Ab initio potential energy surfaces for the O2-O2 system and derived thermophysical properties.

New intermolecular potential energy surfaces (PESs) for the quintet, triplet, and singlet states of two rigid oxygen (O2) molecules in their triplet ground electronic states were developed. Quintet interaction energies were obtained for 896 O2-O2 configurations by supermolecular coupled cluster (CC) calculations at levels up to CC with single, double, triple, and perturbative quadruple excitations [CCSDT(Q)] with unrestricted Hartree-Fock (UHF) reference wave functions. Corrections for scalar relativistic effects were calculated as well. Triplet interaction energies were obtained by combining the quintet interaction energies with accurate estimates for the differences between the quintet and triplet energies obtained at the UHF-CCSD(T) level of theory. Here, we exploited the fact that the triplet state is almost identical to the readily accessible "broken-symmetry" state, as shown by Valentin-Rodríguez et al. [J. Chem. Phys. 152, 184304 (2020)]. The singlet interaction energies were estimated from the quintet and triplet interaction energies by employing the Heisenberg Hamiltonian description of the spin splittings. The three PESs are represented analytically by site-site models with five sites per molecule and anisotropic site-site interactions. To validate the PESs, we calculated at temperatures from 55 to 2000 K the second virial coefficient using statistical thermodynamics and the shear viscosity, thermal conductivity, and self-diffusion coefficient in the dilute gas phase using the kinetic theory of molecular gases. The calculated property values are in excellent agreement with the most accurate experimental data from the literature. Therefore, we also propose new reference correlations for the investigated properties based solely on the calculated values.

Cross Second Virial Coefficients of the H2O-H2 and H2S-H2 Systems from First-Principles.

The cross second virial coefficients B12 for the interactions of water (H2O) with molecular hydrogen (H2) and of hydrogen sulfide (H2S) with H2 were obtained at temperatures in the range from 150 to 2000 K from new intermolecular potential energy surfaces (PESs) for the respective molecule pairs. The PESs are based on interaction energies determined for about 12 000 configurations of each molecule pair employing different high-level quantum-chemical ab initio methods up to coupled cluster with single, double, triple, and perturbative quadruple excitations [CCSDT(Q)]. Furthermore, the interaction energies were corrected for scalar relativistic effects. Both classical and semiclassical values for B12 were extracted from the PESs using the Mayer-sampling Monte Carlo approach. While our results for the H2O-H2 system validate the older first-principles results of Hodges et al. [J. Chem. Phys. 2004, 120, 710-720], B12 for the H2S-H2 system was, to the best of our knowledge, hitherto neither measured experimentally nor predicted from first principles.

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

Ten different thermodynamic properties of the noble gas krypton were calculated by Monte Carlo simulations in the isothermal-isobaric ensemble using a highly accurate ab initio pair potential, Feynman-Hibbs corrections for quantum effects, and an extended Axilrod-Teller-Muto potential to account for nonadditive three-body interactions. Fourteen state points at a liquid and a supercritical isotherm were simulated. To obtain results representative for macroscopic systems, simulations with several particle numbers were carried out and extrapolated to the thermodynamic limit. Our results agree well with experimental data from the literature, an accurate equation of state for krypton, and a recent virial equation of state (VEOS) for krypton in the region where the VEOS has converged. These results demonstrate that very good agreement between simulation and experiment can only be achieved if nonadditive three-body interactions and quantum effects are taken into account.

Thermodynamic properties of argon from Monte Carlo simulations using ab initio potentials.

Ten different thermodynamic properties of the noble gas argon in the liquid and supercritical regions were obtained from semiclassical Monte Carlo simulations in the isothermal-isobaric ensemble using ab initio potentials for the two-body and nonadditive three-body interactions. Our results for the density and speed of sound agree with the most accurate experimental data for argon almost within the uncertainty of these data, a level of agreement unprecedented for many-particle simulations. This demonstrates the high predictive but yet unexploited power of ab initio potentials in the field of molecular modeling and simulation for thermodynamic properties of fluids.

Eighth-Order Virial Equation of State for Methane from Accurate Two-Body and Nonadditive Three-Body Intermolecular Potentials.

The second to eighth virial coefficients of methane were determined for temperatures up to 1200 K using an existing ab initio-based and empirically fine-tuned two-body potential combined with a new empirical nonadditive three-body potential. Nuclear quantum effects were accounted for by the semiclassical Feynman-Hibbs approach. The numerical evaluation of the high-dimensional integrals through which the virial coefficients are expressed was performed employing the Mayer-sampling Monte Carlo technique. By fitting suitable mathematical functions to the calculated virial coefficients, an analytical eighth-order virial equation of state (VEOS8) was obtained. Pressures p computed as a function of temperature T and density ρ using VEOS8 agree highly satisfactorily with p(ρ, T) values obtained with the experimentally based reference equation of state for methane of Setzmann and Wagner (SWEOS) at state points at which VEOS8 is sufficiently converged. It is shown that it is essential to account for nonadditive three-body interactions in the calculations in order to achieve good agreement with the SWEOS.

