Subject: Analytical CI gradients in semiempirical programs

From: "James J. P. Stewart" <[email-masked]>
Date: Fri, 11 Apr 1997 17:57:46 -0600

To reply again re Dr Pachkovsky's observations:

The "stationary point" he reports yields a heat of formation
of 178.33025 kcal/mol and a gradient norm of over 1 kcal/mol/A.
Geometry optimization results in a similar geometry, reported
by me earlier, with a H.o.F. of 178.32945, and a gradient norm
of 0.09 kcal/mol/A.

The geometry at 178.33025 kcal/mol is not a stationary point,
for two reasons.  First, it is 0.0008 kcal/mol above the
nearby "stationary point", and second, as Dr Pachkovsky points
out, the "stationary point" is, in fact, a hilltop.  The difference
in energy of the two geometries is reponsible for the large
GNORM reported by Dr Pachkovsky.

When I attempted to reduce the GNORM below 0.09 kcal/mol/A, the
geometry changed so as to lower the energy by a few tens of kcal/mol.

That the active space is incomplete can readily be shown by
rerunning the job with C.I.=4.  This results in a large decrease
in energy.  Dr Pachkovsky is correct in that the space is "complete"
as far as CI and gradient calculations are concerned, but because
the effect of increasing the size of the active space has a profound
effect on the results, the calculation is as useful as a single
point calculation on an arbitary geometry.

The fact that the gradient could be lowered to less than 0.1, in
accordance with Dr Pachkovsky's criterion, demonstrates the
falsity of the statement "This is not a legitimate reason for a
breakdown of analytical gradients."

Now to the program itself.  Dr Pachkovsky's data set contains the 
keyword PLCRT=0.0000001, which is not a keyword of MOPAC 93 or MOPAC 7.
This suggests that the program being used by Dr Pachkovsky was
modified after it was received from QCPE.  While MOPAC 93, Revision 2
is, as Dr Pachkovsky suggests, the "latest and greatest", it is not
invulnerable to damage caused by changing the source code.  This
might be the reason for the differences in results.

In case there is any doubt about the validity of Liotard's
analytical derivative method, here is a re-calculation of
Dr Pachkovsky's system in which the system is constrained to be
planar.  Users of MOPAC 93, Revision 2, are invited to repeat
this calculation.

And now that I am heading off to San Francisco, I beg leave to
back out of any further discussion on this topic.

Jimmy Stewart

                     SUMMARY OF  MNDO   CALCULATION

                                                            MOPAC  98.00

  C6  H6 
                                                       Fri Apr 11 18:40:14
1997
    1SCF  GRAD C.I.=2 ROOT=3 SINGLET PRECISE &
  T=1000000 MECI

     1SCF WAS SPECIFIED, SO BFGS WAS NOT USED                 
     SCF FIELD WAS ACHIEVED                                   

          HEAT OF FORMATION       =       178.329472 KCAL =    746.13051 KJ
          ELECTRONIC ENERGY       =     -3211.052760 EV      STATE: SINGLET
Ag  
          CORE-CORE REPULSION     =      2366.325464 EV
          GRADIENT NORM           =         0.000567
          DIPOLE                  =         0.00000 DEBYE    SYMMETRY:
 D2h 
          NO. OF FILLED LEVELS    =         15
          CONFIGURATION INTERACTION WAS USED
          IONIZATION POTENTIAL    =         8.654580 EV
          MOLECULAR WEIGHT        =        78.113
          SCF CALCULATIONS        =         1
          COMPUTATION TIME =   0.413 SECONDS

          FINAL GEOMETRY OBTAINED                                    CHARGE
    1SCF  GRAD C.I.=2 ROOT=3 SINGLET PRECISE &
  T=1000000 MECI
 
  C    0.00000000  0    0.0000000  0    0.0000000  0    0    0    0
-0.0603
  C    1.38675637  1    0.0000000  0    0.0000000  0    1    0    0
-0.0609
  C    1.54669847  1  119.6677872  1    0.0000000  0    2    1    0
-0.0609
  C    1.38675161  1  119.6677106  1    0.0000000  0    3    2    1
-0.0603
  C    1.38675663  1  120.6645001  1    0.0000000  0    4    3    2
-0.0609
  C    1.38675212  1  120.6645308  1    0.0000000  0    1    2    3
-0.0609
  H    1.09300947  1  119.6675465  1  180.0000000  0    1    2    3
0.0580
  H    1.08399943  1  123.4960132  1  180.0000000  0    2    1    3
0.0621
  H    1.08399997  1  116.8360371  1 -180.0000000  0    3    2    1
0.0621
  H    1.09300943  1  119.6680004  1  180.0000000  0    4    3    2
0.0580
  H    1.08399948  1  123.4959112  1  180.0000000  0    5    4    3
0.0621
  H    1.08399988  1  123.4962036  1  180.0000000  0    6    1    2
0.0621