Subject: CCL:SUMMARY:weekness for atomic cahrge using fitting to electrostatic potential methods

From: <[email-masked]>
Date: Fri, 25 Oct 1996 15:08:31 +0900

I send you a summary of answers about ESP-charges.　I would like to 
thank everybody for many advices. I hope this summary will help everybody.
Masao Masamura

Date: Sun, 29 Sep 96 13:30:49 +0100
From: Konrad Hinsen <[email-masked]>
To: [email-masked]
Subject: Re: CCL:weekness for atomic cahrge using fitting to electrostatic
potential methods

There was a similar question a few days ago, so I'll just send you
the reply I sent then:

Date: Wed, 25 Sep 96 20:19:42 +0100
From: Konrad Hinsen <[email-masked]>
To: [email-masked]
Cc: [email-masked]
In-Reply-To: <[email-masked]>
        ([email-masked])
Subject: CCL:G:Correlation effect on calc atomic Charges
Sender: Computational Chemistry List <[email-masked]>
Errors-To: [email-masked]
Precedence: bulk

> 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.

-------------------------------------------------------------------------------
Konrad Hinsen                          | E-Mail: [email-masked]
Laboratoire de Dynamique Moleculaire   | Tel.: +33-76.88.99.28
Institut de Biologie Structurale       | Fax:  +33-76.88.54.94
41, av. des Martyrs                    | Deutsch/Esperanto/English/
38027 Grenoble Cedex 1, France         | Nederlands/Francais
-------------------------------------------------------------------------------
<my reply>

        I thank you for your replay. 

        A several years ago, I found that the CHELP cannot reproduce the
atomic charge for HCOO-(H2O)n (n = 0,1,2,3,4,5,6). I think CHELP cannot
reproduce the atomic charge for clusters. I will publish these results.

        Thank you.

============================================================================
=====
Masao Masamura 
Okayama University Dental School
Department of Preventive Dentistry
Fax: 81-86-225-3724
e-mail: [email-masked] 
============================================================================
=====

Date: Mon, 30 Sep 96 10:28:30 +0100
From: Konrad Hinsen <[email-masked]>
To: [email-masked]
Subject: Re: Thanks

>         A several years ago, I found that the CHELP cannot reproduce the
> atomic charge for HCOO-(H2O)n (n = 0,1,2,3,4,5,6). I think CHELP cannot
> reproduce the atomic charge for clusters. I will publish these results.

What do you mean by "CHELP cannot reproduce the atomic charge"? Which
atomic charge? There is no measurable or even well-defined quantity
called "atomic charge". In reality, you have well-localized nuclear
charges plus strongly delocalized electronic charge distributions.
The point of ESP procedures such as CHELP is to reproduce the
electrostacic potential of this complicated charge distribution.
-- 
-------------------------------------------------------------------------------
Konrad Hinsen                          | E-Mail: [email-masked]
Laboratoire de Dynamique Moleculaire   | Tel.: +33-76.88.99.28
Institut de Biologie Structurale       | Fax:  +33-76.88.54.94
41, av. des Martyrs                    | Deutsch/Esperanto/English/
38027 Grenoble Cedex 1, France         | Nederlands/Francais
-------------------------------------------------------------------------------
<My replay>

        I thank you for your valuable opinion. 
        The CHELP cannot reproduce the charge on H' of H'COO-(H2O)n
(n=0,1,2,3,4,.5.6) as follows: When n becomes larger, Natural population
analysis predict the charge on the H' becomes more positive (J.Phys.Chem.,
97, 3157(1993)). I think the prediction of Natural population analysis is
correct for the following reasons:  I showed the cause for the elongation
of the H-C bond in HCOO- in the gas phase. This elongation results from the
contribution of H-...CO2 as resonance structure to the HCOO-. When more
water molecules attach HCOO-, more minus charge withdraws from HCOO- to
water molecules. Consequently, it is predicted that the resonance
structure, H-...CO2, contributes less to HCOO- with n increment. Due to
less contribution of the resonance structure H-...CO2 with each n
increment, the charge on the H' becomes more positive with n increment.
        However, the CHELP disagrees with this prediction.
        That results for CHELP is old. Thus, I will recalculate the charge
on the H' with GAUSSIAN 94. Also, I will use CHELPG.  

