Subject: Charge Fit w/ DFT: The Summary

From: "Michael D. Bartberger" <[email-masked]>
Date: Thu, 13 Feb 1997 06:44:56 -0500 (EST)

A few weeks back I had posed the question of the "validity" of the use of
various charge-fitting methodologies in conjunction with DFT wavefunctions.
I've received some interesting replies (and one preprint!) in response to 
the question, and would now like to summarize.

As it looks, from responses and our own experience, DFT methods (in
particular, B3LYP) in conjunction with ESP-based fits yield values that
are not drastically different from those obtained by SCF.

Many thanks to those who responded.   The original question and replies follow
(.sigs deleted for brevity.)

-MDB

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From: "Michael D. Bartberger" <[email-masked]>
Subject: ESP / AIM charge fits based ON DFT wavef'n?

Hello all:

I was curious as to whether anyone had considered the 'validity' of
various methods of charge fitting using DFT densities, as compared to
those of, say, SCF or MP2.

We are investigating B3LYP in the computation of bond energies in a
series of hydrofluorocarbons.  We are interested in partial charges and
how this relates to the BDE.  As we have the DFT BDE values, I'd like to
use charges based on this method as well, rather than than that of SCF or
MP2.

I suppose the question is, has anyone considered the use of the 
typical (Mulliken, ESP, or AIM-based) charge schemes with DFT densities,
and / or compared them to those using SCF or MP2 values?  I'd appreciate
any references, personal accounts, or general sentiments about this. 
I'll certainly summarize.  

Thanks very much,

-Michael

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From: Modesto Orozco <[email-masked]>

Dear -Michael

We did some comparison analysis of ESP charges using different DFT methods,
MP2, MP4, CIPSI and even Full CI calculations. The results will appear in few
months in J.Comp.Chem.

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From: Grzegorz Bakalarski <[email-masked]>

For comparison of ESP charges fitted from HF, MP2, BLYP and B3LYP wavefuncions
for DNA bases you can look in our paper :

Bakalarski, G. et al. (1996) Chemical Physics , 204, pp.301-311

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From: Andrei Kutateladze <[email-masked]>

Michael,

I am not sure that this will answer your question but in my view one of the
best possible combinations would be B3LYP with Frank Weinhold's NBO charges.
This is not to say that DFT does better job than, say, MP2.  However, if you
are interested in an inexpensive alternative, B3LYP with natural charges will
do a decent job.

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From: Lou Noodleman <[email-masked]>

Michael,
We have compared Mulliken vs. ESP charges for various
transition metal complexes using density functional methods.
Typically (but not always), the ESP charges are more polar
than the Mulliken, and this is particularly true for fairly
polar systems. Charge shifts on oxidation/reduction show
greater similarities comparing Mulliken with ESP, which 
shows that the description of relaxation effects is fairly
comparable with the 2 different methods of analysis.
Ref's are Li et al., Inorg. Chem. 1996,35,4694-4702;
Fisher et al, J. Phys. Chem. 1996, 100, 13498-13505,
Mouesca et al, J. Am. Chem. Soc. 1994,116, 11898-11914,
for transition metal ions in aqueous solution, an active
site model of Mn-superoxide dismutase, and FeS complexes.
Earlier, we did considerable work with Xa-Scattered Wave
methods, which include a charge partitioning based different
spatial regions. Compare Noodleman et al. JACS 1985,107,3418
(XASW for FeS clusters) with Noodleman and Baerends JACS 1984,
106, 2316 (XA-LCAO) for 2Fe2S complexes with Mulliken population
analysis. Basically, spatial charge partitioning (overlapping
spheres) and Mulliken give similar results, particularly considering
that different methods were used to solve the X-alpha SCF equations.
In other earlier work using XASW on main group systems (with overlapping
spheres charge partitioning), we looked at the charge distribution in O3,
Banna et al. Chem. Phys. Lett 1977, 49, 213-217, cyclic phosphazines,
SO2, and SO2F2, and substituted amines, Chem. Phys. Lett. 1977,
47, 265-268, CPL 1978, 58, 252-258, Inorg. Chem. 1978, 17, 2709,
Inorg. Chem. 1979, 18, 354-360. While all of these calculations had
additional objectives besides studying charge distributions, all of
these systems are quite challenging, and can be compared with ab initio
results. This is just my group's experience and is obviously not
comprehensive. Also, as part of our studies of solvation and
pKa 's of organic molecules, we determined ESP charges in a
variety of systems using DFT-self-consistent-reaction-field
methods, Chen et al, J. Phys. Chem. 1994, 98, 11059;
Richardson, Peng, Bashford, Case, Noodleman Int. J. Quant. Chem.
,in press. The explicit ESP charges were not published, but dipole
moments were.
I hope this is helpful.
Lou Noodleman

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From: Bryan Marten <[email-masked]>

While a grad student under Rich Friesner at Columbia one part of one
project was to compute QM dipole moments using the 6-31G** basis set and
several levels of theory: HF, Local MP2/h, GVB/h, B3LYP, and MP2 for a set
of ~20 small molecules to compare to exptl dipole moments.  All
calculations were performed with the program PS-GVB except for the standard
MP2 calc which was performed with Gaussian 92.  A "/h" means that only
bonds between "heteroatoms" were correlated meaning all bonds between atoms
which were not C-C or C-H were correlated (ie. only "polar" bonds were
correlated since that amount of correlation was shown previously by us to
reproduce dipole moments resulting from full correlation very closely at a
reduced CPU cost).  Of those 5 different levels of theory, B3LYP had the
smallest average error, smallest max error, and smallest standard deviation
in the error compared to experimental dipole moments.  These results are
one small part of a larger paper which is currently being written up for
publication on quantum/continuum solvation.

From this, I would say that the B3LYP charge distribution is very good.  A
separate issue is how you represent that charge distribution, like in the
form of a set of point charges, and how much you then "believe" those
charges.  Much has been written about that on the CCL and in the printed
literature and I won't go into that here.

I will say, though, that I have used almost exclusively ESP-derived
charges.  In their favor, those almost always reproduce the QM dipole
moment to within a few hundredths of a Debye (in my experience primarily
with PS-GVB).  I have also compared HF and B3LYP ESP charges.  The HF
charges are generally slightly larger in absolute magnitude which is
consistent with the well-known observation that HF dipole momenst are
typically larger than expt dipole moments (and with the info above showing
that B3LYP dipole moments are close to expt dipole moments).  There are no
pathological differences between the HF and B3LYP ESP-derived charges.

I'm not sure what program you're using for these calculations but if you're
not using PS-GVB and are instead using Gaussian then you might look into
some archived discussions on the CCL some time ago about the different
implementations of B3LYP in Gaussian.  I've forgotten the details but I
seem to recall that for a time there was some debate on the nomenclature.

-- 

From: A J Turner <[email-masked]>

Hi!

My fealing is that an in vacuo charge fit has little meaning unless you
are dealing with gases.  If you have a liquid or sloid state system then
fitting of a qm/mm gradient function can provid a good charge fit (to be
published).  

As this is method independent, then the differnce between dft and mp2 is
the difference in the accuracy of the gradients.  As the second
derivitives and thus the frequencies are a function of gradient, I guess
dft is the better choice.

All the best

Alex

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