Subject: Re: CCL:Does optimized structure depend on the input?

From: [email-masked] (Teerakiat Kerdcharoen)
Date: Mon, 10 Apr 1995 13:18:10 +0200 (DFT)

: Dear all CCLers:
: 
: Recently I come up with a question that using Gaussian 92, does the 
: optimized geometrical structure depend on the initial input? Since the 
: result is a local minimum, the answer seems yes. But how to avoid this 
: local minimum to obtain a global minimum? Please give me a reply if you 
: have an idea. Thank you!
: 
: Shubin

Dear Shubin,
	Gaussian 92 will locate to the next (closet) minima using
various methods, steepest descent, conjugated gradient and so on.
Therefore, you are right that the optimized geometrical structure
definitely depends on the initial input.
	To my limit knowledge, there is no ultimate method to locate
the global minimum, especially when the potential hypersurface
is rather complicated. The most promising method in the modern
days is "simulated annealing" [1] with the help of statistical mechanics,
molecular dynamics and Monte Carlo simulations to find the global
minimum. The idea is to search all the energetically possible
areas as much as possible by increasing temperature so that
molecular complexe can wander over the energy barrier (Gaussian
can't do that since it always goes downhill) and then gradually
decrease the temperature to allow the molecular complex to relax
to the lowest minimum. Statistical mechanics tools are used to
search the possible potential hypersurface. Somebody believes
that this is the ONLY gauranteed method to find the global minimum.[2,3]
The method is applied in connection with DFT and HF theory for mimization
of geometry and wave-function paremeters on the fly. This approach
is so-called Car-Parinello molecular dynamics [4] (see review in
[5]) which successfully works with solid-state but now extends 
to organic chemistry [6].

Reference
=========

1. S. Kirkpatrick, C. D. Gelatt Jr. and M. P. Vecchi, Science 220: 4598 (1983)
2. P. J. M. van Laarhoven and E. H. L. Aarts, Simulated Annealing:
   Theory and Applications (Reidel, Dordrecht, 1987).
3. B. Hartke and E. A. Carter, J. Chem. Phys. 97: 6569 (1992).
4. R. Car and M. Parinello, Phys. Rev. Letters 55: 2473 (1985).
5. D. K. Remler and P. A. Madden, Mol. Phys. 70: 921 (1990).
6. U. C. Singh and P. A. Kollman, J. Comput. Chem. 7: 718 (1986).

	Hope this helps somehow.
						take care,
						Teerakiat
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Teerakiat Kerdcharoen
E-mail:   [email-masked] (University of Innsbruck)
          [email-masked] (Bangkok)  (Permanent E-mail address)
Homepage  http://www-c724.uibk.ac.at/noy/       
          http://atc.atccu.chula.ac.th/noyhome/    
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From: Shubin Liu <[email-masked]>
Date: Mon, 10 Apr 1995 12:17:49 -0400 (EDT)

Dear all CCLers:

Last Friday, I posted the question of whether the optimized structure 
depends on the input. I recieved a number of reponses from you guys. 
Thanks are due to all of you who promptly responsed my qusetion. 
Following are the answers:

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From [email-masked] Apr 10 09:51:49 1995

There is no optimization method to my knowledge that can GUARRANTEE to
reach a global minimum.  Searching a global minimum becomes more 
difficult with increase of the number of variables.  For small molecules,
chemical (or any) intuition is at times the only guide for searching what
is desired.  For instance, when dealing with TiCl_6 complex, it's good
to try Oh symmetric geometry first.  The "best" way other than the
Good luck.
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From: David Close <[email-masked]>

  Part of what you say is true.  But part of the answer depends on the
types of problems your are dealing with.  A good example of a local
minimum would be trying to do a calculation on an isolated molecule.
As torsion angles vary there are going to be geometries encountered
where strong intra-molecular hydrogen bonds form.  Often times the
calculation stops at this local minima.  However in a more realistic
situation, the atoms forming the intra-molecular bond are most likely
tied up with H-bonds to neighboring molecules.  But few of us can
afford the computer time to add very many neighboring molecules.  One
trick here is to use small neighboring molecules like waters of hydra-
tion.  But there are many other things that one can do.  First of all,
what systems are you studying, and what are you trying to learn?
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From [email-masked] Apr 10 09:52:30 1995

Most geometry optimization algorithms find a nearby local minimum,
as opposed to a global minimum. In general, it is not an easy task
to find out the global minimum of a molecule, especially when the
molecule becomes larger. But there are mothods for locating global
minima. The simulated annealing method is one example.
However, in general, we don't know how many conformers there will
be in a given molecule. So we try to find out as many (low-energy)
conformers as possible in a conformational space.
This is called 'conformational searching'.
There are two major categories in the conformational searching:
1) deterministic method
2) stochastic method
Method 1) is used in small to medium systems and method 2) in 
medium to large systems.
You can get more information from A. R. Leach "A Survey of Methods for
Searching the Conformational Space of Small and Medium-Sized Molecules"
in Reviews in Computational Chemistry, Ed. K. B. Lipkowitz and D. B. Boyd,
Vol. 2, VCH, 1991.
-Dongchul Lim
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From [email-masked] Apr 10 09:52:42 1995

