Nested Markov chain Monte Carlo sampling of a density functional theory potential: equilibrium thermodynamics of dense fluid nitrogen.

An optimized variant of the nested Markov chain Monte Carlo [n(MC)(2)] method [J. Chem. Phys. 130, 164104 (2009)] is applied to fluid N(2). In this implementation of n(MC)(2), isothermal-isobaric (NPT) ensemble sampling on the basis of a pair potential (the "reference" system) is used to enhance the efficiency of sampling based on Perdew-Burke-Ernzerhof density functional theory with a 6-31G(*) basis set (PBE6-31G(*), the "full" system). A long sequence of Monte Carlo steps taken in the reference system is converted into a trial step taken in the full system; for a good choice of reference potential, these trial steps have a high probability of acceptance. Using decorrelated samples drawn from the reference distribution, the pressure and temperature of the full system are varied such that its distribution overlaps maximally with that of the reference system. Optimized pressures and temperatures then serve as input parameters for n(MC)(2) sampling of dense fluid N(2) over a wide range of thermodynamic conditions. The simulation results are combined to construct the Hugoniot of nitrogen fluid, yielding predictions in excellent agreement with experiment.