Direct minimization: Alternative to the traditional [formula omitted] norm to derive partial atomic charges

Abstract

Partial charges play an important role in simulating and understanding molecular properties. The derivation of an accurate charge model for monopolar atoms is a significant part of the parameterization of today’s classical molecular mechanics force fields used in molecular dynamics simulations (MD). Hence, interest in the accurate prediction of partial charges from ab initio methods exists for a long time. Several methods have been developed, either based on population analysis that partitions the electron density into atomic populations, or on the assignment of partial atomic charges to reproduce a precalculated electrostatic potential (ESP method). In the latter approach, the charges are represented by parameters that are optimized by minimizing a loss function. ESP charge fitting, which is addressed in our work, is in most cases performed by minimization of a least squares or L2 like loss functions. To our knowledge, no attempt was made to use different metrics such as least absolute deviations L1 and to study their influence on the derived charges. The possibility of using different metrics to derive atomic charges is explored in this paper as a further extension of the ESP method. A direct iterative steepest descent minimization approach is employed in order to treat loss functions based on norms such as L1. The implemented algorithm allows for dealing with chemical equivalency and total charge constraints while permitting using different loss functions. We compare the results from the L1 norm to the values obtained from the standard L2 norm and the L4 norm for the 20 standard amino acids.We suggest that close to the solution the L1 norm expresses the impact of the electrostatic potential on the partial atomic charges to be obtained more accurately.