Thermophysical properties of krypton-helium gas mixtures from ab initio pair potentials

Impact of Combination Rules, Level of Theory, and Potential Function on the Modeling of Gas- and Condensed-Phase Properties of Noble Gases

The systems of noble gases are particularly instructive for molecular modeling due to the elemental nature of their interactions. They do not normally form bonds nor possess a (permanent) dipole moment, and the only forces determining their bonding/clustering stems from van der Waals forces─dispersion and Pauli repulsion, which can be modeled by empirical potential functions. Combination rules, that is, formulas to derive parameters for pair potentials of heterodimers from parameters of corresponding homodimers, have been studied at length for the Lennard-Jones 12-6 potentials but not in great detail for other, more accurate, potentials. In this work, we examine the usefulness of nine empirical potentials in their ability to reproduce quantum mechanical (QM) benchmark dissociation curves of noble gas dimers (He, Ne, Ar, Kr, and Xe homo- and heterodimers), and we systematically study the efficacy of different permutations of combination relations for each parameter of the potentials. Our QM benchmark comprises dissociation curves computed by several different coupled cluster implementations as well as symmetry-adapted perturbation theory. The two-parameter Lennard-Jones potentials were decisively outperformed by more elaborate potentials that sport a 25-30 times lower root-mean-square error (RMSE) when fitted to QM dissociation curves. Very good fits to the QM dissociation curves can be achieved with relatively inexpensive four- or even three-parameter potentials, for instance, the damped 14-7 potential (Halgren, J. Am. Chem. Soc. 1992, 114, 7827-7843), a four-parameter Buckingham potential (Werhahn et al., Chem. Phys. Lett. 2015, 619, 133-138), or the three-parameter Morse potential (Morse, Phys. Rev. 1929, 34, 57-64). Potentials for heterodimers that are generated from combination rules have an RMSE that is up to 20 times higher than potentials that are directly fitted to the QM dissociation curves. This means that the RMSE, in particular, for light atoms, is comparable in magnitude to the well-depth of the potential. Based on a systematic permutation of combination rules, we present one or more combination rules for each potential tested that yield a relatively low RMSE. Two new combination rules are introduced that perform well, one for the van der Waals radius σij as ( 1 2 ( σ i 3 + σ j 3 ) ) 1 / 3 and one for the well-depth ϵij as ( 1 2 ( ϵ i - 2 + ϵ j - 2 ) ) - 1 / 2 . The QM data and the fitted potentials were evaluated in the gas phase against experimental second virial coefficients for homo- and heterodimers, the latter of which allowed evaluation of the combination rules. The fitted models were used to perform condensed phase molecular dynamics simulations to verify the melting points, liquid densities at the melting point, and the enthalpies of vaporization produced by the models for pure substances. Subtle differences in the benchmark potentials, in particular, the well-depth, due to the level of theory used were found here to have a profound effect on the macroscopic properties of noble gases: second virial coefficients or the bulk properties in simulations. By explicitly including three-body dispersion in molecular simulations employing the best pair potential, we were able to obtain accurate melting points as well as satisfactory densities and enthalpies of vaporization.

Transport coefficients of isotopic mixtures of noble gases based on ab initio potentials

The transport coefficients such as viscosity, thermal conductivity, diffusion and thermal diffusion of neon, argon, krypton, and xenon are computed for a wide range of temperatures taking into consideration their real isotopic compositions. A new concept of isotopic thermal diffusion factor is introduced and calculated. The Chapman-Enskog method based on the 10th order approximation with respect to the Sonine polynomial expansion is applied. Ab initio potentials of interatomic interactions are employed to compute the transport cross-sections as they are part of the coefficient expressions. To study the influence of the isotopic composition, the same transport coefficients have been calculated for the single gases having an average atomic mass. The estimated numerical error of the present results is a function of the temperature and is different for each coefficient. At the room temperature, the relative numerical error of viscosity, thermal conductivity and diffusion coefficient is on the order of 10-6. The numerical error of the thermal diffusion factor affects the fifth decimal digit. The influence of the isotopic composition on viscosity and thermal conductivity depends on the gas species. It is negligible for argon and significant (about 0.02%) for xenon, while neon and krypton are weakly affected by the isotopic composition. The diffusion coefficient for each pair of isotopes differs from the corresponding self-diffusion coefficient by about 3%. The thermal diffusion factor of each isotope differs from the thermal self-diffusion factor in the third decimal digit.