============================================================================
=====
Masao Masamura 
Okayama University Dental School
Department of Preventive Dentistry
Fax: 81-86-225-3724
e-mail: [email-masked] 
============================================================================
=====
Date: Thu, 3 Oct 96 13:00:31 +0100
From: Konrad Hinsen <[email-masked]>
To: [email-masked]
Subject: Re: CHELP and CHELPG

>         However, the CHELP disagrees with this prediction.
>         That results for CHELP is old. Thus, I will recalculate the charge
> on the H' with GAUSSIAN 94. Also, I will use CHELPG.  

You should try an SVD-based method such as CHELP-SVD. Older methods
use a numerically unstable algorithm for finding the charges, and
therefore might produce random numbers in difficult cases.
There is a paper on this in J. Comp. Chem. 3 (1996).
-- 
-------------------------------------------------------------------------------
Konrad Hinsen                          | E-Mail: [email-masked]
Laboratoire de Dynamique Moleculaire   | Tel.: +33-76.88.99.28
Institut de Biologie Structurale       | Fax:  +33-76.88.54.94
41, av. des Martyrs                    | Deutsch/Esperanto/English/
38027 Grenoble Cedex 1, France         | Nederlands/Francais
-------------------------------------------------------------------------------
Date: Mon, 30 Sep 1996 09:28:57 -0400
From: [email-masked] (Donald E. Williams)
Apparently-To: [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
representations of the molecular electric potential based on a variety
of models.  The program is easy to use, flexible and powerful.  Results
are obtained in a single iteration and a complete error treatment is
made which includes estimated standard deviation and correlation of
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 
with a temporary password to receive the program.
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
-------------------------------------------------------------------------

<my replay.>

        I thank you for your valuable opinion. 

        I used PDM88 (QCPE 568). The PDM88 cannot reproduce the charge on
H' of H'COO-(H2O)n (n=0,1,2,3,4,.5.6) as follows: When n becomes larger,
Natural population analysis predict the charge on the H' becomes more
positive (J.Phys.Chem., 97, 3157(1993)). I think the prediction of Natural
population analysis is correct for the following reasons:  I showed the
cause for the elongation of the H-C bond in HCOO- in the gas phase. This
elongation results from the contribution of H-...CO2 as resonance structure
to the HCOO-. When more water molecules attach HCOO-, more minus charge
withdraws from HCOO- to water molecules. Consequently, it is predicted that
the resonance structure, H-...CO2, contributes less to HCOO- with n
increment. Due to less contribution of the resonance structure H-...CO2
with each n increment, the charge on the H' becomes more positive with n
increment.
        However, the PDM88 disagrees with this prediction.

        Why PDM88 cannot reproduce the previous prediction.
============================================================================
=====
Masao Masamura 
Okayama University Dental School
Department of Preventive Dentistry
Fax: 81-86-225-3724
e-mail: [email-masked] 
============================================================================
=====
From: "Donald E. Williams" <[email-masked]>
Date: Thu, 3 Oct 1996 10:43:33 -0400
X-Mailer: Z-Mail (3.2.3 08feb96 MediaMail)
To: [email-masked]
Subject: Re: PDM88
Content-Type: text/plain; charset=us-ascii