First-Principles Diffusivity Ratios for Atmospheric Isotope Fractionation on Mars and Titan.

Recent work used the kinetic theory of molecular gases, along with state-of-the-art intermolecular potentials, to calculate from first principles the diffusivity ratios necessary for modeling kinetic fractionation of water isotopes in air. Here, we extend that work to the Martian atmosphere, employing potential-energy surfaces for the interaction of water with carbon dioxide and with nitrogen. We also derive diffusivity ratios for methane isotopes in the atmosphere of Titan by using a high-quality potential for the methane-nitrogen pair. The Mars calculations cover 100 K to 400 K, while the Titan calculations cover 50 K to 200 K. Surprisingly, the simple hard-sphere theory that is inaccurate for Earth's atmosphere is in good agreement with the rigorous results for the diffusion of water isotopes in the Martian atmosphere. A modest disagreement with the hard-sphere results is observed for the diffusivity ratio of CH3D in the atmosphere of Titan. We present temperature-dependent correlations, as well as estimates of uncertainty, for the diffusivity ratios involving HDO, H2 17O, and H2 18O in the Martian atmosphere, and for CH3D and 13CH4 in the atmosphere of Titan, providing for the first time the necessary data to be able to model kinetic isotope fractionation in these environments.

Calculation of third to eighth virial coefficients of hard lenses and hard, oblate ellipsoids of revolution employing an efficient algorithm.

We provide third to eighth virial coefficients of oblate, hard ellipsoids of revolution and hard lenses in dependence on their aspect ratio ν. Employing an algorithm optimized for hard anisotropic shapes, highly accurate data are accessible with comparatively small numerical effort. For both geometries, reduced virial coefficients B[over ̃]_{i}(ν)=B_{i}(ν)/B_{2}^{i-1}(ν) are in first approximation proportional to the inverse excess contribution α^{-1} of their excluded volume. The latter quantity is directly accessible from second virial coefficients and analytically known for convex bodies.

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.

Systematic formulation of thermodynamic properties in the NpT ensemble.

Molecular expressions for thermodynamic properties and derivatives of the Gibbs energy up to third order in the isobaric-isothermal (NpT) ensemble are systematically derived using the methodology developed by Lustig for the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994)10.1063/1.466446; Mol. Phys. 110, 3041 (2012)10.1080/00268976.2012.695032]. They are expressed by phase-space functions, which represent derivatives of the Gibbs energy with respect to temperature and pressure. Additionally, expressions for the phase-space functions for temperature-dependent potentials are provided, which, for example, are required when quantum corrections, e.g., Feynman-Hibbs corrections, are applied in classical simulations. The derived expressions are validated by Monte Carlo simulations for the simple Lennard-Jones model fluid at three selected state points. A unique result is that the phase-space functions contain only ensemble averages of combinations of powers of enthalpy and volume. Thus, the calculation of thermodynamic properties in the NpT ensemble does not require volume derivatives of the potential energy. This is particularly advantageous in Monte Carlo simulations when the interactions between molecules are described by empirical force fields or very accurate ab initio pair and nonadditive three-body potentials.

First-Principles Diffusivity Ratios for Kinetic Isotope Fractionation of Water in Air.

Kinetic isotope fractionation between water vapor and liquid water or ice depends on the ratio of the diffusivities of the isotopic species in air, but there is disagreement as to the values of these ratios and limited information about their temperature dependence. We use state-of-the-art intermolecular potential-energy surfaces for the water-nitrogen and water-oxygen pairs, along with the kinetic theory of molecular gases, to calculate from first principles the diffusivities of water isotopologues in air. The method has sufficient precision to produce accurate diffusivity ratios. For the HDO/H2O ratio, we find that the often used hard-sphere kinetic theory is significantly in error, and confirm the 1978 experimental result of Merlivat. For the ratios involving 17O and 18O, the simple kinetic theory is relatively close to our more rigorous results. We provide diffusivity ratios from 190 K to 500 K, greatly expanding the range of temperatures for which these ratios are available.

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.

The Zero-Density Limit of the Residual Entropy Scaling of Transport Properties.

