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

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.