Subject: geometry optimization methods (more!)

From: Dale Andrew Braden <[email-masked]>
Date: Tue, 8 Apr 1997 21:09:21 -0700 (PDT)

Dear CCL,

I have been very pleased with the many responses to my question about
whether there is any situation in which a Cartesian optimization would be
faster than an optimization in redundant internal coordinates.  There
seems to be a difference of opinion on this, and I hope to keep the
discussion going by giving here a summary (in my own words) of the
responses so far, as well as a bit more information about my particular
problem.  I'll give a complete summary later, including due acknowledgment
to the many people who have responded.

It appears that a cartesian optimization can be faster overall for very
large systems, because the overall scaling with cartesians becomes more
favorable. I note here that, although the idea of using redundant internal
coordinates has been around for some time, not all electronic structure
packages employ it.  For example, the Spartan program uses Cartesian
coordinates.  This makes sense if the above is true, since people often
use the program to model very large molecules. 

It also appears that ordinary Z-matrix coordinates are not always inferior
to cartesians OR to redundant internals.  I was given the example of
azulene, whose geometry fails to converge when a redundant internal
optimization is performed, but which converges nicely when the
optimization is constrained to nonredundant internals.  And if the initial
geometry is bad, then, even with a good Hessian, a straight Z-matrix
optimization can be faster than one in cartesians.  I believe I have read
somewhere about fused ring systems causing problems for redundant internal
coordinates.

I have been trying to optimize the structure of a hydrogen-bonded dimer in
a solvent medium (which, I neglected to mention, I am treating as a
dielectric continuum, and not as a collection of discrete molecules).  I
first performed the optimization in the absence of a dielectric, so that I
would have a good starting geometry and Hessian.  In the presence of a
dielectric, the geometry failed to converge when I used a straight
Z-matrix, even after 30 steps.  I then switched to redundant internals
(which I should have been using from the start anyway), and it proceeded 3
more steps, and then stumbled into a region in which the energy, forces
and displacements went way up.  Then the SCF failed, and that was that. 

The high dielectric medium is causing the problem, since the optimization
without it converged rapidly (even using a straight Z-matrix).  What I
should do is freeze the intermolecular coordinates (whose displacements
remained large throughout the failed optimization) and optimize everything
else, then unfreeze them, and continue.

Again, thank you to all those who have responded so far!

Yours,

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