Example: Orbitals in cyclopentadienes

We compare methyl- and fluorocyclopentadiene. Both were created and calculated in Sybyl, using the internal MOPAC, and two flags switched on: 'molecular orbitals' and 'molecular orbital plotfile'.
For the methyl compound, the .out file contains the 'vectors', the coefficients of the AO's in the MO's:

           -11.96813   -11.92047   -11.08297    -9.18033     0.56755     2.23107
  						 (HOMO)
  
  S  C   1   0.05110    -0.04287     0.01080    -0.00355    -0.00590     0.00330
 PX  C   1  -0.07109     0.13833    -0.01448     0.00474     0.00378    -0.00102
 PY  C   1   0.23254    -0.38051     0.01808    -0.00671    -0.00799     0.00431
 PZ  C   1  -0.06001    -0.03016     0.29754     0.56633    -0.53996     0.42023
  
  S  C   2  -0.05148    -0.05744    -0.00382     0.00003     0.00188    -0.00098
 PX  C   2   0.08183    -0.13563     0.01049    -0.00268    -0.00167     0.00140
 PY  C   2  -0.25391     0.04044    -0.00772     0.00065     0.00027     0.00061
 PZ  C   2  -0.07274    -0.01540     0.51030     0.42061     0.41127    -0.56764
  
  S  C   3  -0.05112     0.05776    -0.00383    -0.00002     0.00184     0.00095
 PX  C   3   0.21693     0.13199     0.01295     0.00258    -0.00152    -0.00083
 PY  C   3   0.15620    -0.04848     0.00003    -0.00108     0.00078     0.00129
 PZ  C   3  -0.07264     0.01592     0.51026    -0.42066     0.41129     0.56763
  
  S  C   4   0.05135     0.04256     0.01080     0.00358    -0.00586    -0.00324
 PX  C   4  -0.19688    -0.33521    -0.02233    -0.00780     0.00778     0.00335
 PY  C   4  -0.14696    -0.22432    -0.00610    -0.00254     0.00428     0.00294
 PZ  C   4  -0.05987     0.03055     0.29746    -0.56634    -0.53998    -0.42021
  
  S  C   5   0.02760    -0.00011     0.00474     0.00000     0.01624    -0.00002
 PX  C   5   0.42256     0.14584     0.02904     0.00285    -0.01103     0.00213
 PY  C   5  -0.13664     0.45035    -0.00951     0.00872     0.00359     0.00660
 PZ  C   5  -0.05218     0.00017    -0.33256     0.00003    -0.04150     0.00000
  
  S  H   6  -0.10087     0.19459     0.00072     0.00153     0.00034    -0.00078
  
  S  H   7   0.19965    -0.15160     0.01071    -0.00250    -0.00304     0.00170
  
  S  H   8   0.20064     0.15037     0.01068     0.00248    -0.00302    -0.00165
  
  S  H   9  -0.10207    -0.19397     0.00071    -0.00154     0.00030     0.00072
  
  S  H  10  -0.25233     0.00078    -0.29280     0.00003     0.18518     0.00002
  
  S  C  11  -0.02334     0.00008     0.06363    -0.00001    -0.09554     0.00000
 PX  C  11  -0.39411    -0.10748     0.11500    -0.01122    -0.09729     0.00665
 PY  C  11   0.12776    -0.33282    -0.03760    -0.03432     0.03182     0.02028
 PZ  C  11   0.05650    -0.00022     0.26137    -0.00005    -0.14270    -0.00002
  
  S  H  12   0.21312     0.27623    -0.03154     0.03926     0.03087     0.03028
  
  S  H  13  -0.28147     0.00114    -0.11848     0.00005    -0.00510     0.00001
  
  S  H  14   0.21096    -0.27781    -0.03159    -0.03930     0.03084    -0.03029

The Highest Occupied Molecular Orbital is of course a 'pi' orbital, composed of the four p_z orbitals from the carbons 1 to 4. This orbital has the same symmetry as the anti-symmetric combination S (H12) - S (H14), which mixes in with small coefficients (due to the large energy difference): 0.0393.
This mixing causes a difference between the two sides of the plane; the orbital is not 'pure' p_z, p_x and p_y contribute slightly.

