Subject: Residual Forces Summary

From: Greg Rechtsteiner <[email-masked]>
Date: Thu, 29 Jun 2000 12:50:49 -0500

Hello:

I would like to thank everyone for the prompt reponses to my
inquiry concerning residual forces from a geometry optimization.
A summary is included below:

Original Question:

 > Hello:
 >
 > I have been performing geometry optimizations using Gaussian 94 and 98,
 > and I have the following question(s).
 >
 > An optimization is considered complete when it converges
 > according to the specified convergence criteria, in my case,
 > the default values for G9x are max. component of force 0.00045,
 > rms forces 0.0003, displacement 0.0018 and rms displacement 0.0012.
 >
 > I am interested in what may be learned from the values of the "residual"
 > force components, ie max. component of the force and rms forces
 > that are provided at the final step in the optimization process.
 >
 > For example, I have a structure with residual values of 0.000187 for the
max.
 > force component and 0.000051 for the rms force.
 >
 > (Please note that no imaginary frequencies were found from a freq.
analysis).
 >
 > Do these values tell me anything about the stability of the structure?
 > That is, do larger values (but still within the convergence criteria)
suggest
 > a possible metastable state?

Responses:

1.

The force data tell you only that you are at or approaching a
stationary point and nothing about the stability of the structure. Large
RMS and MAX gradient values indicate only that you have not converged the
stationary point to high precision. Only the Hessian eigenvalues indicate
the curvature of the PES and therefore the (kinetic) stability of the given
stationary geometry. NB, however, that for very flat potential surfaces
(e.g., those often found for weakly-bound complexes), it may be very
difficult to tightly converge the forces. This is a numerical problem,
however, and not a general indicator of stability.
-Daniel
--
T. Daniel Crawford Department of Chemistry
[email-masked] Virginia Polytechnic Institute and
http://zopyros.ccqc.uga.edu/~crawdad/ State University

2.  I don't think that the residual forces tell anything about the
stability of the structure or - more precisely - about the depth of
the potential minimum. They just describe the slopes of the potential
surface in respect to geometry changes. A purpose for quoting them
is only to indicate how far the geometry is from the ideal minimum at
which all the forces are zero. The second derivatives are (in frame
of the harmonic approximation) related to a depth of the minimum, but
they are equally informative as the frequencies calculated from the
second derivatives, which are (the frequencies) more common for esti-
mating of what you call the stability.

Sincerely,
Darko Babic

Institute "Rudjer Boskovic"
HR-10002 Zagreb, P.O.B. 180
Croatia

3.  In almost all cases I don't think they give any useful information:
The figures just reflect the path that the optimization followed: not
any intrinsic property of the molecule itself. The sole exception
that I can think of is where the optimization stops with very small
forces but large displacements thus indicating that the minima has
low curvature that is is very flat and this may indicate that the
molecule is quite soft and floppy

All the best Larry Cuffe

4. The stability of a structure depends on the second derivative not
the first. The residual force does indicate that the structure lies
slightly off the point of zero force but except in the case of a very
flat potential energy surface the small displacements suggest that
the difference in structure is small compared to the other uncertainties.

The FREQ calculation can tell you if the point is a maximum on the
potential energy surface along some displacement, this should break the
symmetry of the molecule if the prior optimization is properly done. It
will also give you a better estimate of the displacement to find the
minimum by improving the force constants and estimates of the displacement.

Note that there can also be instabilities in the wavefunction at any
point on the potential energy surface. Most often FREQ will also uncover
instabilities in the wavefunction but not in a concrete fashion, rather if
the wavefunction is unstable you get nonsense for frequencies. The STABLE
or STABLE=OPT options are better if you have concerns here.

Doug Fox (Gaussian Support)