement     0.000808     0.001800     YES
 RMS     Displacement     0.000348     0.001200     YES
 Predicted change in Energy=-7.221414D-08
 Optimization completed.
 -- Stationary point found.

Optimising the transition state

Log file

Low frequencies --- -956.1913   -2.4763   -0.0806   -0.0237   -0.0032    1.3323
Low frequencies ---    1.8129  147.1963  246.6339
******    1 imaginary frequencies (negative Signs) ******

        Item               Value     Threshold  Converged?
Maximum Force            0.000018     0.000450     YES
RMS     Force            0.000003     0.000300     YES
Maximum Displacement     0.000236     0.001800     YES
RMS     Displacement     0.000065     0.001200     YES
Predicted change in Energy=-1.854275D-09
Optimization completed.
   -- Stationary point found.

Diels-Alder regiochemistry

Optimising the reactants and products

Click the name of the structure for the log file.
Name	Item table
Maleic anhydride	Item Value Threshold Converged? Maximum Force 0.000058 0.000450 YES RMS Force 0.000023 0.000300 YES Maximum Displacement 0.000486 0.001800 YES RMS Displacement 0.000217 0.001200 YES Predicted change in Energy=-6.279573D-08 Optimization completed. -- Stationary point found.
Cyclohexa-1,3-diene	Item Value Threshold Converged? Maximum Force 0.000149 0.000450 YES RMS Force 0.000031 0.000300 YES Maximum Displacement 0.000994 0.001800 YES RMS Displacement 0.000274 0.001200 YES Predicted change in Energy=-2.137334D-07 Optimization completed. -- Stationary point found.
Endo product	Item Value Threshold Converged? Maximum Force 0.000298 0.000450 YES RMS Force 0.000071 0.000300 YES Maximum Displacement 0.001745 0.001800 YES RMS Displacement 0.000399 0.001200 YES Predicted change in Energy=-1.393585D-06 Optimization completed. -- Stationary point found.
Exo product	Item Value Threshold Converged? Maximum Force 0.000119 0.000450 YES RMS Force 0.000018 0.000300 YES Maximum Displacement 0.000575 0.001800 YES RMS Displacement 0.000136 0.001200 YES Predicted change in Energy=-9.548720D-08 Optimization completed. -- Stationary point found.

Optimising the transition states

Click the name of the structure to see the log file.

Name

Item table

Low frequencies

Endo TS

        Item               Value     Threshold  Converged?
Maximum Force            0.000085     0.000450     YES
RMS     Force            0.000015     0.000300     YES
Maximum Displacement     0.001105     0.001800     YES
RMS     Displacement     0.000184     0.001200     YES
Predicted change in Energy=-9.246807D-08
Optimization completed.
   -- Stationary point found.

Low frequencies --- -806.3465   -1.6863   -0.2649   -0.0104    0.3781    1.9347
Low frequencies ---    2.4359   62.5325  111.7260
******    1 imaginary frequencies (negative Signs) ******

Exo TS

        Item               Value     Threshold  Converged?
Maximum Force            0.000018     0.000450     YES
RMS     Force            0.000002     0.000300     YES
Maximum Displacement     0.000774     0.001800     YES
RMS     Displacement     0.000132     0.001200     YES
Predicted change in Energy=-5.136273D-09
Optimization completed.
   -- Stationary point found.

Low frequencies --- -812.1657   -1.3932   -1.1206   -0.0047    0.3175    1.0003
Low frequencies ---    2.5428   60.8779  123.8812
******    1 imaginary frequencies (negative Signs) ******