Subject: Summary: wfn stability

From: Dale Andrew Braden <[email-masked]>
Date: Mon, 16 Jun 1997 14:13:46 -0700 (PDT)

Dear CCL,

I recently posted a question about RHF wavefunction instability.  Most of
the responses addressed the problem of spin contamination rather than
wavefunction stability, but these two are interrelated anyhow.  Useful
references for these two topics are given at the end of this post.  I
thank all of those who responded! 

Some of the respondents felt that this "problem" was not terribly
serious, because much more sophisticated ab initio methods are available
now that are not as fraught with problems as HF.  I am inclined to agree
with this now.

Consider benzene.  I optimized the geometry at the RHF/6-31+G* level, and
found that the final wfn had a RHF-->UHF instability.  I then reoptimized
the wfn at the UHF level, and found that the energy decreased, and spin
contamination was introduced, as expected.  The problem with the spin
contamination, from an experimentalist's point of view, is that this UHF
description of benzene indicates that, for example, it would give an ESR
signal, because the spin density around the nuclei is no longer zero. 
This is an unrealistic description of benzene.  People have tried to
salvage the situation by projecting out the contaminating states of higher
multiplicity, but the resulting wfn is no longer optimized with respect to
the original parameters.  I suppose the best one can do if HF theory must
be used is to stick with the RHF wfn and simply say that it has an
instability. 

The point I wanted to make is that, although the use of RHF/UHF/ROHF/PUHF
techniques is perhaps decreasing, the use of Moller-Plesset perturbation
methods is, I think, still very common.  Since MPx perturbations are
carried out on HF wavefunctions, the MPx results are also affected by
stability/contamination problems.  I think this is more serious,
especially if RHF-->UHF instabilities are as common as Chambaud et al. 
(ref. below) indicate. 

One last point, which was made by one of the respondents.  Typically, the
hamiltonian (or Fock operator) includes no energy terms that depend upon
electron spin (like a spin-orbit operator).  This means that spin
energetics are not included in the "optimized" wfn, which is determined
when the total energy stops changing in the SCF calculation.  Thus spin
energetics do not play a role in determining the final spin distribution
in the molecule.  (Spin-orbit coupling is assumed to be small for many
molecules, but it can be large for organometallics.)  From this point of
view, spin "contamination" is not only arbitrarily defined, but quite
meaningless.

For wfn stability, see the following references (and references therein!):

Chambaud, Levy, and Millie; Theor. Chim. Acta 48 (1978) 103.

Schlegel and McDouall in Computational Advances in Organic Chemistry;
Ogretir and Csizmadia, eds. Kluwer 1991.

Ma, Wong, Paddon-Row, and Li; Chem. Phys. Lett. 213 (1993) 189.

For spin contamination:

Nandi, Kar, and Sannigrahi; Theochem 362 (1996) 69. (And refs. therein!).

Cheers to all, 

Dale Braden
Department of Chemistry
University of Oregon
Eugene, OR 97403-1253
[email-masked]