Subject: Re: CCL:symmetry and stationary points

From: [email-masked] (Joerg Hill)
Date: Wed, 27 Apr 1994 11:18:27 -0700

E. Lewars wrote:

> [ ... ]
> Theresa Windus says "while the molece with symmetry may not be the global
> minimum...it is certainly some sort of stationary point..."  Does anybody
> know of a formal theorem that says non-C1 structures are always stationary
						 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> points, or some place where this is explicitly stated?  It's just that it
  ^^^^^^
If you OPTIMIZE your molecule under the restriction of a specific point group
and you find a point where all force vanish you have found a stationary point
(that's how stationary points are defined). So it doesn't matter whether the
molecule possesses symmetry or not at this point of its potential surface.

> would be nice to see some sort of proof; it's not quite obvious that it 
> MUST be so, altho' I do see that it looks reasonable.

But the probability that you have found a MINIMUM is very small. In most cases
you will found one or even more imaginary frequencies and you have to optimize
further using a subgroup of your current point group (C1 is a always a subgroup)
and starting with a distortion of your current geometry (preferably along a
normal mode with an imaginary frequency), since otherwise you stay at your
current stationary point of the potential surface (there are no force your
optimizer can minimize).

Using symmetry makes sense if you know from experiment that your molecule belongs
to a special point group or your chemical intuition tells you that symmetry may
play a role. Use of symmetry for speeding up or making calculations possible has
always to be considered as giving you wrong answers (no minima). If your molecules
are models for larger systems and the imaginary frequencies affect only parts
of the molecule which are not present in your larger system, you may use symmetry,
too.

Joerg-R. Hill