From owner-chemistry@ccl.net Sun Apr 19 11:01:01 2015
From: "Jacco van de Streek jacco.vandestreek##sund.ku.dk" <owner-chemistry^server.ccl.net>
To: CCL
Subject: CCL: Optimization in Z-matrix vs Cartesian coordinates
Message-Id: <-51272-150419105957-10589-6hgIRLTauDmQzBOHDi/flQ^server.ccl.net>
X-Original-From: "Jacco  van de Streek" <jacco.vandestreek%x%sund.ku.dk>
Date: Sun, 19 Apr 2015 10:59:56 -0400


Sent to CCL by: "Jacco  van de Streek" [jacco.vandestreek~!~sund.ku.dk]
> I initially supposed that a geometry optimization, if it is performed in
> properly composed Z-matrix, takes less optimization steps than if it runs in
> Cartesian coordinates. Is that wrong?

For a molecular compound, if the alternative is x,y,z coordinates, that should be correct. A Z-matrix in principle allows for a more natural description of the degrees of freedom in terms of bonds, valence angles and torsions. As you write, this is only true for "a properly composed Z-matrix" because a Z-matrix description is not unique and Z-matrix descriptions in which e.g. rotatable torsions do not correspond to chemical torsions would get you into trouble even though the Z-matrices would all be mathematically equivalent.

A trivial example where a Z-matrix description should be vastly superior to optimisation in x,y,z coordinates is as follows: imagine a fully energy-minimised biphenyl molecule. Now distort the molecule by changing the length of the central bond connecting the two phenyl rings by moving the two phenyl rings slightly apart (or closer), leaving the minimised geometry of the phenyl rings intact. A geometry optimisation in Z-matrix description should only change the central bond and this should converge very quickly, whereas a geometry optimisation in Cartesian coordinates will distort neighbours of the central atoms in the first step, which will ripple out to the extremes of the molecule and then back. At least that is the theory and the very little experimenting I have done and have heard/read about supports this.

>  A properly constructed Z-matrix, as far
> as I suppose, must use dummy atoms for each aromatic cycle in the
> molecule (the dummy atom is placed in the center of a cycle).
> I don't mean here the symmetry constraints. I want to compare the speed of
> geometry optimization of a non-symmetrical molecule (C1) in Z-matrix and
> Cartesian coordinates.
> I have this question because I have implemented automatic generation of Z-
> matrix in my program Chemcraft, and I wonder whether this feature can be
> useful. I appreciate any suggestions, in which cases such feature can be
> used.

There is a more general method for choosing the optimal coordinates for an geometry optimisation, called "delocalised internal coordinates": Baker, J.; Kessi, A.; Delley, B. J. Chem. Phys. 1996, 105, 192.

Best wishes,
-- 
Dr Jacco van de Streek
Department of Pharmacy
University of Copenhagen