Development of a Hybrid Statistical Physics – Quantum Mechanical Methodology for Computer Simulations of Condensed Phases and Its Implementation on High-Performance Computing Systems

Abstract

A hybrid, complex statistical mechanics – quantum mechanical approach which enables exact computational modeling of condensed phases at finite temperatures has been developed and implemented on high-performance computing systems. The computational approach is robust and inherently sequential. First, the studied physico-chemical system is modeled by a statistical physics approach, either Monte Carlo (MC) or molecular dynamics (MD). Though in the first phase it is often sufficient to carry out a classical MC or MD simulation, in particular cases, when it is necessary, one can also perform a quantum molecular dynamics simulation (e.g. ADMP, BOMD or CPMD). Even the classical MC/MD simulations carried out in the first phase can be based on interaction potentials which have been derived by quantum chemical calculations. Sequentially to the first phase of the computation, which actually generates either a MD trajectory or an appropriate sample of the system’s configurational space, the generated trajectories are analyzed employing time-series analytic methods. On the basis of such analysis, a representative number of configurations representing the state of the physico-chemical system at finite temperature is chosen, which are further analyzed by a quantum mechanical approach. These, appropriately chosen configurations for the system of interest, are further modeled by exact quantum mechanical (QM) approach. The particular approach that needs to be implemented depends on the quantity that needs to be computed. For example, in the case of X-H stretching vibrations, the anharmonic X-H vibrational frequency is computed in a quantum mechanical manner with respect to both electronic and nuclear subsystem. In this case, first a 1D cut through the vibrational potential energy surface is computed at series of suitably generated points, and subsequently, the vibrational Schrodinger equation is solved either by diagonalization approach or using a variant of the discrete variable representation (DVR) methodology. As the statistical mechanics simulations are often done implementing periodic boundary condition, the exact QM calculations in the final simulation phase are often done implementing some sort of embedding of the relevant part of the system. All these aspects of our developed methodology are illustrated through a particular example – the fluoroform solvated in liquid Kr and the noncovalently bonded complexes which are formed between fluoroform and dimethylether in liquid Kr. A vast variety of condensed phase systems can be treated by the developed approach. Achieving good parallel efficiency for calculations of such type is far from a trivial task without the use of high-performance low-latency MPI interconnect (such as, e.g. a supercomputer or HPC cluster).