Empirical classical interaction functions for molecular simulation

Abstract

With the continuing increase of the power of computers, the past decades have seen a rapid increase in the number, performance and accuracy of theoretical computational methods in chemistry [1,2]. One can distinguish three major classes of methods for the theoretical study of molecular properties, listed in order of decreasing computational expenses: (i) ab initio molecular orbital methods [3]; (ii) semiempirical molecular orbital methods [4,5]; and (iii) empirical classical force-field methods. The computational expenses of ab initio methods are of order O(N f 4 ) (Hartree—Fock level) or higher (configuration interaction, many-body perturbation theory), Nf being the number of basis functions used. Density functional approaches and semiempirical methods scale as O(N f 3 ) or lower. The costs of empirical methods scale as O(N a 2 ) down to nearly O(Na), where Na stands for the number of elementary particles (atoms or groups of atoms). Independently of the scaling with the system size, the evaluation of an empirical interaction function remains usually much cheaper than any other method (size of the prefactor to the scaling) and currently allows for the simulation of systems typically up to 105–106 atoms.