Subject: summary on population analysis

From: Patrick Bultinck <[email-masked]>
Date: Fri, 10 Dec 1993 16:22:45 +0100 (MET)

On Fri, 3 Dec 1993, I, Patrick Bultinck, wrote:

> 
> I have performed some population analysis calculations on covalent
> molecules using ab initio Hartree-Fock. I performed MPA and LPA (mulliken
> and lowdin). The results were often miles apart. The reason, I think, is
> the fact that every value for n in S^nPS^(1-n) will do for defining a
> population analysis formula.
> I do no longer believe very much in the use of population analysis for
> determining atomic charges for atoms in a certain molecule. This
> disbelieve became bigger when last year, during my graduation thesis, I
> studied calculations of dipole moments. Indeed I remembered the formula
> DIP. MOM.=sum(atomic charge*R), sum over all atoms. I thought I could see how
> good PA was by using the PA results to determine the dipole moment (apart
> from the one calculated with the wavefunction). I calculated the different
> cartesian components of the DM, since PA gave me the charges and I knew
> from my input what the cart. coordinates of the atoms were. By putting
> together the cart. comp. of the DM I got to a value of the total dipole
> moment. Needless to say that the value was sometimes miles apart from
> experiment and from the wave-function derived dipole moment...(using RHF
> and RHF defined PA formulas)
> 
> My question is : 
> What is the use of the S^nPS^(1-n) derived population
> analysis ?
> Is there something crazy about my argumentation to say that PA is not to
> be trusted very much ? (esp. where I used the formula for the DM using the
> PA results...)
> 
> Thanks for replies....
> 
> Patrick Bultinck
> University of Ghent
> E-Mail : [email-masked]
> 
> 
> 

Thanks everybody who helped me out, or more exactly convinced me of the
fact that PA is a strange thing. Indeed some people were right to state
that looking at atoms in a molecule as spheres is dangerous, but I thought
about that very fact when I was making my thesis and suspected that even
that approx. could not be guilty of the (very) big deviations.

IMPORTANT : there was a mistake in Mr. Stones reference, the correction
can be found below

Patrick Bultinck
University of Ghent
E-Mail --->  [email-masked]

From: [email-masked] (Carlos Faerman)
To: [email-masked]
Subject: charges, dipoles,...

Patrick
        I recommend that you read Anthony Stone's papers on this very
subject. He is the expert in this field since he proposed a better way
to partition the electron density among atoms and therefore provide
a better set of partial charges. He is certainly not alone in this club
of disbelievers of Mulliken analysis. Richard Bader has also advocated
a very fancy partition scheme to get decent charges.
Richard Bader is at McMaster Univ. , Hamilton , Canada while Anthony Stone
works in Cambridge , UK
Perhaps reading their numerous papers might clarify/answer your ideas/questions
Regards
Carlos

From: [email-masked] (Steven Bachrach)
To: [email-masked]
Subject: Re: POPULATION ANALYSIS

Your results are exactly as expected - population analysis defined in terms
of orbital populations is garbage. I have recently ritten a review of
population analysis in Reviewss of Computational Chemistry, volume 5
which was just published. This review goes into some detail on the failings of
traditional populations methods.

Steven Bachrach
Department of Chemistry
Northern Illinois University
DeKalb, Il 60115
[email-masked]

From: Lipkowitz <[email-masked]>
Subject: RE: POPULATION ANALYSIS
To: Patrick Bultinck <[email-masked]>

For your information, there is a good review, albeit low level, of population
analyses in Reviews of Computational Chemistry, Volume 5, chapter 3 by S.
Bachrach.  The book is published by VCH Inc., 1994....ie, it will be out on the
market soon. Kenny Lipkowitz.
_______________________________________________________________________________
From: [email-masked]
Subject: 
To: [email-masked]

Dear Patrick:

	Reliable net atomic charges can be found by fitting the molecular
electric potential obtained by ab initio quantum mechanical methods. The
idea is to find the best atomic charges which will reproduce the potential. 
Program PDM93 also allows atomic dipoles/quadrupoles, bond dipoles, and
addition of lone pair electron sites if necessary in order to fit the
electric potential.  A particularly useful feature of the program is the
transparent way in which dependency conditions are specified.  I append 
information about this program.

 -Don Williams

Program PDM93, Potential Derived Multipoles
The following is a brief description of this program.

	Molecules interact with each other via their electric potential.
PDM93 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 Unix,
Vax, and other computers with F77 capability.

