-- James R. Buchwald Doctoral Candidate, Dept. of Chemistry and Chemical Biology Rensselaer Polytechnic Institute Graduate Researcher, Dinolfo Laboratory Teaching Assistant, Experimental Chemistry IV

GAMESS documentation has an extended discussion about geometry = optimization and what representation of the coordinates provides the = best, and most rapid convergence to the optimum.

http://= www.msg.ameslab.gov/gamess/GAMESS_Manual/refs.pdf

Page 149 and following.

John is correct when he notes redundant or natural internal coordinates = are preferred.=C2=A0 Using Gamess or Firefly, the natural internals can = be auto-generated from a Z-matrix or Cartesian = input.

Jim

From:<= /b> = owner-chemistry+jimkress35=3D=3Dgmail.com * ccl.net = [mailto:owner-chemistry+jimkress35=3D=3Dgmail.com * ccl.net] On Behalf = Of John McKelvey jmmckel*o*gmail.com
Sent: Sunday, April = 19, 2015 12:01 PM
To: Kress, Jim
Subject: = CCL: Optimization in Z-matrix vs Cartesian = coordinates

Just curious.. Where does redundant = internal coordinates optimization fit in this discussion? Does it = change the discussion about biphenyl, my favorite test case also? =

John

On Sun, = Apr 19, 2015 at 10:59 AM, Jacco van de Streek jacco.vandestreek##sund.ku.dk <owner-chemistry() ccl.net> = wrote:

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

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