Thermodynamic properties of krypton from Monte Carlo simulations using ab initio potentials

An Accurate Machine-Learned Potential for Krypton under Extreme Conditions

We have developed two machine-learned pair potentials for krypton based on CCSD(T) quantum chemical calculations on two and three atom clusters. Through extensive testing with molecular dynamics, we find both potentials give good agreement with the experimental equation of state, melting point, and neutron scattering data for the fluid. Compared with the most widely used Lennard-Jones model, our potentials produced similar results in low-pressure melting and equation of state. However, extending the regime to higher pressures of ≤30 GPa showed a remarkable divergence of the Lennard-Jones model from the experimental (solid) equation of state. Our potential showed extremely good agreement, despite having no solid phases in the training set.

Corresponding-states framework for classical and quantum fluids-Beyond Feynman-Hibbs

Effective potential methods, obtained by applying a quantum correction to a classical pair potential, are widely used for describing the thermophysical properties of fluids with mild nuclear quantum effects. In case of strong nuclear quantum effects, such as for liquid hydrogen and helium, the accuracy of these quantum corrections deteriorates significantly, but at present no simple alternatives are available. In this work, we solve this issue by developing a new, three-parameter corresponding-states principle that remains applicable in the regions of the phase diagram where quantum effects become significant. The new principle emerges from a mapping procedure, which shows that quantum-corrected pair potentials can be made conformal to their underlying classical pair potential by modifying the latter's repulsive range. This mapping enables an accurate description of fluids with quantum-corrected interactions based on off-the-shelf methods for classical fluids (e.g., equations of state, classical density functional theory, and entropy scaling) using effective, mapped intermolecular-potential parameters. These effective parameters depend on temperature and molecular mass; simple analytic equations in case of a classical Mie potential with Feynman-Hibbs quantum corrections are presented. Using Mie Feynman-Hibbs force fields from the literature, we show that this procedure provides accurate predictions for the properties of fluids with mild nuclear quantum effects, such as neon or hydrogen at moderate temperatures. Moreover, by adjusting the functional form of the effective intermolecular-potential parameters to experimental data for helium and hydrogen, we are able to apply the corresponding-states principle for optimal quantum-corrected pair potentials that far surpass the accuracy of the Feynman-Hibbs correction.

Calculation of thermodynamic properties of helium using path integral Monte Carlo simulations in the NpT ensemble and ab initio potentials

We apply the methodology of Lustig, with which rigorous expressions for all thermodynamic properties can be derived in any statistical ensemble, to derive expressions for the calculation of thermodynamic properties in the path integral formulation of the quantum-mechanical isobaric-isothermal (NpT) ensemble. With the derived expressions, thermodynamic properties such as the density, speed of sound, or Joule-Thomson coefficient can be calculated in path integral Monte Carlo simulations, fully incorporating quantum effects without uncontrolled approximations within the well-known isomorphism between the quantum-mechanical partition function and a classical system of ring polymers. The derived expressions are verified by simulations of supercritical helium above the vapor-liquid critical point at selected state points using recent highly accurate ab initio potentials for pairwise and nonadditive three-body interactions. We observe excellent agreement of our results with the most accurate experimental data for the density and speed of sound and a reference virial equation of state for helium in the region where the virial equation of state is converged. Moreover, our results agree closer with the experimental data and virial equation of state than the results of semiclassical simulations using the Feynman-Hibbs correction for quantum effects, which demonstrates the necessity to fully include quantum effects by path integral simulations. Our results also show that nonadditive three-body interactions must be accounted for when accurately predicting thermodynamic properties of helium by solely theoretical means.

Vapor-liquid equilibrium and thermodynamic properties of saturated argon and krypton from Monte Carlo simulations using ab initio potentials

Vapor-liquid equilibria and thermodynamic properties of saturated argon and krypton were calculated by semi-classical Monte Carlo simulations with the NpT + test particle method using ab initio potentials for the two-body and nonadditive three-body interactions. The NpT + test particle method was extended to the calculation of second-order thermodynamic properties, such as the isochoric and isobaric heat capacities or the speed of sound, of the saturated liquid and vapor by using our recently developed approach for the systematic calculation of arbitrary thermodynamic properties in the isothermal-isobaric ensemble. Generally, the results for all simulated properties agree well with experimental data and the current reference equations of state for argon and krypton. In particular, the results for the vapor pressure and for the density and speed of sound of the saturated liquid and vapor agree with the most accurate experimental data for both noble gases almost within the uncertainty of these data, a level of agreement unprecedented for many-particle simulations. This study demonstrates that the vapor-liquid equilibrium and thermodynamic properties at saturation of a pure fluid can be predicted by Monte Carlo simulations with high accuracy when the intermolecular interactions are described by state-of-the-art ab initio pair and nonadditive three-body potentials and quantum effects are accounted for.