Subject: x,y,z vs. internal coordinates

From: [email-masked] (Folke Noertemann)
Date: Sat, 18 Jul 1998 15:06:13 +0200

Cartesian  <-> internal coordinates:
This question has to be answered with is clear
"It depends".

Usually cartesian coordinates introduces a great
deal of undesired couplings. One may get rid of them
by choosing the right internal coordinates.
My experience is that nothing can beat a well-chosen
Z-matrix. Other internal coordinate systems, e.g.
Pulays natural internal coordinates compare also very
well in the literature.
However, the choice of the coordinate system depends
-at least in my view- entirely on two things:

1. The nature of the molecule one wishes to optimize.
   Establishing a Z-matrix for polycyclic systems is a
   nightmare that nobody really wants to go through.
   Some people claim that it is impossible to compose 
   a good Z-matrix for such a system. So if the only two
   options available are cartesians and Z-matrix AND the
   molecule is unpleasantly complex, cartesians
   should be preferred. 
   In agreement with this, many papers mention that cartesians
   are superior to anything else for polycyclic molecules.
   However, these statements are NOT independent of 2.)

2. The quality of the initial Hessian that is available.
   Because of the couplings they introduce, cartesians do
   in general not have the best reputation. However,
   Baker and Hehre showed that if a good approximation to the Hessian
   is available, cartesians perform comparably to other
   sets of internal coordinates. They also stress, that for
   FLEXIBLE polycyclic systems (whatever that may be) they found
   the performance of cartesian coordinates to be below internal
   coordinates.

A few of the relevant references are:
J.Baker and W.J. Hehre, J.Comp.Chem. 12, 606 (1991)
J.Baker, J.Comp.Chem. 14, 1085 (1993)
J.Baker and D.Bergeron, J.Comp.Chem. 14, 1339 (1993)
P.Pulay and G.Fogarasi, J.Chem.Phys. 96, 2856 (1991)

 Hope this helps,
 Folke

Folke Noertemann
Lehrstuhl f. Theoret. Chemie
TU Muenchen
[email-masked]