The multiscale coarse-graining method: Assessing its accuracy and introducing density dependent coarse-grain potentials

Abstract

The ability of particle-based coarse-grain potentials, derived using the recently proposed multiscale coarse-graining (MS-CG) methodology [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] to reconstruct atomistic free-energy surfaces in coarse-grain coordinates is discussed. The MS-CG method is based on force-matching generalized forces associated with the coarse-grain coordinates. In this work, we show that the MS-CG method recovers only part of the atomistic free-energy landscape in the coarse-grain coordinates (termed the potential of mean force contribution). The portion of the atomistic free-energy landscape that is left out in the MS-CG procedure contributes to a pressure difference between atomistic and coarse-grain ensembles. Employing one- and two-site coarse-graining of nitromethane as worked examples, we discuss the virial and compressibility constraints to incorporate a pressure correction interaction into the MS-CG potentials and improve performance at different densities. The nature of the pressure correction interaction is elucidated and compared with those used in structure-based coarse-graining. As pairwise approximations to the atomistic free-energy, the MS-CG potentials naturally depend on the variables describing a thermodynamic state, such as temperature and density. Such dependencies limit state-point transferability. For nitromethane, the one- and two-site MS-CG potentials appear to be transferable across a broad range of temperatures. In particular, the two-site models, which are matched to low and ambient temperature liquid states, perform well in simulations of the ambient crystal structure. In contrast, the transferability of the MS-CG models of nitromethane across different densities is found to be problematic. To achieve better state-point transferability, density dependent MS-CG potentials are introduced and their performance is examined in simulations of nitromethane under various thermodynamic conditions, including shocked states.

Multiscale modeling of energetic materials: Easy to say, harder to do

“…We are pursuing a bottoms-up method to develop these potentials (known as MS-CG), which effectively homogenizes atomistic information obtained from either QMD or classical MD into a particle based CG model. The details of this methodology and applications to nitromethane and RDX are detailed in recent publications [11,12]. In these, we have shown that CG MD results for structural, vibrational and elastic properties are in good agreement with atomistic simulation results for these systems, as well as agreement of shock properties, thus validating proper homogenization.…”

Hybrid simulations: combining atomistic and coarse-grained force fields using virtual sites

“…A pressure correction is applied to the potentials to match the pressure of the reference atomistic system. Although the relation between pressure on the CG and AA level is non-trivial (for instance, one cannot simultaneously reproduce both pressure and compressibility [44][45][46] ), we decide here on the pressure, in a similar way the adaptive resolution methods do, because we want to combine atomistic and CG models and they should have the same pressure. Details of the methods pertaining the current application are presented below.…”

“…Strictly speaking, this type of pressure correction is not formally correct in the case of force matching. Pressure correction for force matching does exist, 45,51 it is however not yet implemented in the VOTCA package.…”

Computer Simulations of Soft Matter: Linking the Scales

“…In another group of approaches, one numerically generates CG interaction functions with the aim of reproducing the configurational phase space sampled in an atomistic reference simulation. These approaches may rely on different types of reference properties such as structure functions [77][78][79][80][81][82][83][84][85][86][87][88][89], mean forces [90][91][92][93][94][95] or relative entropies [96][97][98]. In the following subsection, a few basic notions of coarse-graining theory will be introduced, together with examples of the strategies that can be employed to perform the coarse-graining in practice.…”