Subject: Summary : Z-matrices

From: Patrick Bultinck <[email-masked]>
Date: Wed, 27 Jul 1994 10:34:13 +0200 (MET DST)

Dear netters,

Please hereby find a summary to a question on Z-matrix I posted about a 
week ago !!!!
Thanks to those who reacted ....

Original message :

Dear Netters,

I was wondering if anyone had some clues or ideas on how to set up a 
Z-matrix.
The trouble is that some of my optimizations do not converge to a 
stationary point. However when I make another alternative Z-matrix I 
converge to the Stat. Point. Now my question is : how does one judge, 
given e.g. five different possibilities, which is the best Z-matrix.

Is this a matter of "Zen" or rather a matter of "science" ?

Thanks for your time, a summary will be made if useful answers get to me.

Patrick, University of Ghent, Belgium

[email-masked]

And these are the replies ...

I build up my Z-matrices buy building the structure in a molecular editor,
at the moment I use the one InsightII (Biosym) but any will do. When you add
an atom to the existing structure make sure it is bonded to an atom that is
already described in the structure. If possible build up your structure such
that each consecutive atom is connected to the existing atoms and can make
proper torsion angles, not improper torsions. Once you have built the
structure, what I do is run a single point calculation in the AMPAC/MOPAC
module of InsightII to get z-matrix, but it build the matrix based on the
atom orders. The long and the short of the process is to get a z-matrix which
as only bond lengths for the distance coordinate, bond angle for the first
angle coordinate and proper torsion angle for the second angle coordinate.

	I know I haven't explained this very well but this method seems to
work for me. If you follow this method you should be able to look at the
z-matrix and see that the first column of coordinates are all under 2.0 Angs,
The second column has values from about 100 to 135 (note 180 deg bond angles
are not good), the torsion angles of the third column of coordinates can be
-180 to +180, but it is worth checking to see if aromatics etc have reasonable
values.

Hope this is of some help.

Andy.
--
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In my experience, the most common cause of of a Z-matrix defined in *internal*
coordinates not giving a stationary point is this:  the degrees of freedom
in the molecule are not independent.  I have never seen or heard a proper
expaination of how to *know* you are avoiding this when you define the 
Z-matrix.

Because of these difficulties, I began defining all my structures in 
*cartesian* coordinates.  This avoids the problem of angles being dependent
on bonds and so forth.  The important thing to remember when optimizing
a structure in this way is to define six of the 3n coordinates to be constant,
thus eliminating the rotational and translational degrees of freedom.  This 
must be done carefully and not simply at random to avoid constraining the 
molecule in some way.  Usually, you'll want to hold all three coords of 
on atom constant, two of one bonded to the first, and one of another.  Make 
sure that the bond between the first two atoms is along one of the three axes
of your coord system.  This, then, does not constrain any of the bonds and so
forth, since, of course, any two points define a line, and any three define
a plane.  Defining them as I have suggested merely specifies *which* line and
plane.

If you are using Gaussian92 (I don't think you specified a program...) then
the Fopt keyword will check your Z-matrix and make sure all degrees of freedom
are present and independent.  One must also be careful here, since if the
program finds some initial symmetry, say CS, then it only acknowledges the 
number of deg of freedom appropriate to this symmetry, and Fopt stops, 
believing that there are not enough.  One may avoid this by pushing one atom 
ever so slightly out of, say, a mirror plane so that the program finds 
C1 symmetry initally.

I hope I have been of some help.  I have no doubt that you'll receive many 
responses, but just let me know if you have any questions about what I've 
suggested.

Anthony Kurt Grafton
Department of Chemistry and Biochemistry
University of Oklahoma, Norman, USA
[email-masked]

  Patric,

  There are some clear criteria for making good Z-matrices but not so
clear for the "best" Z-matrix. A good article is Schlegel, in 
New Theoretical Concepts for Understanding Organic Reactions", 
Bertran and Csizmadia (ed) Kluwer Academic Press (1989).  One option
for automatically making Z-matrices with Gaussian is newzmat.  Given
a Z-matrix you can use

newzmat -redoz old_zmat.in new_zmat.in

Doug Fox

Dear Patrick,

	If you have access to a relatively new GAMESS-US manual (less
than six months old), read the "further information" section on internal
coordinates.  A new version of the manual, as well as the GAMESS-US program
is available from Mike Schmidt at [email-masked].

