Fitting of dihedral terms in classical force fields as an analytic linear least-squares problem.

Abstract

The derivation and optimization of most energy terms in modern force fields are aided by automated computational tools. It is therefore important to have algorithms to rapidly and precisely train large numbers of interconnected parameters to allow investigators to make better decisions about the content of molecular models. In particular, the traditional approach to deriving dihedral parameters has been a least-squares fit to target conformational energies through variational optimization strategies. We present a computational approach for simultaneously fitting force field dihedral amplitudes and phase constants which is analytic within the scope of the data set. This approach completes the optimal molecular mechanics representation of a quantum mechanical potential energy surface in a single linear least-squares fit by recasting the dihedral potential into a linear function in the parameters. We compare the resulting method to a genetic algorithm in terms of computational time and quality of fit for two simple molecules. As suggested in previous studies, arbitrary dihedral phases are only necessary when modeling chiral molecules, which include more than half of drugs currently in use, so we also examined a dihedral parametrization case for the drug amoxicillin and one of its stereoisomers where the target dihedral includes a chiral center. Asymmetric dihedral phases are needed in these types of cases to properly represent the quantum mechanical energy surface and to differentiate between stereoisomers about the chiral center.