Subject: Charges

From: [email-masked] (Wendy Cornell)
Date: Mon, 26 Sep 1994 21:38:21 -0700

A number of posters have asked about atom-centered
charges.  I discuss here their derivation for use 
in molecular mechanical calculations.  The philosophy
of the Kollman group (AMBER) has been that
the accurate representation of electrostatic
interactions is crucial for a force field intended
for application to biological molecules.  

"We note that the choice of a particular force field
should depend on the system properties one is interested
in.  Some applications require more refined force
fields than others.  Moreover, there should be a
balance between the levels of accuracy or refinement
of different parts of a molecular model.  Otherwise
the computing effort put into a very detailed and
accurate part of the calculations may easily be wasted
due to the distorting effect of the cruder parts of
the model."   (van Gunsteren, W.F and Berendsen, H.J.C.,
Angew. Chem. Int. Ed. Engl. 29, 992 (1990) -- an incredibly
lucid and succinct review of MD applications to chemistry).

In other words, a force field which has
a complicated potential form for representing bonds 
and angles and is very precise in terms of reproducing 
geometries and vibrational frequencies will not
accurately model complex intermolecular interactions
if the charge model is not also of high quality.

Piotr Cieplak and I have derived charges for the new
"AMBER" force field.  We have already published
two papers describing the new AMBER approach to
calculating ESP (electrostatic potential) fit charges.  
The new charges are called RESP charges, for Restrained 
ESP fit.  This method was developed by Chris Bayly who
was a postdoc in our group.

The 2 references for these papers are:

1.
 BAYLY CI; CIEPLAK P; CORNELL WD; KOLLMAN PA.
  A WELL-BEHAVED ELECTROSTATIC POTENTIAL BASED METHOD USING CHARGE
  RESTRAINTS FOR DERIVING ATOMIC CHARGES - THE RESP MODEL.
  JOURNAL OF PHYSICAL CHEMISTRY, 1993 OCT 7, V97 N40:10269-10280.

2.
 CORNELL WD; CIEPLAK P; BAYLY CI; KOLLMAN PA.
  APPLICATION OF RESP CHARGES TO CALCULATE CONFORMATIONAL ENERGIES, HYDROGEN
  BOND ENERGIES, AND FREE ENERGIES OF SOLVATION.
  JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, 1993 OCT 20, V115 N21:9620-9631.

Earlier, I posted a summary of our new charge model and
I would be happy to mail a copy to any interested parties 
who missed that posting.

I believe the original work in the area of ESP fitted charges
was carried out by Frank Momany:

   Momany, F., J. Phys. Chem., 82, 592 (1978).

This work was later extended by others:

  Cox, S.R. and Williams, D.E., J. Comp. Chem., 2, 304 (1981)
 
  Singh, U.C. and Kollman, P.A., J. Comp. Chem., 5, 129 (1984)
   (Gaussian80/UCSF)

  Chirlian, L.E. and Francl, M.M., J. Comp. Chem., 8, 894 (1987)
   (CHELPG)

  Williams, D.E., Biopolymers, 29, 1367 (1990)

  Bessler, B.H., Merz, K.M., Jr. and Kollman, P.A., J. Comp.
   Chem., 11, 431 (1990).  (MOPAC)

Gaussian 92 includes an option for calculating "Merz-Singh-Kollman"
CHELP, and CHELPG style charges. 

The basic idea with electrostatic potential fit charges is
that a least squares fitting algorithm is used to derive a
set of atom-centered point charges which best reproduce
the electrostatic potential of the molecule.  In the AMBER
charge fitting programs, the potential is evaluated at a
large number of points defined by 4 shells of surfaces
at 1.4, 1.6, 1.8, and 2.0 times the VDW radii.  These
distances have been shown to be appropriate for deriving
charges which reproduce typical intermolecular interactions
(energies and distances).  The dipole moment of the molecule
is well reproduced.  

Other programs have embedded the molecule in a cubic grid
of points to evaluate the potential.  We believe that
assigning the points along the contours of the molecule
provides a better sampling of the esp around each atom.

The value of the electrostatic potential at each grid
point is calculated from the quantum mechanical wavefunction.
The charges derived using this procedure are basis set
dependent.  For example, the Weiner et al force field
(AMBER) employs STO-3G based charges, whereas the new
Cornell et al force field (AMBER) uses charges derived
using the 6-31G* basis set.  The 6-31G* basis set is
bigger and, for the most part, "better."  Because quantum
mechanics calculations scale as the number of basis
functions to about the 2.7 power (HF as implemented in G92),
the bigger 6-31G* basis set was prohibitively large for
use in developing the last force field.  

The 6-31G* basis set tends to result in dipole moments
which are 10-20% larger than gas phase.  This behavior
is desirable for deriving charges to be used for
condensed phase simulations within an effective two-body
additive model, where polarization is being represented 
implicitly.  In other words a molecule is expected to
be more polarized in condensed phase vs. gas phase due to
many body interactions, so we "pre-polarize" the charges.

A study by St-Amant, Cornell, Halgren, and Kollman
(submitted) calculated DFT charges for a number of
small molecules and found them to be smaller than 
HF/6-31G* derived ones.  DFT charges for methanol did
not reproduce the relative free energy of solvation of
methanol.  Such charges may be more appropriate for
use with a non-additive model.  (I should note that
the DFT model reproduced the gas phase dipole moments
very well.)  

ESP fit charges have many advantages.  They reproduce
interaction energies well.  They can be calculated in
a straightforward fashion.  They have been shown to
perform well at reproducing conformational energies.
The second paper listed above (Cornell et al, JACS)
provides much of the validation of our new charge model.
A study by Howard, Cieplak, and Kollman (J Comp Chem,
in press) showed how ESP and RESP charges performed
quite well at modelling the conformational energies of
a series of 1,3-dioxanes.  Also, a more thorough study
of the performance of RESP charges at calculating
small molecule conformational energies is currently
underway in our group.

It should be noted that
Mulliken charges do NOT reproduce the electrostatic
potential of a molecule very well.  Mulliken charges
are calculated by determining the electron population
of each atom as defined by the basis functions.  When
the density is associated with the square of a single
basis function, that density is assigned to the atom
associated with that basis function.  Similarly, if
the density is associated with 2 basis functions which
are on a common atom, the density is assigned to that
atom.  The ambiguity arises when the density is associated
with 2 basis functions lying on different atoms.  In
that case the density is partitioned equally onto each
atom.

Another charge model is that of Gasteiger-Marsili.
(Gasteiger and Marsili, Tet. Lett., 36, 3219 (1980)).
This approach involves the partial equalization of
electronegativity between bonded atoms.

Finally, it's a little dangerous to look too closely
at charges.  Sometimes ones that look "funny" or
"too big" actually perform quite well at reproducing
the desired properties.
-----------------------------------------------------------------------
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