The modified residual entropy scaling approach has been shown to be a successful means of scaling dense phase transport properties. In this work, we investigate the dilute-gas limit of this scaling. This limit is considered for model potentials and highly accurate results from calculations with ab initio pair potentials for small molecules. These results demonstrate that with this approach, the scaled transport properties of noble gases can be collapsed without any empirical parameters to nearly their mutual uncertainties and that the scaled transport properties of polyatomic molecules are qualitatively similar, and for sufficiently high temperatures they agree with "universal" values proposed by Rosenfeld in 1999. There are significant quantitative differences between the model potentials and real fluids in these scaled coordinates, but this study provides a thorough coverage of model fluids and simple real fluids, providing the basis for further study. In the supporting information we provide the collected calculations with ab initio pair potentials from the literature, as well as code in the Python language implementing all aspects of our analysis.

Ab initio intermolecular potential energy surface for the CO2-N2 system and related thermophysical properties.

A four-dimensional potential energy surface (PES) for the interaction between a rigid carbon dioxide molecule and a rigid nitrogen molecule was constructed based on quantum-chemical ab initio calculations up to the coupled-cluster level with single, double, and perturbative triple excitations. Interaction energies for a total of 1893 points on the PES were calculated using the counterpoise-corrected supermolecular approach and basis sets of up to quintuple-zeta quality with bond functions. The interaction energies were extrapolated to the complete basis set limit, and an analytical site-site potential function with seven sites for carbon dioxide and five sites for nitrogen was fitted to the interaction energies. The CO2-N2 cross second virial coefficient as well as the dilute gas shear viscosity, thermal conductivity, and binary diffusion coefficient of CO2-N2 mixtures were calculated for temperatures up to 2000 K to validate the PES and to provide reliable reference values for these important properties. The calculated values are in very good agreement with the best experimental data.

Virial coefficients of anisotropic hard solids of revolution: The detailed influence of the particle geometry.

We provide analytical expressions for the second virial coefficients of differently shaped hard solids of revolution in dependence on their aspect ratio. The second virial coefficients of convex hard solids, which are the orientational averages of the mutual excluded volume, are derived from volume, surface, and mean radii of curvature employing the Isihara-Hadwiger theorem. Virial coefficients of both prolate and oblate hard solids of revolution are investigated in dependence on their aspect ratio. The influence of one- and two-dimensional removable singularities of the surface curvature to the mutual excluded volume is analyzed. The virial coefficients of infinitely thin oblate and infinitely long prolate particles are compared, and analytical expressions for their ratios are derived. Beyond their dependence on the aspect ratio, the second virial coefficients are influenced by the detailed geometry of the particles.

State-of-the-art ab initio potential energy curve for the xenon atom pair and related spectroscopic and thermophysical properties.

A new ab initio interatomic potential energy curve for two ground-state xenon atoms is presented. It is based on supermolecular calculations at the coupled-cluster level with single, double, and perturbative triple excitations [CCSD(T)] employing basis sets up to sextuple-zeta quality, which were developed as part of this work. In addition, corrections were determined for higher coupled-cluster levels up to CCSDTQ as well as for scalar and spin-orbit relativistic effects at the CCSD(T) level. A physically motivated analytical function was fitted to the calculated interaction energies and used to compute the vibrational spectrum of the dimer, the second virial coefficient, and the dilute gas transport properties. The agreement with the best available experimental data for the investigated properties is excellent; the new potential function is superior not only to previous ab initio potentials but also to the most popular empirical ones.

Intermolecular potential energy surface and thermophysical properties of propane.

A six-dimensional potential energy surface (PES) for the interaction of two rigid propane molecules was determined from supermolecular ab initio calculations up to the coupled cluster with single, double, and perturbative triple excitations level of theory for 9452 configurations. An analytical site-site potential function with 14 sites per molecule was fitted to the calculated interaction energies. To validate the analytical PES, the second virial coefficient and the dilute gas shear viscosity and thermal conductivity of propane were computed. The dispersion part of the potential function was slightly adjusted such that quantitative agreement with the most accurate experimental data for the second virial coefficient at room temperature was achieved. The adjusted PES yields values for the three properties that are in very good agreement with the best experimental data at all temperatures.

Nonadditive three-body potential and third to eighth virial coefficients of carbon dioxide.

