Computing and viewing orbitals

See also the general page on MOPAC input files and
the MOPAC submit page

Before we start with the chemistry, we'll discuss some of the tools that are available for MO calculations and visualization.
In earlier tutorials the MOPAC submit option has been used. Starting with an input file (a .dat file, either from a web page or from your directory), this service produces a series of output files, and a web page with the structures.
For orbitals extra keywords are necessary on the first line of the input file: VECTORS and GRAPH.
VECTORS results in the inclusion of orbital coefficients in the output (.out) file: the nine highest occupied and the seven lowest unoccupied ones.
For a simple example, the allyl cation, all orbitals (15) are printed:

          NO. OF FILLED LEVELS    =          8
...
                EIGENVECTORS  


   Root No.    1       2       3       4       5       6       7       8

              1 a1    1 b2    2 a1    3 a1    2 b2    3 b2    4 a1    1 b1  

           -41.876 -33.823 -26.895 -22.731 -21.458 -19.426 -18.520 -17.806
  
  S   C  1 -0.4632  0.5709  0.3131 -0.0672 -0.0502  0.0355 -0.0584  0.0015
  Px  C  1 -0.1644 -0.0022 -0.3207  0.2335  0.4301  0.2686 -0.1989  0.0040
  Py  C  1  0.0229  0.0431 -0.0954 -0.4005  0.2691 -0.4442 -0.3251  0.0022
  Pz  C  1  0.0000  0.0000 -0.0001  0.0003  0.0006 -0.0021  0.0061  0.4794
  S   C  2 -0.6273  0.0000 -0.4648  0.0237 -0.0005 -0.0002  0.0708 -0.0013
  Px  C  2  0.0608 -0.3391 -0.1021 -0.2299 -0.4200 -0.2367  0.2330 -0.0039
  Py  C  2  0.1110  0.1851 -0.1870 -0.4216  0.2341  0.1256  0.4304 -0.0059
  Pz  C  2  0.0000  0.0001 -0.0001  0.0005  0.0010 -0.0041  0.0109  0.7354
  S   H  3 -0.1295  0.2360  0.1815 -0.3344 -0.0246 -0.3913 -0.1837  0.0007
  S   H  4 -0.1451  0.2032  0.2845  0.1007 -0.3465  0.1970  0.3203 -0.0033
  S   H  5 -0.1769  0.0001 -0.3030 -0.2200 -0.0001 -0.0024  0.4353 -0.0063
  S   C  6 -0.4626 -0.5717  0.3127 -0.0675  0.0504 -0.0349 -0.0587  0.0006
  Px  C  6  0.1082 -0.0373  0.0931 -0.4642  0.0070  0.5195 -0.1606  0.0077
  Py  C  6 -0.1257 -0.0214 -0.3209 -0.0207 -0.5074  0.0175 -0.3432  0.0070
  Pz  C  6 -0.0001  0.0000  0.0002  0.0020  0.0018 -0.0058  0.0099  0.4787
  S   H  7 -0.1452 -0.2034  0.2838  0.1021  0.3462 -0.2600  0.3186 -0.0062
  S   H  8 -0.1293 -0.2363  0.1815 -0.3352  0.0254  0.3923 -0.1794  0.0050

  Root No.    9      10      11      12      13      14      15

              1 a2    2 b1    5 a1    6 a1    4 b2    5 b2    7 a1  

            -7.910  -4.661  -2.557  -2.314  -2.309  -1.816  -1.422
  
  S   C  1  0.0005  0.0006  0.3672  0.1580 -0.3144 -0.2138  0.0571
  Px  C  1  0.0010  0.0006  0.2300 -0.1367 -0.0997  0.3679 -0.4619
  Py  C  1  0.0000  0.0000  0.1694 -0.2400  0.3447 -0.1585  0.1729
  Pz  C  1 -0.7064  0.5207 -0.0003  0.0007  0.0006 -0.0001 -0.0002
  S   C  2 -0.0002  0.0002 -0.3759 -0.1849  0.0229  0.0040  0.3967
  Px  C  2 -0.0003  0.0006  0.1634 -0.1189 -0.3630  0.1331 -0.0740
  Py  C  2 -0.0004  0.0004  0.3084 -0.1200  0.2152 -0.0727 -0.1482
  Pz  C  2 -0.0003 -0.6776  0.0008 -0.0017 -0.0009  0.0003  0.0005
  S   H  3 -0.0003 -0.0004 -0.3935  0.0320 -0.0868  0.4763 -0.3708
  S   H  4 -0.0002  0.0001 -0.0528 -0.4247  0.5008  0.2265 -0.1191
  S   H  5 -0.0012 -0.0014 -0.0345  0.4176 -0.0443 -0.0036 -0.1699
  S   C  6  0.0000 -0.0003  0.3722  0.2212  0.2695  0.2125  0.0492
  Px  C  6  0.0042  0.0038  0.0253 -0.2274 -0.3023  0.3390  0.3892
  Py  C  6  0.0027  0.0025  0.2693 -0.2855 -0.0488 -0.2258 -0.3011
  Pz  C  6  0.7078  0.5194 -0.0021  0.0036  0.0029 -0.0013 -0.0012
  S   H  7 -0.0001  0.0019 -0.0581 -0.5225 -0.4005 -0.2235 -0.1188
  S   H  8  0.0001 -0.0014 -0.3940  0.0453  0.0824 -0.4813 -0.3597

This system has 8 occupied orbitals and 7 unoccupied ones, among which we can easily distinguish between the pi MO's (#8, 9 and 10) with only pz coefficients, and the sigma MO's with s, px and py coefficients.
The HOMO (#8) is symmetric (0.4794, 0.7354, 0.4787), the LUMO has one nodal plane (-0.7064, 0, 0.7078), LUMO+1 two (0.5207, -0.6776, 0.5194, see picture below).

In non-flat systems, e.g. Diels-Alder transition states, this distinction between sigma and pi orbitals is absent. Visualization of the orbitals is of great help then.

GRAPH as a MOPAC keyword triggers the creation of a .gpt file, necessary for displaying orbitals. MOLDEN can read such a file (you cannot, it's binary) and display the orbitals (and electron density) in a number of ways. Moreover, it can write VRML files.
In these web-based tutorials we use the latter. Either as a gif picture, a small VRML viewer screen (see below if you have one installed as a VRML plugin) or as a link to the VRML file which invokes a full viewer page in your web browser. (Keep in mind that VRML files can be quite large, even when gzip-ped!).

MOLDEN offers a web service to create VRML files, starting from .gpt files.
The latter can be obtained by our MOPAC submit service, by adding the keyword GRAPH, and subsequent saving (Shift-click) of the .gpt file from the MOPAC result page.

As an exercise, try this sequence with hexatriene. The input file is available here.
First, perform the MOPAC calculation, try to find the numbers of the pi orbitals in the .out file. Then submit the .gpt file to the MOLDEN web service and look at the symmetry of the orbitals.