Thermophysical properties of low-density neon gas from highly accurate first-principles calculations and dielectric-constant gas thermometry measurements

New interatomic potential energy and interaction-induced polarizability curves for two ground-state neon atoms were developed and used to predict the second density, acoustic, and dielectric virial coefficients and the dilute gas shear viscosity and thermal conductivity of neon at temperatures up to 5000 K. The potential energy curve is based on supermolecular coupled-cluster (CC) calculations at very high levels up to CC with single, double, triple, quadruple, and perturbative pentuple excitations [CCSDTQ(P)]. Scalar and spin-orbit relativistic effects, the diagonal Born-Oppenheimer correction, and retardation of the dispersion interactions were taken into account. The interaction-induced polarizability curve, which in this work is only needed for the calculation of the second dielectric virial coefficient, is based on supermolecular calculations at levels up to CCSDT and includes a correction for scalar relativistic effects. In addition to these first-principles calculations, highly accurate dielectric-constant gas thermometry (DCGT) datasets measured at temperatures from 24.5 to 200 K were analyzed to obtain the difference between the second density and dielectric virial coefficients with previously unattained accuracy. The agreement of the DCGT values with the ones resulting from the first-principles calculations is, despite some small systematic deviations, very satisfactory. Apart from this combination of two virial coefficients, the calculated thermophysical property values of this work are significantly more accurate than any available experimental data.

Conformal Analytical Potential for All the Rare Gas Dimers over the Full Range of Internuclear Distances

An analytical model for the potential between two rare gas atoms at distances between R=0 to R→∞ is assumed to be conformal with the previously published potential for He_{2} [J. Chem. Phys. 142, 131102 (2015)JCPSA60021-960610.1063/1.4916740]. The potential curves of the rare gas dimers all have the same shape and only depend on the well parameters D_{e} and R_{e}. The potentials and the vibrational levels for the 11 homonuclear and heteronuclear dimers for which recent ab initio calculations are available agree, within several percent, with the ab initio results. For the other rare gas dimers, the new potential provides the first realistic estimates for the potentials.

Eighth-order virial equation of state and speed-of-sound measurements for krypton

An eighth-order virial equation of state (VEOS) for krypton, valid for temperatures up to 5000 K, was developed using the accurate potential functions proposed by Jäger et al. [J. Chem. Phys. 144, 114304 (2016)] for the pair interactions and nonadditive three-body interactions between krypton atoms. While the second and third virial coefficients were already calculated by Jäger et al., the fourth- to eighth-order coefficients were determined in the present work. A simple analytical function was fitted individually to the calculated values of each virial coefficient to obtain the VEOS in an easy-to-use analytical form. To enable a stringent test of the quality of the new VEOS, we measured the speed of sound in krypton in the temperature range from 200 K to 420 K and at pressures up to 100 MPa with a very low uncertainty (at the 0.95 confidence level) of 0.005%-0.018% employing the pulse-echo technique. In order to verify that the isotopic composition of the krypton sample conforms to that of natural krypton in air, high-precision measurements of krypton isotope ratios using a high-sensitivity noble gas mass spectrometer were performed. The extensive comparison with the new speed-of-sound data as well as with experimental p-ρ-T and speed-of-sound data from the literature indicates that pressures and speeds of sound calculated using our new VEOS have uncertainties (at the 0.95 confidence level) of less than 0.1% at state points at which the VEOS is sufficiently converged.