Program PDM93 has a unique combination of features:

o  general sites, 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
o  generalized input from other quantum mechanics programs
o  automatic generation of electric potential grid points
o  provision for custom generation of grid points
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)588-5975 Fax:(502)588-8149 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 to academic institutions ........$495

Choose the preferred method of shipment:

	Via ftp, purchaser furnishes valid ftp address................n/c

	Via magnetic media, specify type..............................$20
		DC6150 tape cartridge, unix tar format
	or	MP120 tape cartridge (8mm), Vax backup format
	or	9-track 1600 bpi ascii tape
	or	9-track 6250 bpi ascii tape

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-------------------------------------------------------------------------

From: [email-masked]
Subject: Re:  POPULATION ANALYSIS
To: [email-masked]

Mulliken himself said "Population analyses must be used with
appropriate caution... even though the method is faulty, it has the
insidious appeal of always giving definite numbers."

Mulliken and Lowdin analyses are based on completely arbitrary
partitioning of what space belongs to which atoms, and are strongly
dependent on the basis set itself as well.  It is even possible for
Mulliken population to be negative, which is pretty nonphysical.

These problems have long been known, but many many people still take
them as gospel.  They certainly can be meaningful indicators in
selected cases, which must be thoughtfully analyzed, but the usual
blind trust is entirely inappropriate.

Bader and others have developed population analyses schemes that try
to eliminate some of the problems with the traditional S^n P S^(1-n)
methods.  Bader's method uses numerical integration to locate zero
flux surfaces in the density which are the basis for defining "atoms"
in his scheme.  This is _much_ more expensive than a couple of matrix
multiplications, and people have observed cases where some atoms don't
have "atomic basins" (the region enclosed by a zero flux sheet).

So population analysis in general is a tough problem and the methods
like Mulliken and Lowdin are about the simplest possible (and
therefore most troublesome) approach.
--
David E. Bernholdt                       | Email: [email-masked]
Molecular Science Research Center        | Phone: 509 375 4387
Pacific Northwest Laboratory, P.O.B. 999 | Fax:   509 375 6631
Richland, WA  99352-0999                 |

From: [email-masked]
To: [email-masked]
In-Reply-To: Patrick Bultinck's message of Fri, 3 Dec 1993 16:14:35 +0100 (MET) <Pine.3.07.9312031635.B15543-b100000@allserv>
Subject: POPULATION ANALYSIS

>Is there something crazy about my argumentation to say that PA is not to
>be trusted very much ? 

Certainly not, in my view. Many chemists have an urge to assign charges
to atoms within a molecule. However, such charges do not exist as
observable quantities (eigenvalues of the wavefunction, quantum mechanically
speaking), so anyone insisting on having them will have to rely on
one arbitrary scheme or another.....

Richard Bader (Hamilton, Canada) has suggested a scheme based on 
topological analysis of the electron density. Space is divided into 
parts "belonging to" different atoms or fragments in a molecule.
The results look sounder than Mulliken ones.
Still, some peculiar results come out from time to time, especially
when partitioning space between atoms that differ greatly in electro-
negativity. Also, this approach rely on a good electron density to
start with. 

Population analysis is a controversial and interesting topic, but
still most people (including me) use Mulliken because it's there
in the software, it is much better than nothing, and perhaps more
important, it is well tested: Even if it is far from ideal, it's area 
of validity is more or less known.

Just some thoughts,

                     Ole Swang.

From: [email-masked]
To: [email-masked]
Subject: popln. analysis and dipoles

Patrick B.'s comments on population analysis and dipole
moments strike a cord.  I have heard these complaints(and
made some myself) for a number of years.
1)  the choice of divison of the overlap population is
arbitrary... various lines of thought have gone into the
derivation of literally hundreds of methods of doing this
but the bottem line is that you do not have a quantum mechanical
operator for the population in an 'orbital' on a particular
atom that 'belongs' to that atom. Perhaps the most attractive
methods are those that arise through the use of quantum
mechanics, do not use arbitrary boundaries and as well
apply to the total density. (eg. Richard Bader et al's
theory of mol. structure)
2) the 'charge' on an atom is not a point charge, this is
a gross assumption that in itself can lead to large errors.
It appears to arise from the conceptually appealing picture
of nice spherical atoms in molecules. The density
is, however, not spherical around each atom in a molecule. Thus,
using a point charge model with populations calculated through
arbitrary division of the overlap populations has a good chance
of giving poor results.
  The above being said, these different methods of treating
the problem of population analysis has led to a lot of chemical
insight for various problems. You must keep the weaknesses in
mind when choosing an approach.

 Any other thoughts on this?
                            Ken Edgecombe

   ----- End of the message -----

From: [email-masked] (Dominic Ryan)
To: [email-masked]
Subject: Population analysis

As was pointed out, population analysis is not unique.  There are a host 
of methods available for partitioning density between sites.  One must 
ask what the charges will be used for. 

In a force field context an atomic charge is simply one more fudge factor
available in the system for tuning to get the 'right' answer.  Early days
of force field development concentrated on intramolecular energies, in
vacuo at that.  After you make pretty good guesses at bond stretching and
angle bending components (and cross terms when part of your flavor of
force field) you are left with torsion terms, VDW terms and charges.

