Integral equation theory based direct and accelerated systematic coarse-graining approaches

Coarse-grained (CG) molecular dynamics (MD) simulations have become popular for investigating systems on multiple length and time scales ranging from atomistic to mesoscales. In CGMD, several atoms are mapped onto a single CG bead and the effective interactions between CG beads are determined. Iterative coarse-graining methods, such as iterative Boltzmann inversion (IBI), are computationally expensive and can have convergence issues. In this paper, we present a direct and computationally efficient theoretical procedure for coarse-graining based on the Ornstein-Zernike (OZ) and hypernetted chain (HNC) integral equation theory. We demonstrate the OZ-HNC-based CG method by coarse-graining a bulk water system, a water-methanol mixture system, and an electrolyte system. We show that the accuracy of the CG potentials obtained from the OZ-HNC-based coarse-graining is comparable to iterative systematic coarse-graining methods. Furthermore, we show that the CG potentials from OZ-HNC can be used to reduce the number of iterations and hence the computational cost of the iterative systematic coarse-graining approaches, like IBI and relative entropy minimization.