From: 
"R.G.A. Bone" <rgab \\at// purisima.molres.org> 
Date: 
Wed, 27 Apr 94 10:14:17 0700 
Subject: 
Symmetry: In Reply to Dan Severence 
In reply to Dan Severence's comments:
i) Gaussian calculations.
>> "Gaussian" finds symmetry present in the input nuclear coordinates and
>> applies it unless you explicitly switch it off. But geometry optimizations
>> will typically, irritatingly, quit as soon as a change in point group occurs.
>
> If you wish to force the symmetry, this can be averted by using the
>same variable name for the symmetric lengths and angles, thus there is
>no possibility of a change in point group.
>
Yes, Dan is correct, provided that you can do it. Constraining the
internal coordinates in the Zmatrix is the way out. But I had one fiendish
example once (in "C_i" symmetry) where it was not possible to do this: two
related angles could not be specified by the same internal coordinate and
the optimization failed as soon as these angles became slightly inequivalent.
ii) I was very careful in my comment about the gradient.
>> The gradient of the energy w.r.t. nuclear displacements should transform as
>> the totally symmetric 'irrep' in whatever point group you happen to be in.
>>For 'closedshell' systems (no electronic degeneracies) this means in practice
>> that 'symmetric' structures are usually stationary points. The only
>
> There are actually a number of cases where this is indeed not the
> case. Amides, for instance, tend not to be planar but are slightly
> puckered at the N. It often doesn't take much energy to force it to
> be planar, but nonplanar is the minimum at any levels of theory that
> I've seen. Also, quite bulky molecules often avoid a symmetric
> form in favor of spreading out the steric interactions.
>
Note that I said that symmetric structures are usually STATIONARY POINTS,
not 'MINIMA'. Nothing I said contradicted the example of a nonplanar amide.
But, symmetry can not be interpreted to be 'local' either. I was about to
venture that the configuration in which the bonds about the Natom are planar
would probably be a 'transition state' but of course such a structure may not
be a stationary point at all if there are other 'outofplane' atoms in the
molecule which are not related to one another by reflection in the plane.
(Remember those nonbonded interactions ...). If the _whole_ molecule is
planar or has a plane of symmetry then (if closedshell, and in the absence of
totally symmetric distortions) it will be a stationary point but I couldn't
tell you, a priori, what sort.
N.B., Just because symmetric structures are usually stationary, does not mean
the converse, either, viz: stationary points do not have to be 'symmetric'.
There are clearly a number of pitfalls and potential confusions in the
discussion of symmetry. I will shortly post a useful referencelist to CCL
which not only provides background to my own comments but should hopefully
be a useful almanac to anybody with an interest in this field.
Watch this space .........
Richard Bone
================================================================================
R. G. A. Bone.
Molecular Research Institute,
845 Page Mill Road,
Palo Alto,
CA 943041011,
U.S.A.
Tel. +1 (415) 424 9924 x110
FAX +1 (415) 424 9501
Email rgab()at()purisima.molres.org
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