Subject: Semiempirical parameterization yet again...

From: <[email-masked]>
Date: Mon, 18 Apr 1994 19:04:04 -0600 (CST)

Netters,

   What a firestorm a few innocent comments in answer to a relatively 
simple question started up!  I'd like to very carefully (flame-proof
clothing, I hope) take an opportunity to answer some of the issues 
raised by some of the people in a few previous postings last week in
answer to my discussion of AM1 vs. PM3.  (An item I posted in reply
to a direct question, I might add.)
   First, what seem to be the issues?  I have identified a few from
the postings by Joe Leonard (JL) of Wavefunction, Craig Burkhart (CB)
at Goodyear, John McKelvey at Kodak (JM), and Chris Cramer (CC) at 
the University of Minnesota.  (I don't want to put words in anyone's
mouth, but below seems to an accurate rendering to me.  I have also
"shaded" them perhaps with questions I have been asked and comments
I have heard in the course of my travels and correspondence, so there
may be some inferences here they didn't intend.) 

1.  The parameterization of semiempirical methods is a relatively
simple "number-twiddling" task that is only limited by the speed 
of the computers at hand.  (JL and lots of other people)

2.  Larger molecules should be used in the molecular basis sets for 
parameterization (we call this the MBSP).  (JL, CB)

3.  More molecules and problem systems should be included in the MBSP
for better results.  (JL, CB)

4.  Better experimental data is now available to parameterize against
and should be used.  (JL, CB)

5.  Re-parameterization could give better results within the present
semiempirical models of AM1 and PM3.  (JL)

6.  Property-specific semiempirical methods should perhaps be developed
to compute only what we are interested in and to allow us to forget the
rest.  (JL, CB, CC)

7.  Perhaps a new model is needed.  (CC)

8.  Effort at semiempirical development is being duplicated.  (CC, JM)

("The snake oil salesman mounted the soapbox to confront the angry 
crowd.  He began to speak:") 

I'd like to try to answer these more or less one at a time, but first
a few general comments, which I clearly identify as MY SCIENTIFIC 
OPINION.  As such, I would ask that it be respected just as you would
anyone else's opinion.  This includes not calling me nasty names or 
accusing me of evil intentions.

  The development of a semiempirical quantum mechanical model is indeed 
similar to the development of a molecular mechanics force field in that
the objective is to reproduce experimental data.  That is about where
the similarity ends.  The underlying guts of the models are totally
different!  I can safely say that MM has nothing to do with chemistry,
but is more or less a fit to a convenient set of functions.  It
does have chemical validity in that it gives us good answers to some 
questions.
  QM is an entirely different situation, in that the actual arbiters of 
chemistry, the electrons, are treated directly by mathematical functions.
The chemistry come OUT of a model that describes the electrons.
This may seem to be a matter of degree to some, but I think that it is an
important distinction, especially as it finally applies to parameterization
of quantum chemical models.

  Now, to answer the numbered items above.  

(1), (2), (3)  The speed of computers has indeed greatly enhanced the 
efficiency of parameterization.  Rather than develop "Several/many sets 
of params" quickly, my group has elected use this power to do parameter-
izations more carefully than ever before possible.   This involves 
including larger systems and more molecules in the MBSP, a concept with 
which I heartily agree!  There are some things that will never be modeled 
properly unless we include them in the MBSP as larger molecules.  One  
of these gentlemen, John McKelvey pointed this out to me quite directly 
when referring to the poor reproduction of the twist angle in the diphenyl 
system with AM1.  We have also taken more care at examining the structure 
and complexity of the parameter hypersurface than ever before.  This 
hypersurface is an incredibly complex multidimensional mathematical 
construct.  One must examine it very carefully to find good starting 
points for further refinement.  This concept is directly analogous to 
the multiple-minima problem for conformer searches.  This discussion is
also somewhat applicable to item (5).

(4)  Agreed, more and better experimental data is available now.  We
are trying to make use of this as much as possible.  It should be noted
that this is only a marginal improvement over what went before rather than
a quantum enhancement.

