Effective potentials from complex simulations: a potential-matching algorithm and remarks on coarse-grained potentials

Abstract

The projection of complex interactions onto simple distance-dependent or angle-dependent classical mechanical functions is a long-standing theoretical challenge in the field of computational sciences concerning biomolecules, colloids, aggregates and simple systems as well. The construction of an effective potential may be based on theoretical assumptions, on the application of fitting procedures on experimental data and on the simplification of complex molecular simulations. Recently, a force-matching method was elaborated to project the data of Car-Parrinello ab initio molecular dynamics simulations onto two-particle classical interactions (Izvekov et al 2004 J. Chem. Phys. 120 10896). We have developed a potential-matching algorithm as a practical analogue of this force-matching method. The algorithm requires a large number of configurations (particle positions) and a single value of the potential energy for each configuration. We show the details of the algorithm and the test calculations on simple systems. The test calculation on water showed an example in which a similar structure was obtained for qualitatively different pair interactions. The application of the algorithm on reverse Monte Carlo configurations was tried as well. We detected inconsistencies in a part of our calculations. We found that the coarse graining of potentials cannot be performed perfectly both for the structural and the thermodynamic data. For example, if one applies an inverse method with an input of the pair-correlation function, it provides energetics data for the configurations uniquely. These energetics data can be different from the desired ones obtained by all atom simulations, as occurred in the testing of our potential-matching method.