Subject: charges

From: [email-masked] (Wendy Cornell)
Date: Tue, 27 Sep 1994 19:44:21 -0700

I've gotten some encouraging feedback regarding the
usefulness of my previous post so I am now going to
post a description of our (Kollman group) current
charge model (RESP) and also a a discussion of some
of the pitfalls of esp-fit charges.

MULTIPLE CONFORMATION RESP MODEL

Our current charge model is the RESP (restrained ESP) model.
This model evolved from work by Chris Bayly which showed
that charges on buried atoms (such as alkyl carbons) were
not well determined by the electrostatic potential points.
Such buried charges often assumed large values during the
fitting process and the values of these charges showed 
great conformational variability.  The basic idea of the 
RESP model is that restraints are added to charges on non-hydrogen
atoms during the charge fit.  The charges are restrained to
an "optimal" value of zero.  The restraints are hyperbolic in
nature, so approximately the same amount of force is felt by
charges of all magnitudes.  An earlier model employed harmonic 
restraints, but they reduced the values of the heteroatom
charges too drastically since those values (typically +/- 0.6
or higher) fell in the steep part of the function.  The
details of the derivation of this method are given in the
Bayly et al JPC paper.

The RESP method involves a two-stage approach where charges on
atoms such as methyl hydrogens are not forced to be equivalent
until the second stage.  At that point they are refit while
charges on the other atoms are constrained to their values 
>from stage one.  Forcing methyl hydrogens to have equivalent
charges during the first stage can adversely affect the
values of the heteroatom charges, because such hydrogens
are not equivalent in a static conformation.  In the standard
ESP model, methyl hydrogen charges were typically averaged
after the fit, but this averaging often changed the value of
the dipole moment as well as the fit to the potential.

One problem with electrostatic potential fit charges in
general is that they reproduce the molecular potential
and the dipole moment very well *for the conformation of
the molecule employed in the fit*.  However, when those
charges are applied to other conformations, the agreement
is not as good.  A solution to this problem was proposed
by Chris Reynolds:

 REYNOLDS CA; ESSEX JW; RICHARDS WG.
   ATOMIC CHARGES FOR VARIABLE MOLECULAR CONFORMATIONS.
   JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, 1992 NOV 4,
   V114 N23:9075-9079.

The solution is simply to use multiple conformations of
a molecule in the charge fitting process.  In fitting
the amino acid charges for our new force field, we
used 2 conformations for each amino acid -- the first
conformation had the backbone in an extended conformation
and the second had it in an alpha-helical conformation.
Each of those 2 conformations then had different values
for chi1, chi2, etc.  

I should repeat that for our new force field we are using
6-31G* fit charges because that basis set provides the
enhanced polarity necessary for carrying out balanced
(with respect to the water model) condensed phase simulations
within an additive model (no polarization).
Charges derived using a higher level of theory (either in
terms of a bigger basis set or through the inclusion of
correlation) won't necessarily be better for such applications
if they do not result in dipole moments which are enhanced
over the gas phase values.

We have found that multiple conformation RESP fitting
results in fairly robust charges.  Software for carrying
out these fits will be available with the next release of
AMBER.  The new software (C. Bayly) also allows for specifying
additional lagrange constraints so that (e.g.) blocking groups
can be forced to have net neutral charges and molecules can
be spliced together more algorithmically.

PITFALLS OF esp-FIT CHARGES

In general, standard esp-fit charges perform well at 
reproducing desired properties such as DNA base pair, NMA 
dimer, and methanol-water interaction energies.   This is 
not always the case, however.  For example, Yax Sun in our
group calculated ESP charges for a spherand for the purpose
of carrying out free energy perturbation studies to compare
the binding of Li+ and Na+ to the spherand.  The spherand
looked like this:

             /\
        {   |  |_   }
             \/      6
              |
              O
               \
                CH3

Standard ESP charges were calculated from a 3-unit,
non-cyclic, methyl-blocked analog.  The charges were
then taken from the central residue.  The standard
ESP fit charges underestimated the interaction energies
between the spherand and the ions.  As the charge on
the oxygen was on the low side, this was thought to be
the source of the error.  Sun and Kollman then refit
the charges, this time with electrostatic potential
points within 5 A of the oxygen weighted more heavily
than those around the rest of the molecule.  The resulting
charges resulted in a relative free energy of binding in 
much better agreement with experiment.  

There also cases where polarization or lone pairs are
required to reproduce interaction energies.

Electrostatic potential fit charges also do not always
result in good conformational energies.  For example,
multiple conformation (C5/aR) RESP charges calculated for
glycine and alanine dipeptides do not result in conformational
energies which are in good agreement with the quantum
mechanically calculated values.  These charges were derived
using the 6-31G* basis set and were applied with a 1-4
electrostatic scale factor of 1/1.2 (Cornell et al JACS).  
The reason for this performance is unclear.  It is possible
that the 6-31G* charges overstabilize the C7 (7-membered
H-bonded ring) conformations.  When these charges are scaled
back to gas-phase-like values (q*0.88), the conformational
energies show good agreement with the QM data.  

My statement in the previous post that ESP/RESP charges
resulted in good conformational energies referred to the 
6-31G* based model with the 1-4 elect. scale factor of 1/1.2

I've given 2 examples where esp-fit charges were not able
to be applied in a straighforward fashion.  Overall, however,
we have found these charge models (ESP and RESP) to be quite
useful for modelling biomolecular systems.  The alternatives
usually involve either (1) models such as Mulliken charges
which do not necessarily reproduce the molecular electrostatic
potential or (2) empirically derived charges such as those
fit to reproduce interaction energies and distances (CHARMM)
or liquid properties (OPLS).  Because electrostatic potential
fit charges can be calculated fairly easily, they allow the
force field to be extended to other molecules.  Overall we
find them to be a very useful and relatively general model.

-----------------------------------------------------------------------
Wendy D. Cornell                           Graduate Group in Biophysics 
Box 0446                                   (415) 476-2597 (phone)
Department of Parmaceutical Chemistry      (415) 476-0688 (fax)          
University of California, S.F.             [email-masked]
San Francisco, CA  94143-0446 USA