Subject: CCL:Summary: X,Yx,Z vs. internal coordinates

From: [email-masked]
Date: Wed, 22 Jul 1998 09:29:00 +0900

Dear Sir:

        I summarized x,y,z vs. internal coordinates.

Masao Masamura
Preventive Dentistry
Okayama University Dental School
Shikata-cho, 2-5-1
Okayama 700
Japan
FAX: 81-86-235-6714
e-mail: [email-masked] 

<my question 1>

        I ask about the following.

(1)  The optimization using x,y,z coordinates is faster than that using
internal coordinates.

(2)  Do you experience that the optimization using x,y,z coordinates
converges  unexpected optimized structure ?   The optimization using
internal coordinates is more safe than the optimization using x,y,z
coordinates ?

        Thank you.

<responce 1-1>

> (1)  The optimization using x,y,z coordinates is faster than that using
> internal coordinates.

No, generally not. Because in internal coord. you optimize 3N-6
variables, whereas in xyz you have 3N.

> 
> (2)  Do you experience that the optimization using x,y,z coordinates
> converges  unexpected optimized structure ?   The optimization using
> internal coordinates is more safe than the optimization using x,y,z
> coordinates ?

Yes and no. For cyclic systems or bigger molecules, a little deviation
of one variable like an angle can cause big distortions of your
molecule. For example, since C1 and C6 in a 6-membered ring are not
"connected", changing the dihedral 2-3-4-5 by 50 causes a relativily
great change in bond length for C1-C6. 

There are more types of coordinates like the redundant internal
coordinates used in Gaussian. There is also a neverending debate about
the "right" ones.
See their manual at www.gaussian.com for references.

-- 
                                Andreas Goeller

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   Dr. Andreas Goeller       Institut fuer Physikalische Chemie
                               Friedrich-Schiller-Universitaet
                                       Lessingstr. 10
phone: +49(0)-3641-948352               D-07743 Jena
  fax: +49(0)-3641-948302 (secretary)     Germany
email: [email-masked]
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   Dr. Andreas Goeller   ehemals Computer Chemie Centrum

email: [email-masked]
http://www.organik.uni-erlangen.de/clark/goeller/goeller.html
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<my question 2>

       I would like to ask about the following.

(1)  The redundant internal coordinates is more reliable ?
(2)  What is www.gaussian.com ?
(3)  The optimization using the redundant internal coordinates is faster
than the optimization using x,y,z coordinates ?

<responce 2-1>

> (1)  The redundant internal coordinates is more reliable ?

They say so. These coord. have the advantage of being redundant, i.e., 
there are achieved additional coord. from your input., so the system can
change to other coord. during opt.
> (2)  What is www.gaussian.comwww.gaussian.com ?
http://www.gaussian.com
> (3)  The optimization using the redundant internal coordinates is faster
> than the optimization using x,y,z coordinates ?
More likely leeding to convergence I would think

<responce 1-2>

About the second item I have no experience, although it sounds a bit strange.
However, for the first one, I can say that generally it is the opposite and
optimization in the internal coordinates are much faster than cartesian
coordinates. For some special cases, however, it is not straightforward to set
up a suitable internal coordinate set which can be properly used during the
optimization and one has to use the XYZ coordinates (or redundant internal
coordinates, if implemented).

<responce 1-3>

I have heard arguments on both sides. One the one hand,
optimization steps taken in torsion space are thought by
many to follow more closely the natural low energy pathways
in molecules, or at least in proteins. This argument seems to 
be backed up by recent numerical experiments in Ruben Abagyan's group:

Abagyan R.A. and Totrov, M.M. J. Mol. Bio 235 (1994) 983

(which admittedly I have not read), in which they measure how 
far one can move away from a local minimum and still return via
optimization.

Others argue that by restricting the conformational search
to torsion space, the energy barriers are made higher
and the search space becomes "topologically" more complex
as a result. Note that the ECEPP forcefield used by Abagyan
has adjusted torsional barrier heights, supposedly to 
compensate for this.

Personally, I think this is comparing apples with oranges until
someone can perform an optimization in ALL internal coordinates
(including bends, stretches etc. but excluding redundant coordinates)
so that the number of degrees of freedom are the same. I suspect,
however, that internal coords will win for the reasons stated above.
Anybody know of a progam that can do FULL internal coordinate 
optimization?

Richard Gillilan
Cornell Theory Center

<responve 1-4>

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]