From rgab;at;purisima.molres.org Wed Feb 16 18:24:54 1994 Received: from purisima.molres.org for rgab;at;purisima.molres.org by www.ccl.net (8.6.4/930601.1506) id RAA07196; Wed, 16 Feb 1994 17:36:17 -0500 Message-Id: <199402162236.RAA07196 {*at*} www.ccl.net> Received: by purisima.molres.org (1.37.109.4/16.2) id AA15320; Wed, 16 Feb 94 14:38:40 -0800 Date: Wed, 16 Feb 94 14:38:40 -0800 From: "R.G.A.Bone" To: chemistry-: at :-ccl.net Subject: determining point groups Concerning the various perspectives on deducing the geometric symmetry of a molecule from its nuclear coordinates: i) The Gaussian package readily does this, (one of its more irritating features I should add), though you can turn symmetry off with a whole manner of flags at the various levels of calculation, you know, dep- ending on how you want to "fix" your result (cf. 'symmetry-broken' solutions in UHF). ii) Philosophically (regrettably) given that assemblies of nuclei (i.e., molecules) are not static - there are continuous vibrations, etc., the only molecules which will have any geometric symmetry at all, at any instant, are triatomics (a plane of symmetry) and diatomics. The latter will have the infinite-fold rotation axis (and a whole "bunch" of others if homonuclear). Thus, only if two nuclei have symmetry-related coordinates (to some arbitrary level of precision) is geometric symmetry present. Of course, one could specify this level of precision to be the dimension of a nucleus (typically femtometres). But, being chemists, with an under- standing of spectroscopy, we know a little better and assume that, for all intents and purposes point-symmetry operations commute with the vibronic Hamiltonian so this issue does not arise and the 'time-averaged' position of the nuclei, or the geometry at the well in the potential is what counts. iii) But, if you are a computer, to examine a number of nuclear coordinates and determine symmetric-relationships between them requires some intell igent decision concerning what is "near-symmetry" and what is "exact- symmetry". Suppose there are small rounding errors in the data: e.g., 2 nuclear positions: 1.00000000 0.50000000 2.34567890 1.00000000 0.50000000 -2.34567889 Are these 2 nuclei symmetrically-related? Well, surely yes, although their z-coordinates differ by a trivial amount. The algorithm must contain a threshold-cutoff which copes with cases like this. iv) In response to the comment that you need to know the nuclear identity as well as the coordinates in order to deduce symmetry. Well, except for the trivial case of diatomics, I challenge anybody to find 2 nuclei in a molecule which are NOT identical but which are in exactly-symmetry- related coordinates, to say 10^-6 Angstrom precision. Of course, there may be circumstances under which it is desirable to label (for example iso- topic) substituents as symmetrically-equivalent, and cases where it is not. But that's moving the goal-posts. It also depends on the source of the data: is it an experimental or theoretical geometry for the isotopomer? (i.e., have zero-point effects been included or not ?) Basically, this matter of deducing the point group from a set of coordinates does have a slight algorithmic difficulty, which is perhaps why it has not been widely implemented. Arguably also, let's face it: almost all molecules on this planet don't have any symmetry at all; (theoretical) chemists' obsession with symmetry comes from 1) the small size of molecules they are accustomed to dealing with (symmetry is more preponderent in small molecules), 2) the fact that, even for small molecules, use of symmetry can make a big calculation more practical. Furthermore, there are hardly any molecules for which the point group can't be deduced "by inspection", unless there happens to be a potential confusion between "near-symmetry" and actual-symmetry. One might argue that that difficulty increases as molecules increase in size, but then the amount of symmetry typically decreases in the same way (crystal-lattice unit-cells, excepted). 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^ purisima.molres.org ------------------------------------------------------------------------------- --------------------- Every Theory has its "Grassy Knoll" --------------------- -------------------------------------------------------------------------------