Subject: SUMARY:PD atomic charges

From: <[email-masked]>
Date: Wed, 2 Oct 1996 09:31:18 +0200

Hello,

Last week I posted a question about the methods to get
atomic charges.
Here is my original question:

I'm calculating atomic charges with Gaussian using Mulliken population
analysis and fitting to electrostatic potential methods.
I've noted some important differences between Mull and ESP derived charges.
More , for ESP derived charges the use of correlated densities (MP2 density in this case)
gives important differences with the use of HF density.
So I would like to know if someone could advise me some references (review article would
be nice) about the comparison of this methods and about the effect of correlation
on the caculated charges.
Another question : Does it make sense to do a Mulliken population analysis with the MP2
density ??
Any comment or help is welcome.
Results will be summarized for everybody.
Thanks.

Here is the sumary of the answers I got:

********************************************
>From Dr. Donald E. Williams
     University of Louisville

E-Mail: [email-masked]
********************************************

New Software Available

        Molecular interactions occur during host-substrate docking, cluster,
and crystal formation - whenever molecules associate with one another.  The
energy and geometry of molecular association is determined by the force field.
As a component of the force field, an accurate set of net atomic charges is
needed.
        Reliable net atomic charges can be found by fitting the molecular
electric potential with program PDM96.  The program provides a choice of
geodesic, Connolly, cubic, or user specified grid points for the electric
potential.  In addition to net atomic charges, program PDM96 also allows
any combination of atomic dipoles/quadrupoles, bond dipoles, as well as the
addition of lone pair electron sites if required.
        A particularly useful feature of the program is the transparent way
in which fixed charges and charge dependency conditions are specified.  By
specififying appropriate charge dependencies (e.g., equal charges or equal
sums of charges), chemical intuition can assist to produce charges which are
transferable between related types of molecules.  A complete error treatment
with standard deviations and correlations is made.

Program PDM96, Potential Derived Multipoles

The following is a brief description of this program.
        Molecules interact with each other via their electric potential.
PDM96 finds optimized net atomic charges and other site multipole
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variables.  The program is written in Fortran 77 and runs on any
computer with F77 capability.

Program PDM96 has a unique combination of features:

o  excellent agreement with quantum mechanical multipole moments
o  general sites, e.g. united atoms, not necessarily at atomic locations
o  each site may have any combination of monopole, dipole, or quadrupole
o  bond dipole model is supported
o  restricted (along the bond direction) bond dipole model is supported
o  provision for site dipole vectors in sp2 or sp3 directions
o  selected fixed atomic charges
o  selected groups of atoms with fixed charge
o  atomic charge equalities or symmetry relations
o  rotational invariance of site charges
o  provision for optional foreshortening of X-H bonds
o  comparison with Mulliken charges and Mulliken electric potential
o  direct input from Gaussian-92 or G-94 output file
o  generalized input from other quantum mechanics programs
o  geodesic, Connolly, and cubic grids for MEP are available
o  provision for custom generation of MEP grid points
o  error analysis with standard deviations and correlations
o  on-line program manual
o  comprehensive examples are provided

A  review of potential-derived charges may be found in Reviews of
Computational Chemistry, Vol. II, pp. 219-271 (1991).  For further
information contact Dr. Donald E. Williams, Department of Chemistry,
University of Louisville, Louisville, Kentucky 40292, USA.

Tel:(502)852-5975 Fax:(502)852-8149 E-mail:[email-masked]
-----------------------------------------------------------------------
Ordering information

Program package consisting of manuals, Fortran-77 source files,
and demonstration example files....................................$2,000

Special discount price is available for academic use only... ........$395

Normal shipment is via ftp; please provide an account protected 
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Inquire about shipment via other media.

Make check payable to the University of Louisville and mail to:
Dr. Donald E. Williams
Department of Chemistry
University of Louisville
Louisville, KY 40292
-------------------------------------------------------------------------

************************************************
>From Bill Ross
   
E-Mail: [email-masked]
************************************************

We have references & discussion on http://www.amber.ucsf.edu/amber/ -
see the section on the Cornell et al. force field and the one on
charge derivation philosophy.

Bill Ross

************************************************
>From Konrad Hinsen
     Laboratoire de Dynamique Moleculaire
     Institut de Biologie Structurale
     38027 Grenoble Cedex 1, France

E-Mail : [email-masked]
************************************************

> I'm calculating atomic charges with Gaussian using Mulliken population
> analysis and fitting to electrostatic potential methods.

You didn't say *why* you are doing this, so I assume that the goal
is obtaining partial charges for an empirical force field.

> I've noted some important differences between Mull and ESP derived charges.
> More , for ESP derived charges the use of correlated densities (MP2 density in this case)
> gives important differences with the use of HF density.

