(685f) Virial Coefficients of Flexible Molecules Using Path Integral Monte Carlo Methods to Capture Nuclear Quantum Effects

Virial coefficients and other cluster integrals can be used to compute various physical properties of gases, such as the pressure, critical properties, Joule-Thomson coefficient, and others. For small molecules, it becomes feasible to use first-principles methods, or potentials derived from first-principles considerations, to model the molecular interactions that are input to the cluster-integral calculation. Given this input, Mayer Sampling Monte Carlo (MSMC) can be used to evaluate virial coefficients efficiently. An important consideration when attempting to work with first-principles models is explicit treatment of nuclear quantum effects, which are significant for light atoms and/or low temperatures.

The Path-integral Monte Carlo (PIMC) methods provide a convenient way to incorporate these quantum effects, and interface well with the MSMC algorithm. PIMC operates by discretizing the positions of a molecule as “beads” that form a closed ring. Neighboring beads act as if they are connected by a harmonic spring with a spring constant that is proportional to temperature and mass. For multi-atomic molecules such as H₂ or H₂O, the PIMC is significantly more complicated to implement, because of the need for the path integrals to consider molecular orientation and internal degrees of freedom. These complexities directly affect the sampling efficiency involved in the MSMC method and capturing them accurately is a difficult task. In this presentation, we describe how we have accounted for both changing orientations and bond lengths in the PIMC technique, and used these developments to evaluate the virial coefficients using the MSMC method. We present results for second and third order virial coefficients of some multi-atomic molecules, examining both rigid and flexible potentials, and compare these results with experimental data as well as available values in the literature.