Subject: Re: CCL:G:geometry optimization methods

From: Anthony P Scott <[email-masked]>
Date: Tue, 8 Apr 1997 10:12:05 +1000 (EST)

Dale,

In my experience one needs to be careful on where you use either
cartesian, redundant or internal co-ordinates in geometry optimizations.

a case in point. Take azulene. write a z-matrix for it and attempt to
optimize in the default redundant co-ordinates. It does not converge. Now
use explicitly z-matrix. converges in just a few steps. Not too sure
about explicitly using cartesians however.

In my work, where I am looking a cyclic type h'bonded systems I always
use z-matrix.

hope this helps.

tony
______________________________________________________________________________
Dr. Anthony P. Scott,
Computational Chemistry Group,      Office Ph.: 61-6-249-3573
Research School of Chemistry,       Dept. Ph.:  61-6-249-3637
Australian National University,     Fax:        61-6-249-0750
Canberra, ACT 0200,                 Email:      [email-masked]
AUSTRALIA.
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From: Anatoli Korkin <[email-masked]>
Date: Mon, 7 Apr 1997 22:08:44 -0400 (EDT)

Dale,

You may try to optimize your system using Z-matrix and making separate
optimizations for parameters with small and large force constants.
Afetr one or two ineractions you may start the final optimization of
all of them. Do frequency calculation at a lower level first, and use
force constants from it (opt=readfc) in your subsequent optimization at
a higher level.

Anatoli Korkin

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From: A J Turner <[email-masked]>
Date: Tue, 8 Apr 1997 05:58:56 +0100 (BST)

Hi!

I am not very familier with g94 - but I do write optimisers my self.  The
effect you are seeing can often be caused by a poor initial hessian
matrix.

Rather than look to a different optimiser, how about trying a hessian
generated from a lower theory level to start the thing off?

cheers

Alex

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|Alexander J Turner         [email-masked]                  |
|Post Graduate              |http://www.bath.ac.uk/~chpajt/home.html|
|School of Chemistry        |+144 1225 8262826 ext 5137             |
|University of Bath         |                                       |
|Bath, Avon, U.K.           |Field: QM/MM modeling                  |
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From: "Dr. Heinz Schiffer" <[email-masked]>
Date: Tue, 08 Apr 1997 09:25:23 +0200

Hi Dale,

Optimization with Z-matrix coordinates is always the worst that you
can do, next come cartesian coordinates, and the best are the natural
internal coordinates of Pulay. Cartesian coordinates are o.k. if you
have a good initial guess of the Hessian matrix (e.g. computed by
a less expensive method). See : Jon Baker, Techniques for Geometry
Optimization : A Comparison of Cartesian and Natural Internal
Coordinates, J. Comput. Chem. 14(9) (1993) 1085-1100.

Ciao,
Heinz

--
Dr. Heinz Schiffer              Phone   ++49-69-305-2330
Hoechst CR&T                    Fax     ++49-69-305-81162
Scientific Computing, G864      Email   [email-masked]
65926 Frankfurt am Main                 [email-masked]

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From: Alain Kessi <[email-masked]>
Date: Tue, 8 Apr 1997 10:21:35 +0200

> A brief question:  Are there any circumstances in which a geometry
> optimization in Cartesian coordinates would be *faster* than in
redundant
> internal coordinates?

Most definitely: For very large systems, a Cartesian optimization step
will be faster than a redundant internal coordinate step (though the
internal coordinate optimization will likely take less steps, but not
enough so to compensate for the time each step takes). This is due to the
n^3 scaling of internal coordinate steps (where n is the number of
Cartesian coordinates), compared to the n^1 scaling of Cartesian steps.
Note that in both Cartesian and internal coordinates, the number of steps
probably scales something like n^1 (convergence guaranteed in n+1 steps
for harmonic potentials). 

> The reason I am asking is because I am trying to optimize the geometry
of
> a hydrogen-bonded dimer in a solvent medium using Gaussian 94, and the
> change in the two intermolecular Z-matrix coordinates (distance and
angle)
> remains large for many, many iterations.  The geometry isn't exactly
> oscillating between two structures, but it isn't settling down, either,
> and I thought that perhaps by changing the optimization method from
> redundant internal coordinates (the default method in G94) to
cartesians,
> the optimization might proceed more smoothly to a converged minimum.  I
> don't want to try this unless it can work, because the calculation is
> expensive.

Generally speaking, tightly bound structures converge in Cartesians about
as fast as in internal coordinates. In all other cases, internals should
do better. My guess as to what could go wrong with your system is that the
choice of internal coordinates is inadequate. There are many ways to
choose internal coordinates, and many probably perform worse (not better)
than Cartesian coordinates. Also, performance seems to drop when you add
internals to an already complete set. 

The reason can be sought in the fact that internals are better than
Cartesians because the potential energy surface is more harmonic expressed
in internals, which means that the Hessian information collected along the
way will be more useful. If you take the wrong set of internals, you will
not end up with a more harmonic potential. I would look for the problem in
the modelling of the solvent. Probably the best way to describe it is with
the internal coordinates for each molecule of the solvent, plus as few
extra internals as possible to link the molecule to its direct neighbor.
This will probably consist in one stretch, one bend and one dihedral for
each neighbor pair. 

Hope this helps in some way ...

Alain

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From: Alain Kessi <[email-masked]>
Date: Tue, 8 Apr 1997 14:50:24 +0200

> Coordinates, J. Comput. Chem. 14(9) (1993) 1085-1100.

You may also want to have a look at our more recent paper

Jon Baker, Alain Kessi and Bernard Delley, The generation and use of
delocalized internal coordinates in geometry optimization, J. Chem. Phys.
105(1) (1996) 192-212.

which shows some trends for much larger systems.

Alain

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From: John McKelvey <[email-masked]>
Date: Tue, 08 Apr 1997 11:16:02 +0100

> Coordinates, J. Comput. Chem. 14(9) (1993) 1085-1100.

I think I do not agree entirely with this.  Localised sub units, such as
rings whose relative torsion angles are uncertain pose challenging
problems. A bad initial guess at the angle will make cartesians a bad
choice, and a good Hessian won't help much.  Then, either Z-matrices or
redundant internals are FAR superior.  If the torsion has a low barrier
then the Hessian becomes very important.  Torsion angles and all their
characteristics are rampant in dyes, and we have to worry more about
then than any other single geometry factor.

Regards,

John