From owner-chemistry@ccl.net Thu May 25 10:53:00 2006
From: "Jimmy J. Stewart MrMOPAC(~)att.net" <owner-chemistry^server.ccl.net>
To: CCL
Subject: CCL: C2v pointgroup & coordinate system convention
Message-Id: <-31838-060524192420-4144-gxIXHjLJ+AkdkT3+BChMdQ^server.ccl.net>
X-Original-From: "Jimmy J. Stewart" <MrMOPAC^-^att.net>
Date: Wed, 24 May 2006 19:24:19 -0400


Sent to CCL by: "Jimmy J. Stewart" [MrMOPAC!^!att.net]


Peter  Burger asked:
>the following has puzzled me for a while...
>In the C2v point group different choices have been made in the literature with regard to the x and y axis.
>Several books on symmetry and point groups provide different answers... and sometimes even choose use them either way in different chapters. 
>
>For water for instance, most of them opt for the xz plane as the molecular plane with y pependicular to it while others  refer to the yz as molecular plane with x perpendicular to it. This obviously leads to a change of the b1 and b2 symbols and makes comparisons somehow complicated... 
>
>So I guess my question is - use Al Cottons or Tinkhams book as authorities? Is there somewhere the _real_ truth?


This is a very sophisticated question.  The problem only arises with the groups C2v and D2, of the Abelian groups.  For C2v there are two options for assigning b1 and b2 irreducible representations, and for D2 there are six ways to assign b1, b2, and b3.

The convention used in the symmetry package (written by David Danovich) within MOPAC conforms with Cotton's definition, and is, I believe, the most general.  In this, the b1 IR is unsymmetric in the plane that has the most atoms. In Cotton's C2v group table the plane that has the most atoms is the yz plane.This is a definition.

This is in accord with Dr Johnson's comment that "For planar C2v molecules the convention is to have the x-axis out of the plane."  I would, however, extend this to "For C2v molecules, the convention is to have the x-axis perpendicular to the plane of that has the most atoms."   Similar rules hold for D2. Although these rules cover most cases, there is still some ambiguity in C2v systems of the type AB2C2: is there a convention for those cases where there are the same number of atoms in the various planes? If anyone knows the rule here, please inform me.

Jimmy


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