First of all, Mulliken charges are based on a somewhat arbitrary
assignment of parts of electron densities to the individual atoms.
They may give some indication of polarization etc., but as a source
for partial charge information they are not very useful.

ESP-derived charges depend on
1) the ab-initio reference potential (which includes basis-set dependence)
2) the choice of evaluation points for the potential
3) the method used for fitting the charges.

Dependence 1) is obvious and if you find that your charges depend on
the level of calculation (provided that you haven't done something
stupid regarding 2) and 3)), then this is a feature of your system
that you have to understand and draw conclusions from. The dependence
on the evaluation points is equally obvious, but there is no single
choice that everyone agrees on (and to some extent it depends on
what you want to do with the fitted charges). Among the strategies
that have been proposed are:
1) points on a grid around the molecule (not recommendable due to
   the dependence on arbitrary grid axes)
2) points on well-defined surfaces around the molecule
3) points chosen at random in a well-defined region around the
   molecule.

Dependence 3) is more problematic, since it shouldn't be there in an
ideal world. The proposed methods differ in numerical stability and in
the exact quantity they are trying to minimize. Basically, everyone
agrees that what we want is a least-squares fit. Such fits are in
general known to be problematic, because the solution is often
underdetermined, and this also occurs for charge fitting. It is
therefore *not* a good idea to simply solve the normal equations for
the least-squares, but unfortunately that is what most people are
doing. A much safer alternative is singular-value decomposition, as
described in most books on matrix computations, or even in the second
edition of Numerical Recipes.

Beyond the problem of numerical stability of the fit, one popular
method (known as RESP) proposes to put a constraint on the absolute
value of the charges, based on the observation that ESP often gives
charges that seem to large. I don't know in how far this is a result
of numerical instabilities (RESP does not use singular value
decomposition) or of some real physical effect; this ought to be
investigated.

Literature:

C.I. Bayly, P. Cieplak, W.D. Cornell and P.A. Kollman
J. Phys. Chem. 97, 10269 (1993)
(This paper describes RESP.)

K. Hinsen and B. Roux
J. Comp. Chem., in print  (contact me for a preprint)
(This paper describes a specific potential function for proton transfer
simulations, but contains an extensive appendix that describes a
charge-fitting strategy based on singular-value decomposition.)

Both papers contain references to older methods. There is another
paper that has appeared earlier this year in J. Comp. Chem. and which
deals explicitly with an SVD-based fitting method, but I haven't
seen it yet.

The reference of this paper is:

M. M. Francl, C. Carey, L. M. Chirlian, D. M. Gange, J. Comp. Chem,
Vol 17, No 3, (1996), p 367-383

********************************************************
>From Christopher J. Cramer
     University of Minnesota

E-Mail : [email-masked]
WWW    : http://pollux.chem.umn.edu/~cramer
********************************************************

   You might be interested in our extensive comparison of charges calculated
by various methods (including our own CM1 methodology) in Storer, J. W.;
Giesen, D. J.; Cramer, C. J.; Truhlar, D. G. " Class IV Charge Models: A New
Semiempirical Approach in Quantum Chemistry" J. Comput.-Aid. Mol. Des. 
1995, 9, 87. This paper is actually maintained on the Web by JCAMD. You can
find it at http://wucmd.wustl.edu/jcamd/278/paper.html

********************************************************
>From Guosheng LI
     Lab. de Chimie Theorique
     Univ. de Nancy-I

E-Mail : [email-masked]
********************************************************

For a good review, see

S.M.Bachrach, "Population analysis and electron densities from quantum
mechanics", in Reviews in Computational Chemistry, Vol.V
K.B.Lipkowitz and D.B.Boyd, VCH publishers, Inc. New York, 1994, Chap.3
p.171-227.

You may also refer to a recent paper:

S.Tsuzuki et al., " Comparison of atomic charge distributions obtained
>from different procedures: basis set and electron correlation effects"
J. Mol. Struc.(Theochem), 365(1996),81-88.

By the way, your interest is on "single-bonded" systems or
"multiple-bonded" systems, and on isolated molecules or complex ?
Electron correlation may have different effects on them. As for the
former point, I agree with Bachrach's opinion, i.e. the effect of
electron correlation on atomic populations is quite small for single-
bonded systems, while much more substantial for multiple-bonded systems.
For complex, situations are much more difficult and according to my
experience, no one procedure can be satisfactory in most of the cases.
(Hope this is not true !)

Hope you will have some new findings.

Guosheng LI
Lab. de Chimie Theorique
Univ. de Nancy-I
[email-masked]

***********************************************************************

I would like to thank everybody for the references and advices given.
I hope this sumary will help everybody.
Francois.

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