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Hybrid Approaches to Coarse-Graining using the VOTCA Package: Liquid Hexanea
Victor Ruhle, Christoph Junghans ¨

Several systematic coarse-graining techniques have been developed in recent years. The method of choice depends on the system of interest and the properties to be reproduced. We present three hybrid schemes to combine force-matching and Boltzmann inversion. The methodsare tested on liquid hexane and the results are compared to iterative Boltzmann inversion. All approaches can easily be extended to mixtures of molecules and provide insight for parametrizing building blocks of bigger molecules. An implementation is provided in the VOTCA package which is available under an open source software license.

Introduction
In recent years, coarse-grained modellinghas evolved into an important tool to extend the accessible range of timeand length-scales of particle based simulations of soft matter systems.[1–10] A low resolution (coarse-grained) description is computationally more efficient due to three reasons. First, less interactions are involved which have to be evaluated. Second, interactions are usually smoother and thus simulations can be performed witha bigger timestep. Third, coarse-graining leads to an intrinsic speedup of the dynamics of the system.[1,11,12] Coarse-grained simulations range from generic models to bottom-up approaches. The latter provide a systematic link between two systems with different numbers of degrees of freedom. The process of deriving a low-resolution model based on a high resolution (reference) model is calledsystematic coarse-graining.

Dr. V. Ruhle, Dr. C. Junghans ¨ Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany E-mail: {ruehle,junghans}@mpip-mainz.mpg.de
a

http://www.votca.org

Various methods have been developed, depending on which properties need to be reproduced by the coarsegrained model. Structure based approaches aim to reproduce selected distributionfunctions (e.g. angle, bond or pair distribution functions) of the reference system. Examples are Boltzmann inversion,[1] iterative Boltzmann inversion (IBI)[4] and inverse Monte Carlo (IMC).[3,13,14] However, these methods use only a subset of distribution functions and often neglect multibody correlations. The multiscale coarse-graining method (MS-CG)[15,16] aims to match the full multibodypotential of mean force. MS-CG is derived from liquid state theory using the variational principle. The resulting equations are identical to the force matching (FM) equations,[17] but extensions are possible.[18] In cases where, e.g. solvation free energies are studied, a parametrization based on free energies can be beneficial. One example is the MARTINI force-field for coarse-grained simulations ofbiomolecules such as lipids[5] or proteins.[19] With the large variety of methods available, the versatile object-oriented toolkit for coarse-graining applications (VOTCA)[20] was designed to offer a consistent implementation. This allows the evaluation of the different methods for new systems via a single tool. Currently, Boltzmann inversion, IBI, IMC and FM are implemented. In ref.,[20] we comparedIBI, IMC and FM[17] by coarse-graining four test systems, namely SPC/E water, methanol, liquid

472

Macromol. Theory Simul. 2011, 20, 472–477 ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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DOI: 10.1002/mats.201100011

Hybrid Approaches to Coarse-Graining using the VOTCA . . . www.mts-journal.de

propane and a single chain of hexane. Several problems werepointed out. For example, IMC can have convergence problems for small system sizes while force-matching may lead to unphysical results if the set of interaction which represent the potential energy surface of the coarse-grained force-field is incomplete. The latter was recently demonstrated for coarse-grained water, where a three-body potential is required to reproduce the pair distribution...