Constant Pressure Path Integral Gibbs Ensemble Monte Carlo Method

Abstract

We present the implementation of a real-space constant pressure path integral Gibbs ensemble Monte Carlo (CP-PIGEMC) method for the simulation of one-component fluid consists of distinguishable quantum particles (henceforth referred to as Boltzmannons) in an external potential field at finite temperatures. We apply this simulation method to study the para-H2 adsorption in NaX zeolite at 77 K and pressures up to 100 bar. We present a new set of effective solid-fluid parameters optimized for path integral simulations of hydrogen isotope adsorption and separation in synthetic zeolites. The agreement among CP-PIGEMC, experiment, and the path integral grand canonical Monte Carlo method (PIGCMC) is very good, even at high pressures. CP-PIGEMC is a particularly useful method for simulation of one-component quantum fluid composed of Boltzmannons at finite temperatures, when the chemical potential is difficult to measure or calculate explicitly.

Intrinsic D2/H2 Selectivity of NaX Zeolite: Interplay between Adsorption and Kinetic Factors

“…We performed simulations of equimolar H 2 /D 2 mixture adsorption on NaX at 77 K and total mixture pressures up to 3 bar using the homemade path integral grand canonical Monte Carlo (PI-GCMC) code. 30,31 We computed the absolute values of H 2 and D 2 mixture adsorption from 23 10) where N k denotes the number of adsorbed molecules (subscript k is either H 2 or D 2 ); L 3 is the volume of the simulation box; and ⟨...⟩ denotes the PI-GCMC ensemble average. The isosteric enthalpy of H 2 /D 2 mixture adsorption in NaX was computed from the Barker estimator 31−33…”

“…23,31 Simulation runs were performed at gradually increasing chemical potentials of the equimolar bulk H 2 /D 2 mixture. The grand canonical ensemble simulations utilized 2 × 10 8 configurations, of which the first 1 × 10 8 was discarded to guarantee equilibration.…”

What is the Smallest Atom as a Probe for Characterizing Nanostructures?

“…The thermodynamic properties of quantum many-body systems have been widely studied using the path integral (PI) MC simulation, in which, according to Feynman’s PI formalism, , quantum particles are replaced by classical ring polymers consisting of beads and springs . The PIMC method has revealed not only the structural and superfluid properties of helium in the bulk phase, ,, on solid surfaces, − and in nanospaces, − but also the structural characteristics of liquid neon. − Moreover, an algorithm was developed for the PI Gibbs ensemble MC method, which enables to the direct computation of phase equilibria for quantum fluids − and the behavior of quantum fluids confined to nanopores under constant pressure . It is worth noting that the PI grand canonical MC (PIGCMC) method, − which is a powerful tool to study the adsorption process of quantum fluids including helium, , neon, , and hydrogen, ,, was also established.…”

“…34−36 Moreover, an algorithm was developed for the PI Gibbs ensemble MC method, which enables to the direct computation of phase equilibria for quantum fluids 37−39 and the behavior of quantum fluids confined to nanopores under constant pressure. 40 It is worth noting that the PI grand canonical MC (PIGCMC) method, 41−43 which is a powerful tool to study the adsorption process of quantum fluids including helium, 44,45 neon, 41,46 and hydrogen, 18,47,48 was also established. These studies have made significant contributions to the understanding of quantum phenomena and visualization of the wave nature of quantum particles.…”

Assessment of the Effects of Anisotropic Interactions among Hydrogen Molecules and Their Isotopologues: A Diffusion Monte Carlo Investigation of Gas Phase and Adsorbed Clusters

“…Leaving aside a handful of notable cases, − theoretical studies tend to neglect the rotational degrees of freedom of the involved diatomic species X 2 (X = H, D, and T), treating them as spherical object interacting via radial potential and forsaking e .g. the quadrupolar nature of their change density. ,− While such an approach is convenient (and often justifiable) in terms of computational costs and algorithmic complexity, the underlaying assumption of a complete decoupling between orientational and translational degrees of freedom may not always be correct. Of course, whether or not such approximation is adequate is dictated by the ratio between the molecular rotational constants (defining the quantum energy gaps) and the difference in potential energy between minima and the transition states connecting them along paths that involve changes in orientations. , Thus, while considering H 2 as a spherical object may be acceptable (but never shown to be correct) in describing its free pure clusters despite the variation of local properties upon increasing the distance between a molecule and cluster centers of mass (CoM), it is definitively not so when X 2 is adsorbed into a narrow carbon nanotube (CNT) , or onto ammonia aggregates. , Currently, the only indirect evidence supporting the possibility of neglecting rotations in X 2 clusters comes from the work by Roy et al, where the shift in X 2 vibrational frequency computed using adiabatically hindered rotor (AHR) interaction potentials reproduced experimental results with good accuracy.…”