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The aim of this project is to show that classical polarization can describe some aspects of chemical bonding, including ligand-protein binding and hydrogen bonding, and to apply the resulting theory to problems relevant to the petroleum industry. Our thesis is that polarizable classical mechanics can describe a regime of bonding, which we named "electrostatic", lying intermediate between the textbook options of ionic and covalent.

Originally I expected that it would be necessary to fix the molecular geometry "by hand" when calculating bond energies (BE), under the assumption that electrostatics alone would not yield a minimum in the potential which determines the bond-length. That approach would be similar to, e.g., the textbook treatment of an ionic bond in KF, where the potential has no minimum at finite bond-length, but the Coulomb energy at the experimental bond-length gives a good approximation to the BE.

Thus I am very pleased to report that, in preliminary studies on binding of CO to myoglobin, we discovered a minimum in the Fe-C potential in the vicinity of the true bond distance, 1.92 Angstroms. The finding that polarizable electrostatics can describe the bound molecular geometry, not just the BE, could be a significant advance (T. Keyes and Raeanne Napoleon, "Polarizable Molecular Electrostatics and Electrostatic Bonding in Protein-Ligand and Aqueous Systems", J. Chem. Phys., submitted (2009)). For example, binding of ligands, and unbinding after photodissociation, can now be simulated with no need to switch the potential between binding and nonbinding forms.

Electrostatic bonding is dominated by the polarization energy, which can be 10x the Coulomb energy at distances typical of chemical bonds. Fe-C electrostatic bonding occurs despite a Coulomb repulsion. The usual approach of representing the electrostatic properties of atoms with point charges and dipoles would lead to unphysical divergences at these distances. We can proceed only because we take the smeared, non-point nature of charge distributions into account, resulting in a damping of the interactions at short distances. Here we benefit greatly from our collaboration with Dr. Christian Burnham, a pioneer in the area of smeared-charge electrostatics.

The intended applications of the project are: 1. electrostatic binding of impurities in crude oil to metal atoms, e.g. cobalt, in biochemical scavengers, and 2. water, oil-water interfaces, water in pores, etc, where we regard hydrogen bonds as electrostatic bonds. Graduate student Raeanne Napoleon was supported in the 2008 fall, and part of the 2009 spring and summer semesters, and worked in both areas.

This work will advance my scientific career by facilitating a desired change into the area of biophysical chemistry, and will prepare Raeanne Napoleon for a future in the biotech or pharmaceutical sectors.

1. Ligand binding

Previously, we showed (P. Mankoo and T. Keyes, "Classical Molecular Electrostatics: Recognition of Ligands in Proteins and the Vibrational Stark Effect", J. Phys. Chem. B 110, 25074 (2006)) that classical polarizable electrostatics agreed well with ab initio calculations for the binding and bending energies of ligands CO, NO, and OO to the heme iron in myoglobin. BE were calculated with the known geometry held fixed.

Prior to considering binding of pollutants cyanide and hydrogen sulfide to cobalt, we further developed the theory. In particular, the damping scheme was greatly improved. As a result, we now find true electrostatic bonds, yielding the geometry as well as the BE. In addition, the new theory is in good agreement with experiment for the Fe-C vibrational frequency, and the enhancement of the vibrational Stark effect and dipole upon binding. For CO only, we obtain the molecular dipole over a wide range of bond-length, in good agreement with quantal calculations, and the correct quadrupole, polarizability, and polarizability derivatives. At this point, application to other systems will be straightforward.

2. Water

As with ligand binding, the foundation of our recently published POLIR water potential (P. Mankoo and T. Keyes, "POLIR: Polarizable, Flexible, Transferable Water Potential Optimized for IR Spectroscopy", J. Chem. Phys. 129, 034504 (2008)) is a careful treatment of short-ranged polarization. In light of the binding minimum found of the Fe-C potential, we re-examined the OH pair polarization energy. As hoped, for an O-H distance in the range of hydrogen bond distances in water, 1.8-2.0 Angstroms, the polarization energy is close to 24 kJ/mol. This is a large step towards the goal of demonstrating that hydrogen bond energy is polarization energy.

The current formulation, in which atoms respond to local fields with their dipole polarizabilities, is quite satisfactory. Nevertheless, we collaborated with Dr. Burnham on an alternative approach, in which electric multipoles of a single molecule are calculated with quantum mechanics in several external electric fields and a sampling of relevant configurations, the results are fit to a functional form, and the properties of clusters, the liquid, and ice are then obtained self-consistently. Raeanne has performed extensive calculations of the dipole-hexadecapole moments. This involves writing a code that takes atomic multipoles from Gaussian and calculates molecular multipoles. The field-dependence builds in dipole and quadrupole polarizabilities. The result is an ab initio, highly accurate, electrostatic model which will be the basis of version 2 of POLIR.