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. Using Gamess or Firefly, the natural internals can be
auto-generated from a Z-matrix or Cartesian input. Jim From:
owner-chemistry+jimkress35==gmail.com * ccl.net
[mailto:owner-chemistry+jimkress35==gmail.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?
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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