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 Z-matrix 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 'closed-shell' 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 non-planar 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 non-planar 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 N-atom 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 'out-of-plane' atoms in the
molecule which are not related to one another by reflection in the plane.
(Remember those non-bonded interactions ...). If the _whole_ molecule is
planar or has a plane of symmetry then (if closed-shell, 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 reference-list 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 94304-1011,
U.S.A.
Tel. +1 (415) 424 9924 x110
FAX +1 (415) 424 9501
E-mail rgab at.at purisima.molres.org
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