A new nonadditive three-body interaction potential for carbon dioxide was determined from supermolecular ab initio calculations up to the coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] level of theory for 9401 configurations. A physically motivated analytical function with terms for describing nonadditive dispersion, induction, and exchange contributions was fitted to the calculated nonadditive three-body interaction energies. For the 7996 configurations with a total interaction energy of less than 3000 K, the mean absolute error of the analytical function is 0.32 K. The new nonadditive three-body potential was applied together with a previously published pair potential [R. Hellmann, Chem. Phys. Lett. 613, 133 (2014)] to calculate the third to seventh virial coefficients of CO2 at subcritical and supercritical temperatures up to 2000 K. The eighth virial coefficient was also calculated, but using only the pair potential and only at temperatures from 600 K to 2000 K because of the enormous computational costs. A simple analytical function was fitted individually to the calculated values of each virial coefficient, including previously determined values of the second virial coefficient, to obtain an analytical virial equation of state (VEOS). For densities at which the VEOS is converged, the agreement in pressure with the reference EOS of Span and Wagner [J. Phys. Chem. Ref. Data 25, 1509 (1996)] is mostly within ±0.5%. However, for temperatures above about 700 K, much larger deviations occur at higher densities, which we ascribe mainly to deficiencies of the reference EOS due to the lack of accurate data for these experimentally difficult conditions.

Calculation of the thermal conductivity of low-density CH4-N2 gas mixtures using an improved kinetic theory approach.

The thermal conductivity of low-density CH4-N2 gas mixtures has been calculated by means of the classical trajectory method using state-of-the-art intermolecular potential energy surfaces for the CH4-CH4, N2-N2, and CH4-N2 interactions. Results are reported in the temperature range from 70 K to 1200 K. Since the thermal conductivity is influenced by the vibrational degrees of freedom of the molecules, which are not included in the rigid-rotor classical trajectory computations, a new correction scheme to account for vibrational degrees of freedom in a dilute gas mixture is presented. The calculations show that the vibrational contribution at the highest temperature studied amounts to 46% of the total thermal conductivity of an equimolar mixture compared to 13% for pure nitrogen and 58% for pure methane. The agreement with the available experimental thermal conductivity data at room temperature is good, within ±1.4%, whereas at higher temperatures, larger deviations up to 4.5% are observed, which can be tentatively attributed to deteriorating performance of the measuring technique employed. Results are also reported for the magnitude and temperature dependence of the rotational collision number, Z(rot), for CH4 relaxing in collisions with N2 and for N2 relaxing in collisions with CH4. Both collision numbers increase with temperature, with the former being consistently about twice the value of the latter.

State-of-the-art ab initio potential energy curve for the krypton atom pair and thermophysical properties of dilute krypton gas.

A new reference krypton-krypton interatomic potential energy curve was developed by means of quantum-chemical ab initio calculations for 36 interatomic separations. Highly accurate values for the interaction energies at the complete basis set limit were obtained using the coupled-cluster method with single, double, and perturbative triple excitations as well as t-aug-cc-pV5Z and t-aug-cc-pV6Z basis sets including mid-bond functions, with the 6Z basis set being newly constructed for this study. Higher orders of coupled-cluster terms were considered in a successive scheme up to full quadruple excitations. Core-core and core-valence correlation effects were included. Furthermore, relativistic effects were studied not only at a scalar relativistic level using second-order direct perturbation theory, but also utilizing full four-component and Gaunt-effect computations. An analytical pair potential function was fitted to the interaction energies, which is characterized by a depth of 200.88 K with an estimated standard uncertainty of 0.51 K. Thermophysical properties of low-density krypton were calculated for temperatures up to 5000 K. Second and third virial coefficients were obtained from statistical thermodynamics. Viscosity and thermal conductivity as well as the self-diffusion coefficient were computed using the kinetic theory of gases. The theoretical results are compared with experimental data and with results for other pair potential functions from the literature, especially with those calculated from the recently developed ab initio potential of Waldrop et al. [J. Chem. Phys. 142, 204307 (2015)]. Highly accurate experimental viscosity data indicate that both the present ab initio pair potential and the one of Waldrop et al. can be regarded as reference potentials, even though the quantum-chemical methods and basis sets differ. However, the uncertainties of the present potential and of the derived properties are estimated to be considerably lower.

Influence of a magnetic field on the viscosity of a dilute gas consisting of linear molecules.

The viscomagnetic effect for two linear molecules, N2 and CO2, has been calculated in the dilute-gas limit directly from the most accurate ab initio intermolecular potential energy surfaces presently available. The calculations were performed by means of the classical trajectory method in the temperature range from 70 K to 3000 K for N2 and 100 K to 2000 K for CO2, and agreement with the available experimental data is exceptionally good. Above room temperature, where no experimental data are available, the calculations provide the first quantitative information on the magnitude and the behavior of the viscomagnetic effect for these gases. In the presence of a magnetic field, the viscosities of nitrogen and carbon dioxide decrease by at most 0.3% and 0.7%, respectively. The results demonstrate that the viscomagnetic effect is dominated by the contribution of the jj¯ polarization at all temperatures, which shows that the alignment of the rotational axes of the molecules in the presence of a magnetic field is primarily responsible for the viscomagnetic effect.