Early work derived VDW terms from rare gas data in part and from crystal
packing (making allowances for the differences one sees there in x-ray,
electron and neutron diffraction).  One is generally left then with
torsions and charges (VDW terms are also modified and combining rules are
modified in Tom Halgren's work).  You try to assign chemically sensible
charges and tweak the torsion terms until conformational energies
reproduce your reference states (quantum mechanical, and experimental).

More recently there has been greater emphasis on intermolecular energies
(lets ignore solvation for now).  These are dominated by electrostatic
forces.  Now one needs to worry more about getting both chemically
sensible charges and charges that will give the 'correct' interaction
energy which must be taken from high level QM where one needs to worry
about basis set effects etc.

A relatively recent method of defining atomic charges calculates the
molecular electrostatic potential around a molecule and constrains the
charges to reproduce this distribution as much as possible.  This has the
advantage of in principle reproducing the bulk of the interaction energy
between two molecules, including the anisotropy.  In practice there are
limitations here as well, and in small molecules particularly (H2O) a set
of atom-centered charges in not sufficient to adequately describe the
potential.  One advantage of using 'fitted' charges is that the dipole
(and higher order molecular multipoles) are well reproduced.  There is a
*lot* of literature on this approch now.  Check out Reviews in
Computational Chemistry, vol. 2 for a recent review.

Bader's method of partitioning charge is consistent but leads to a
different picture of atomic charge from the fitted methods.  Neither one
is *wrong* but they look at different things. 
___________________________________________________________________________
M. Dominic Ryan       (215)-270-6529     SmithKline Beecham Pharmaceuticals 
Headers may be WRONG, do NOT use reply,  use: [email-masked]

From: Lipkowitz <[email-masked]>
Subject: Population Analysis
To: Comp Chem List <[email-masked]>

Netters: There has been, and remains, controversy about how to partition
electrons on atoms for population analysis.  To help me understand what's going
on, Don Boyd and I asked Steve Bachrach to write a book chapter on that topic. 
See Reviews in Computational Chemistry, Volume 5, eds. K. Lipkowitz and D.Boyd,
VCH Publishers Inc., New York, 1994 ( available in January). Kenny

From: Gustavo Mercier <[email-masked]>
Subject: Re: POPULATION ANALYSIS
To: Patrick Bultinck <[email-masked]>

Hi!

To add to the discussion...

In the 70's when the electrostatic potential became popular to explain
molecular reactivity, it was very common to use MK derived charges to
compute the potential from "large" molecules. It was very clear then that
in many cases the dipole computed from the charges was poor. Nevertheless,
the concept was useful, and in spite of poor dipole moments the TOTAL
energy computed with the charges for a CONGENERIC family of molecules
could be used to reproduce trends in chemical reactivity. In these cases
systematic errors probably were controlled by only comparing SIMILAR
molecules. But when is similar "dissimilar"?

mercier
[email-masked]

From: Anthony Stone <[email-masked]>
Subject: Population analysis and dipoles
To: [email-masked]

Population analysis and dipole moments

The dipole moment of a molecule can be expressed in terms of atomic moments
as sum (atom charge)*(position) + sum (atomic dipoles). This is exact if you
define things correctly, but the atomic dipole values will depend on your
choice of definition for the atomic charges. The atomic dipoles are usually
significant, whatever definition you use for the atom charges, so if you leave
them out you will get rotten molecular dipole moments. An exception to this is
potential-fitted point charges, which give quite good values for the molecular
dipole, but they achieve this by representing atomic dipoles by charges on
nearby atoms, so the potential isn't very good in the neighbourhood of a
dipolar atom.

The Distributed Multipole Analysis procedure, described by Stone & Alderton
in Mol. Phys. 110, 123 (1984), generates charges, dipoles, etc. from a
wavefunction in a consistent manner (i.e. so that the overall molecular
moments are correct for the wavefunction), and in such a way that the higher
atomic moments are as small as possible. It is included in the Cadpac
program.  Bader's partitioning, mentioned by Ken Edgecombe, is much more
elegant but it leads to much larger high-rank moments, which is an
inconvenience for most applications.

For a more general discussion see Stone & Price, J. Phys. Chem. 92, 3325
(1988).

Anthony Stone
University Chemical Laboratory,         Internet: [email-masked]
Lensfield Road,                         Phone:    +44 223 336375
Cambridge CB2 1EW, U.K.                 Fax:      +44 223 336362

Thanks to those who have pointed out that I gave the wrong reference in my
recent posting about population analysis and dipole moments. It should have
been Stone & Alderton, Mol. Phys. 56 (1985) 1047.

Anthony Stone
University Chemical Laboratory,         Internet: [email-masked]
Lensfield Road,                         Phone:    +44 223 336375
Cambridge CB2 1EW                       Fax:      +44 223 336362