To  the best of my knowledge there is no direct way to find a global
minima apart from a reasonably exhaustive search for all degrees of
freedom. The approaches may include systematic conformational searches ro
random sampling of conformational space using a molecular mechanics  
force  field level  of theory followed by a more  focused search using 
semi-empirical methods (for poorly  parameterized chemical species) and
ab initio calculations at selected local minima to  verify the global
minima at  a  given level of theory.   
  You should talk  with Alex Tropsha  with  the Pharmacy School  Modelling
Laboratory,   [email-masked].
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From [email-masked] Apr 10 09:52:54 1995

As far as I know, there are numerous tricks, methods and practical recipes, 
but neither has strict guaranties that you will find the global minimum and 
not only a local one. 
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From [email-masked] Apr 10 09:53:27 1995

G92, as all other geometry optimizing theoretical procedures, looks
for minimal energy in a function of the nuclear coordinates. This func-
tion is the electronic hamiltonian of the molecule. If you start from
a geometry very near or very far from the absolute minimum, the result
could be a partial minimum. Gradients are calculated analiticaly, and
very accurate input data can give a first gradient displacement going
farther than the right amount. In such a case, a van der Waals minimum
could be attained (in a predisociative state, for example) in place
of the equilibrium geometry. A too distorted input can conduct to
unpredicatable results.

It is a matter of experience and doing it many times. If not, theore-
tical chemistry research is meaningless, because programs and computers
are doing all things.
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From [email-masked] Apr 10 09:53:42 1995

Shubin Liu ([email-masked]) asked how one can be sure he has found the
global, rather than merely a local, minimum.  I think there is no short answer
to this question.  If you are looking at something like water or methane, where
everyone knows in a general way what the answer looks like, there is no
ambiguity (what's the n-fold analog of an ambiguity?), and you might even
dispense with the frequency job which is usually considered prudent to
characterize a stationary state.  But note that even very simple molecules can
have PES's with >1 minimum.
    If you are working with proteins I suspect that at the current state of
the art you may as well forget about nailing down the global minimum.  Somewhere
between water and a peptide you can worry about finding the global min. If, as
is usually the case, the various possible minima you are concerned about arise
from conformational possibilities, the systematic way to look for the global
one is with a conformational search program as implemented in several commercial
packages, e.g. Spartan.  If you have no hangups about gambling, there is at least
one stochastic search program, PCGlobal, from Serena Software, which randomly
generates a slew of input structures, hopefully including some you may not have
thought of.  If your molecule is not too big you could do the job by hand,
using input structures corresponding to all reasonable-looking possibilities
for minima; your computational chemistry program should slide each one into
the nearest minimum for the level you're using; if size doesn't make it
impractical then do a freq job to see if the lowest-E stationary point is
really a min.
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From [email-masked] Apr 10 09:53:50 1995

  There are a number of possibilities raised by your question about how
the Gaussian input can give rise to a local minimum,

  1) You could have symmetry constrained the input and the true minimum
     does not have the initial symmetry

  2) You could have started near a local minimum and the global minimum
     is separated by a barrier.

  3) You supplied a Z-matrix which does not span the full conformational
     space, either by restricting some internal coordinates, i.e. having
     too few coordinates, or by supplying a set with a redundancy so that
     it effectively has too few variables.

  Only the third would get close to being an input error.  The first two
qualify as constrained solutions and local solutions respectively.  Check
to see that your input spans the full conformational space with the
keyword FOPT in place of OPT. It does not change the algorithm, simply
adds a check that the coordinate supplied are linearly independent and
sufficient in number to span the space.

  If you have symmetry constraing
then the frequency result will guide you in reducing the symmetry and
displacing toward the true minimum.  If you simply have located a local
minimum try SCAN'ing the surface, possibly with a lower cost method, to
locate other potential minima.

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From [email-masked] Apr 10 09:54:01 1995

To obtain a global minimum, the entire PES
has to be scanned, and not a region..this is 
however difficult in some cases where there
is little experimental support.
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From [email-masked] Apr 10 09:54:12 1995

About local and global minimum, there is a simple answer:
we cannot be sure of the minimum is local or global. All optimizer converge
to an local minimum.
To be sure of a global one, try others geometries (a little distorted) and
calculate the energy.

Within gaussian, there is a keyword (I don't remember, perhaps SCAN, see
the documentation) that scan the potential energy surface. So gaussian can
do that for you.
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From [email-masked] Apr 10 09:54:19 1995

Reference
=========

Best regards,

Shubin
.............................................................................
Shubin Liu

Department of Chemistry			    Email: [email-masked]
University of North Carolina		           [email-masked]
Chapel Hill, NC 27599-3290		    Tel  : (919) 962-0150(O)
USA                                                (919) 914-6923(H)
.............................................................................