				Best regards,

					Jan Jensen
					Dept. of Chemistry
					Iowa State University

Patrick,
one of the most important considerations is to make sure that
the z matrix you specify has the required number of variables for
a complete specification of the required symmetry. This can easily
be ensured by using fopt instead of opt (in gaussian92 anyway).
I usually simply check that the number of variables I give the
z matrix is the same as gaussian tells me the particular symmetry
demands. You can find this near the top of the log file around
about where a print out of FRAME is. ie search for "FRAME" and
you will also see the number of variables required.

fopt has the advantage however of also checking for linearly
dependent variables that can slow the rate of convergence
down quite considerable.

A good z matrix IS somewhat of an art, possibly one of the reasons
that optimizations in cartesian space is becoming more commonplace
now (apart from the advent of graphical interfaces).

Hope this is of help. If you would like me to suggest an
appropriate z matrix I would be delighted to be of assistance.

Kind regards,

Anthony P. Scott
Research Officer
Computational Chemistry Group
Research School of Chemistry
Australian National University
Canberra, ACT, Australia

Dear Patrick,

No definite answers, but:

1) problem of generating the Z-matrix.

I have already experienced that different programs treat differrently
the third line of a Z-matrix (the line ending usually with "1 2 0").
Mathematically it's a question of two +/- signs in the algorithm.
The result of this mistake depends also on the original numbering of the
molecule, or when generating the Z-matrix, which atoms are choosen for
the starting 3 atoms.

2) I don't dare to say loudly, but there may be problem with the program.
The above problem, or for example, there are 3 collinear atoms in the
molecule and the program doesn't like this in some phase.

Well, what I should do, to generate 2-3 different Z-matrices from the
same molecule, and to minimaze all of them with two different
programs. From the result I could step forward.

Best wishes
                        Tamas E. Gunda
                        L.Kossuth Univerity
                        Debrecen
                        Hungary

                        [email-masked]

Hi

I did not do any detailed studies on the performance of different
 Z-matrizes, but my experience leads to the following directives:
-- It is good to choose a central atom of the molecule to be the first
   atom in the Z-matrix. This causes the chains in the Z-matrix to be
   as short as possible ( The C-3 of pentane is a better starting-atom
   than the C-1 ). This choice is often necessary if you want to use
   symmetric Z-matrizes.
-- The angles in the Z-matrix should be in the range of 30  to 150 . If    
   they are close to linear, small movements cause relatively great     
  changes in dihedral angles. 
   Another drawback of near-linear-angles is that they more easily run 
   out of the 0  to 180  limits of the Z-matrix angles.
Stefan Fau,

AK Frenking, FB Chemie der Philipps-Universitaet Marburg,
Hans-Meerwein-Str. 35032 Marburg, Deutschland

[email-masked]

Hi again

Here is some more information on the "chain-effect":
You can write a Z-matrix in two different styles: the star-style and the 
chain-style.
In the chain-style the position of a nucleus X is defined by the 
distance to the next nucleus X-1, the angle with X-1 and the 
second-next nucleus X-2 and the dihedral angle with X-1, X-2 and the 
third-next nucleusX-3. So the position of the last nucleus in a long 
chain is defined by the positions of the second-, the third- and the 
fourth-last nucleus of the chain. The positions of these nuclei depend 
on the positions of their predecessing nuclei. As far as I know, the 
new values of the optimization variables are determined without 
accounting for the motion of the predecessing nuclei. This means that 
the actual new position of X is not identical to the intended new 
position of that X because the nuclei X-1 .. X-3 also changed their 
positions. So the Atoms at the end of a chain can not reach their 
optimum positions until the predecessing atoms are at their optimum 
positions.
The other style is star-style: Here the position of any nucleus is 
defined relative to the Positions of three central Atoms A, B and C. 
They should be chosen near the center of mass. So all chains have 
four members: A, B, C and X. The disadvantage of this style is the 
possibility of long distances and correspondingly poor angle 
resolution in the definition of the Z-matrix. In effect this should 
correspond to looser convergence-criteria.
In short:
Chain-style causes the last nuclei in the definition-chain to find their 
optimum places last. The angle-resolution is good. The Z-Matrix is 
easy to understand.
Star-style Z-matrizes should converge faster because there should be 
less random-motion caused by the intermediate nuclei between C and 
X-3. The angle resolution of the outer nuclei is worse than the angle 
resolution of the inner nuclei. The Z-Matrix may be complicated to 
understand.
Stefan Fau,

AK Frenking, FB Chemie der Philipps-Universitaet Marburg,
Hans-Meerwein-Str. 35032 Marburg, Deutschland

[email-masked]