Eur. Phys. J. Special Topics 225, 1347-1372 (2016)
https://doi.org/10.1140/epjst/e2016-60145-x

Regular Article

Parametrizing coarse grained models for molecular systems at equilibrium^*

¹ Department of Mathematics and Applied Mathematics University of Crete, Heraklion, Greece
² Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
³ Department of Mathematics and Statistics, University of Massachusetts at Amherst, Amherst, USA
⁴ Mathematical Sciences, University of Delaware, Newark, Delaware, USA
⁵ Institute of Applied and Computational Mathematics, Foundation for Research and Technology Hellas, IACM/FORTH, G71110 Heraklion, Greece

^a e-mail: evangelia.kalligiannaki@kaust.edu.sa
^b e-mail: harman@uoc.gr

Received: 30 April 2016
Revised: 24 July 2016
Published online: 10 October 2016

Abstract

Hierarchical coarse graining of atomistic molecular systems at equilibrium has been an intensive research topic over the last few decades. In this work we (a) review theoretical and numerical aspects of different parametrization methods (structural-based, force matching and relative entropy) to derive the effective interaction potential between coarse-grained particles. All methods approximate the many body potential of mean force; resulting, however, in different optimization problems. (b) We also use a reformulation of the force matching method by introducing a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (E. Kalligiannaki, et al., J. Chem. Phys. 2015). We apply and compare these methods to: (a) a benchmark system of two isolated methane molecules; (b) methane liquid; (c) water; and (d) an alkane fluid. Differences between the effective interactions, derived from the various methods, are found that depend on the actual system under study. The results further reveal the relation of the various methods and the sensitivities that may arise in the implementation of numerical methods used in each case.