This effect is more distinct in the fluoro compound, where it is the p_y on F which mixes with the p_z orbitals.

    ROOT NO.   13          14          15          16          17          18

           -12.40097   -11.95614   -11.68843    -9.59546     0.09524     1.84551
  						 (HOMO)
  
  S  C   1   0.03013    -0.05482     0.04980     0.00833    -0.01289    -0.00120
 PX  C   1  -0.02381     0.14179    -0.08015    -0.00901     0.00806     0.00488
 PY  C   1   0.18382    -0.38951     0.13881     0.02090    -0.01592    -0.00885
 PZ  C   1  -0.27506    -0.04622     0.26548    -0.56663    -0.53670     0.41919
  
  S  C   2  -0.03612    -0.05206    -0.03275     0.00070     0.00515    -0.00562
 PX  C   2   0.03812    -0.13524     0.07495     0.00484    -0.00569    -0.00108
 PY  C   2  -0.22246     0.03395    -0.09086    -0.00075    -0.00033    -0.00599
 PZ  C   2  -0.34939    -0.02369     0.41219    -0.41878     0.42723    -0.56903
  
  S  C   3  -0.03629     0.05193    -0.03278    -0.00067     0.00516     0.00567
 PX  C   3   0.16180     0.12976     0.11399    -0.00433    -0.00432    -0.00255
 PY  C   3   0.15714    -0.05228     0.02921     0.00233     0.00359    -0.00545
 PZ  C   3  -0.34945     0.02370     0.41221     0.41874     0.42706     0.56914
  
  S  C   4   0.03011     0.05499     0.04963    -0.00841    -0.01277     0.00127
 PX  C   4  -0.12717    -0.34497    -0.14606     0.01968     0.01573    -0.00919
 PY  C   4  -0.13390    -0.23096    -0.06436     0.01150     0.00809    -0.00421
 PZ  C   4  -0.27510     0.04628     0.26553     0.56657    -0.53662    -0.41934
  
  S  C   5   0.06475     0.00004    -0.01705     0.00003     0.03641    -0.00002
 PX  C   5   0.25025     0.13526     0.25908    -0.00450    -0.03079    -0.00257
 PY  C   5  -0.08214     0.41235    -0.08494    -0.01370     0.01001    -0.00797
 PZ  C   5  -0.04963    -0.00003    -0.23059    -0.00001    -0.07685     0.00000
  
  S  H   6  -0.10306     0.19049    -0.03018    -0.00544     0.00079    -0.00473
  
  S  H   7   0.15954    -0.14551     0.09193     0.00613    -0.00705     0.00146
  
  S  H   8   0.15927     0.14594     0.09172    -0.00614    -0.00703    -0.00156
  
  S  H   9  -0.10271    -0.19060    -0.02988     0.00543     0.00072     0.00465
  
  S  H  10  -0.15554    -0.00039    -0.37790     0.00003     0.15080     0.00004
  
  S  F  11   0.01409     0.00000    -0.00007     0.00001    -0.03917     0.00000
 PX  F  11  -0.46915    -0.16985    -0.22538     0.02342    -0.10260    -0.00503
 PY  F  11   0.15378    -0.51740     0.07399     0.07139     0.03359    -0.01530
 PZ  F  11   0.11667    -0.00004     0.29609    -0.00003    -0.11703     0.00001

As the p_y is closer to the p_z's in energy, its coefficient in the HOMO is larger, the C1 and C4 p_x and p_y's contribute more, so all in all the difference between the faces is larger.

From the figures in the two files above it can be concluded that the effect is small. It can hardly be seen by visual inspection of the orbitals in Sybyl: the methyl compound appears symmetrical, in the fluoro derivative a slight difference can be detected, as if the pi lobes are tilted inwards above the plane.
It is proposed that this causes better overlap with the LUMO of a dienophile.

This is part of Chapter 3.
Back to main text of Chapter 3.