On Oct 3,  9:58am, [email-masked] (正村) wrote:
> Subject: PDM88
>         I thank you for your valuable opinion.
>
>         I used PDM88 (QCPE 568). The PDM88 cannot reproduce the charge on
> H' of H'COO-(H2O)n (n=0,1,2,3,4,.5.6) as follows: When n becomes larger,
> Natural population analysis predict the charge on the H' becomes more
> positive (J.Phys.Chem., 97, 3157(1993)). I think the prediction of Natural
> population analysis is correct for the following reasons:  I showed the
> cause for the elongation of the H-C bond in HCOO- in the gas phase. This
> elongation results from the contribution of H-...CO2 as resonance structure
> to the HCOO-. When more water molecules attach HCOO-, more minus charge
> withdraws from HCOO- to water molecules. Consequently, it is predicted that
> the resonance structure, H-...CO2, contributes less to HCOO- with n
> increment. Due to less contribution of the resonance structure H-...CO2
> with each n increment, the charge on the H' becomes more positive with n
> increment.
>         However, the PDM88 disagrees with this prediction.
>
>         Why PDM88 cannot reproduce the previous prediction.
> ============================================================================
> =====
> Masao Masamura
> Okayama University Dental School
> Department of Preventive Dentistry
> Fax: 81-86-225-3724
> e-mail: [email-masked]
> ============================================================================
> =====
>-- End of excerpt from [email-masked] (正村)

Dear Dr. Masamura:
        The fundamental question is the accuracy of the molecular electric
potential calculated by your quantum mechanics program.  Program pdm88 (or the
improved recent release, pdm96) assumes that the MEP is accurate.  In order to
get an accurate MEP, you may have to use a large basis set, perhaps even
including correlation.  We have found, in general, that population analysis
charges fit the MEP very poorly.
        Usually one desires the best representation of the MEP.  However, there
 could be reasons why one would want to use non-optimal charges.  Perhaps one
wants to compare charges in a series of molecule with some chemical model-maybe
just intuition.  Or perhaps PD charges become unreasonably large or small.
        Pdm96 allows for input based on chemical models.  For instance, fixed
charges can be assigned to one or more atoms.  Of course, this will degrade the
fit to the MEP, but perhaps not by much.  One can require charges to be equal,
or for the sum of a group of charges to be zero.  These "chemical" models are
OK provided they do not degrade the fit to the MEP too much.
        Additional information about pdm96 is appended.
-Donald Williams

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
representations of the molecular electric potential based on a variety
of models.  The program is easy to use, flexible and powerful.  Results
are obtained in a single iteration and a complete error treatment is
made which includes estimated standard deviation and correlation of
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
with a temporary password to receive the program.
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
-------------------------------------------------------------------------

-- 
Dr. Donald E. Williams          email:[email-masked]
Department of Chemistry
University of Louisville        phone:502-852-5975
Louisville, KY 40292            fax:  502-852-8149

Date: Wed, 16 Oct 1996 10:17:56 -0500
From: Boyd <[email-masked]>
Subject: charges and potentials
To: "Masamura, Masao" <[email-masked]>
X-Mailer: Mail*Link SMTP-MS 3.0.2
Content-Transfer-Encoding: 7BIT

Dear Dr. Masamura,
About 2 weeks ago you posted a question on the CCL asking about electrostatic
potentials.  Did you get all the information you needed?
You can find additional information in 2 chapters of Volume 2 of "Reviews in
Computational Chemistry".  Donald E. Williams explains Net Atomic Charge and
Multipole Models for the Ab Initio Molecular Electric Potential, and Peter
Politzer and Jane S. Murray explain Molecular Electrostatic Potentials and
Chemical Reactivity.  In Volume 5 (1994), Steven M. Bachrach explains
Population Analysis and Electron Densities from Quantum Mechanics.
I hope you find these chapters helpful.
Sincerely,
Donald B. Boyd, Ph.D.
Research Professor of Chemistry
Editor, REVIEWS IN COMPUTATIONAL CHEMISTRY
Department of Chemistry
Indiana University-Purdue University at Indianapolis
402 North Blackford Street
Indianapolis, Indiana 46202-3274, U.S.A.
Telephone 317-274-6891
Facsimile 317-274-4701
Internet [email-masked]
REVIEWS IN COMPUTATIONAL CHEMISTRY Home Page on the 
World Wide Web URL http://chem.iupui.edu/~boyd/rcc.html