The multiscale coarse-graining method. V. Isothermal-isobaric ensemble

<jats:p>The multiscale coarse-graining (MS-CG) method is a method for determining the effective potential energy function for a coarse-grained (CG) model of a system using the data obtained from molecular dynamics simulation of the corresponding atomically detailed model. The MS-CG method, as originally formulated for systems at constant volume, has previously been given a rigorous statistical mechanical basis for the canonical ensemble. Here, we propose and test a version of the MS-CG method suitable for the isothermal-isobaric ensemble. The method shows how to construct an effective potential energy function for a CG system that generates the correct volume fluctuations as well as correct distribution functions in the configuration space of the CG sites. The formulation of the method requires introduction of an explicitly volume dependent term in the potential energy function of the CG system. The theory is applicable to simulations with isotropic volume fluctuations and cases where both the atomistic and CG models do not have any intramolecular constraints, but it is straightforward to extend the theory to more general cases. The present theory deals with systems that have short ranged interactions. (The extension to Coulombic forces using Ewald methods requires additional considerations.) We test the theory for constant pressure MS-CG simulations of a simple model of a solution. We show that both the volume dependent and the coordinate dependent parts of the potential are transferable to larger systems than the one used to obtain these potentials.</jats:p>