Subject: M:Analytical CI gradients in semiempirical programs

From: "James J. P. Stewart" <[email-masked]>
Date: Fri, 11 Apr 1997 08:37:34 -0600

Serge Pachkovsky writes:

>As it was already pointed out on CCL (by Dr. A. Holder,
>in his message on 13 Jan 1993), " ... some versions of MOPAC and
>AMPAC 2.1 are broken in certain places when it comes to analytical
>gradient computation (CI to name just one.) ... ". Indeed, both
>Mopac6 and Mopac7 Rev. 1 (which I have locally) have problems with 
>the input file given at the end this message. However, it is
>Mopac93 Rev. 2 which is supposed to be the latest and greatest
>of all Mopacs out there (;-)), so I wanted to try that as well.
>
>Unfortunately, Mopac93 Rev. 2 (thank you, Ernst) still produces
>incorrect gradient in my test case, even though it is different
>from the result produced by Mopac6 and Mopac7 Rev. 1. This brings
>me to my question:

The calculation suggested by Dr Serge Pachkovsky, has a solution as 
shown below.  This is not, however, a stationary point, further 
optimization of the geometry yielded a much lower energy.  The active
space selected (C.I.=2) is obviously incomplete, therefore any results
obtained using it are of no value.

I found no faults in the analytical C.I. derivatives.  These derivatives,
developed by D. Liotard and M. J. S. Dewar, are suitable for most systems,
although there are some problems with exotic systems, for example, when
incomplete active spaces are used in high symmetry systems.  In all cases
of this type, the fault can be traced back to faulty data sets.

Jimmy Stewart

                     SUMMARY OF  MNDO   CALCULATION

                                                            MOPAC  93.00

  C6  H6 
                                                       Fri Apr 11 09:14:32
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       =       178.329452 KCAL =    746.13043 KJ
          ELECTRONIC ENERGY       =     -3211.050618 EV      STATE: SINGLET
Ag  
          CORE-CORE REPULSION     =      2366.323321 EV
          GRADIENT NORM           =         0.088379
          DIPOLE                  =         0.00106 DEBYE    SYMMETRY:
 D2h 
          NO. OF FILLED LEVELS    =         15
          CONFIGURATION INTERACTION WAS USED
          IONIZATION POTENTIAL    =         8.654564 EV
          MOLECULAR WEIGHT        =        78.113
          SCF CALCULATIONS        =         1
          COMPUTATION TIME =   0.450 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    1.38679795  1    0.0000000  0    0.0000000  0    1    0    0
-0.0609
  C    1.54669782  1  119.6644424  1    0.0000000  0    2    1    0
-0.0610
  C    1.38669952  1  119.6702375  1    0.0471573  1    3    2    1
-0.0603
  C    1.38681944  1  120.6611367  1   -0.0068056  1    4    3    2
-0.0610
  C    1.38670070  1  120.6704155  1    0.0008064  1    1    2    3
-0.0609
  H    1.09302361  1  119.6655646  1  179.9812673  1    1    2    3
0.0580
  H    1.08399604  1  123.5053120  1  179.9933272  1    2    1    3
0.0621
  H    1.08401053  1  116.8439442  1 -179.9720243  1    3    2    1
0.0621
  H    1.09300380  1  119.6816877  1  179.9776776  1    4    3    2
0.0581
  H    1.08399539  1  123.4911948  1  179.9344594  1    5    4    3
0.0621
  H    1.08399953  1  123.5005382  1  179.9241279  1    6    1    2
0.0621

---

From: [email-masked] (Serge Pachkovsky)
Date: Fri, 11 Apr 1997 20:59:11 +0200 (MDT)

Hi everybody,

First, I would like to nit-pick a bit at the analysis of the CI
gradient problem provided by Dr. Stewart. Anybody not interested
in this can skip to the end of this message, which is much more
dignified. :-)

[nit-picks on]

> J.J.P. Stewart writes:
> optimization of the geometry yielded a much lower energy. 

In all my sincere respect to Dr. Stewart, I beg to disagree. The 
structure given in my original message *is* a stationary point, with a
final Cartesian gradient norm of 1.9 kcal/mol/A. It can be refined
further, if desired. It is not a *minimum* point, as indicated by two 
imaginary frequencies in the vibrational analysis. This should, 
however, have no bearing in the CI computation.

> The active space selected (C.I.=2) is obviously incomplete, therefore 
> any results obtained using it are of no value.

Since neither HOMO nor LUMO are degenerate, and have no close-lying
MOs (HOMO-1 is 1.1 eV below HOMO in the present case, LUMO+1 is 0.75 eV
above LUMO), there is no arbitrariness in the selection of canonical
MOs and the active space constructed from these two orbitals is 
obviously "complete" as far as CI and CI gradient workings are 
concerned. 

Two-orbitals active space is quite obviously unsatisfactory 
("incomplete"?) in a physical sense, since it does not recover 
most of the correlation energy. This is not not a legitimate 
reason for a breakdown of analytical gradients, though ;-)

[nit-picks off]

With the atavistic urges satisfied, here comes the question to
Dr. Stewart which may be of interest to other CCL readers:
Since the master copy of Mopac93 apparently works perfectly 

>           GRADIENT NORM           =         0.088379

while problems seem to exist with the copy of Mopac93 Rev. 2
obtained from QCPE some time in 1996 (I do not have Mopac93 Rev.2
locally, and can't verify it myself, unfortunately):

>           GRADIENT NORM           =         27.74534

, is the Mopac93 Rev. 2 being distributed by QCPE identical to
the master copy of Dr. Stewart? If it is not, how does one
bring his own copy in synch with the latest and greatest of
all Mopacs?

With my best regards,

/Serge.P