(5), (7)  PM3 was essentially a re-parameterization of AM1 using a more
mathematical approach (as opposed to chemical intuition and knowledge)
to deriving parameters and applying very powerful computers.  It was
better for some items than AM1, but as my previous posting showed, it
was only marginally better.  It also possessed some severe problems.
Chris is correct: to get better results, we need a new MODEL.  The work
I am aware of along these lines is underway here in my lab at the 
University of Missouri-Kansas City (with C. Jie and R. Dennington)
and under the direction of Prof. Walter Thiel at the Univ. of Zurich, 
in collaboration with A. Voityuk.

Our work involves SAM1, which is a new model developed primarily under the
guidance of Michael Dewar.  It is indeed a new model and it uses a new
approach to compute the two-electron/two-center repulsion integrals (TERIs)
for all systems.  This new approach allows us to also treat d-orbitals
explicitly.  Results have been published for C, H, On, N, F, Cl, Br, and I
in our new model and we intend to publish a method paper as soon as the final
model for transition metals is finalized and tested.  (M. J. S. Dewar, 
C. Jie, G. Yu, Tetrahedron  23, 5003 (1993);  A. J. Holder, R. D. 
Dennington,  C. Jie, Tetrahedron  50, 627 (1994))

Prof. Thiel's work involves MNDO/d, which uses a new version of the
multipole expansion method to circumvent the TERI problem with d-orbitals.
MNDO/d is an addition to the MNDO model developed by Prof. Thiel in collab-
oration with Prof. Dewar in 1977.  (W. Thiel,  A. A. Voityuk, Theoretica
Chimica Acta  81, 391 (1992);  W. Thiel,  A. A. Voityuk, International 
Journal of Quantum Chemistry  44, 807 (1993))

(8)  As shown above, at least for the cases of Prof. Thiel's work and that
work being done in my lab, effort is NOT being duplicated.  These are two
clearly different approaches to the same problem, and I suspect that
both will find users and adherents.

(6)  I have left the property-specific semiempirical method question for 
last.  This one is also perhaps the one most prone to debate and opinion.
Personally, I disagree with this entire concept.  Chris Cramer
makes the point that one of the strengths of ab initio methods is their
generality.  I would like to make this same case for the more popular
semiempirical methods such as SINDO1, MINDO3, MNDO, AM1, PM3, SAM1, and
MNDO/d.  Contrast these to INDO/S which is acknowledged to really work
only for spectra.  (Yes, I know that papers have shown it works for other
things sometimes, but even the authors of the method think of that as a
fortuitous circumstance.)  Dewar's methods have found such wide approval,
application, and acceptance simply because they are GENERAL.  If we paramet-
erize semiempirical methods for heats for formation only or for a single
class of compounds only, we may gain in accuracy, but we lose in the capa-
bility to have a single approach to many problems.

  Now, back to what I was saying about models above.  (Bet you thought I
wasn't going to get back to that, huh?)  Semiempirical models are chemical
models based on a somewhat direct relationship to nature.  In my way of
thinking, stretching this model away from all correspondence with some
physical quantities (which are actually supposed to be IN THE MODEL) to
gain an additional modicum of accuracy for the property YOU consider critical 
is not model development, it is "number-twiddling" of the highest order! 
Semiempirical parameters must fit into chemistry.  This is why we include
dipole moments in the parameterization of a method that some people use
to only compute heats of formation.  If the method cannot do some sort of
systematic treatment of dipole moments and is based on the same quantum 
mechanical approach that brings us the heats of formation, how can we 
trust it?  

  Finally, (bet you thought I'd never quit) where are the calls for special
ab initio basis sets to compute reaction energetics?  What about special
basis sets for fluoroethers?  Remember, basis sets are "parameterized"
just like semiempirical methods.  (Where do you think those exponents come
from?)  We don't ask for these because they would destroy the generality
of the approach.  While some may choose the track of specialized semiempirical
methods, we will proceed with developing general approaches.

("The snake oil salesman descends from the soapbox to thunderous applause.")

  Andy Holder
    4/18/94

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                          DR. ANDREW HOLDER
         Assistant Professor of Computational/Organic Chemistry

Department of Chemistry          ||  Internet Addr: [email-masked]
Univ. of Missouri - Kansas City  ||  Phone Number:  (816) 235-2293
Spencer Chemistry, Room 315      ||  FAX Number:    (816) 235-5502
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