Accurate Modeling of the Intramolecular Electrostaric Energy of Proteins

The (4, +) energy surface of blocked alanine (N-acetyl-N'-methyl alanineamide) was calculated at the Hartree-Fock (HF)/6-31G* level using ab initio molecular orbital theory. A collection of six electrostatic models was constructed, and the term electrostatic model was used to refer to (1) a set of atomic charge densities, each unable to deform with conformation; and (2) a rule for estimating the electrostatic interaction energy between a pair of atomic charge densities. In addition to two partial charge and three multipole electrostatic models, this collection includes one extremely detailed model, which we refer to as nonspherical CPK. For each of these six electrostatic models, parameters-in the form of partial charges, atomic multipoles, or generalized atomic densities-were calculated from the HF/6-31G* wave functions whose energies define the ab initio energy surface. This calculation of parameters was complicated by a problem that was found to originate from the locking in of a set of atomic charge densities, each of which contains a small polarization-induced deformation from its idealized unpolarized state. It was observed that the collective contribution of these small polarization-induced deformations to electrostatic energy differences between conformations can become large relative to ab initio energy differences between conformations. For each of the six electrostatic models, this contribution was reduced by an averaging of atomic charge densities (or electrostatic energy surfaces) over a large collection of conformations. The ab initio energy surface was used as a target with respect to which relative accuracies were determined for the six electrostatic models. A collection of 42 more complete molecular mechanics models was created by combining each of our six electrostatic models with a collection of seven models of repulsion + dispersion + intrinsic torsional energy, chosen to provide a representative sample of functional forms and parameter sets. A measure of distance was defined between model and ab initio energy surfaces; and distances were calculated for each of our 42 molecular mechanics models. For most of our 12 standard molecular mechanics models, the average error between model and ab initio energy surfaces is greater than 1.5 kcal/mol. This error is decreased by (1) careful treatment of the nonspherical nature of atomic charge densities, and (2) *~uthor to whom all correspondence should be addressed. Journal of Computational Chemistry, Vol. 16, No. 7, 791 -816 (1995) O 1995 by John Wiley & Sons, Inc. CCC 01 92-8651 / 95 1070791 -26