The third and fourth density and acoustic virial coefficients of neon were determined at temperatures between 10 and 5000 K from first principles employing the path-integral Monte Carlo (PIMC) approach. For these calculations, we used the pair potential of Hellmann et al. [J. Chem. Phys. 154, 164304 (2021)], which is based on supermolecular ab initio calculations with basis sets of up to octuple-zeta quality and levels of theory up to coupled cluster with single, double, triple, quadruple, and perturbative pentuple excitations [CCSDTQ(P)]. The potential also accounts for relativistic, retardation, and post-Born-Oppenheimer effects and is provided with reliable uncertainty estimates. To incorporate nonadditive interactions, we developed a nonadditive three-body potential based on extensive supermolecular CCSD(T), CCSDT, and CCSDT(Q) calculations with basis sets of up to sextuple-zeta quality. This potential also accounts for relativistic effects. The very small nonadditive four-body contributions to the fourth virial coefficients were considered using a relatively simple nonadditive four-body potential based on supermolecular CCSD(T) calculations. We calculated the third and fourth density and third acoustic virial coefficients directly by PIMC and the fourth acoustic virial coefficient indirectly using thermodynamic relations between the density and acoustic virial coefficients. The uncertainties of the pair potential and those estimated for our nonadditive three-body potential were rigorously propagated in the PIMC calculations into uncertainties for the virial coefficients. These uncertainties are distinctly smaller than those of almost all of the corresponding experimental virial coefficient data.

We provide recommended values for the second virial coefficient, $B(T)$, and its uncertainty, for molecular nitrogen and oxygen. The temperature range covered is $20-3000$ K for nitrogen and $20-2000$ K for oxygen. The recommendations are based on tuning previously published state-of-the-art ab initio pair potentials so that the $B(T)$ calculated from the potentials match selected high-accuracy experimental data; for nitrogen the tuning utilizes values of $B$ derived from literature density data with greatly reduced uncertainty by analyzing the data with the aid of ab initio calculated higher virial coefficients. Quantum effects on $B$ are fully included with the path-integral Monte Carlo method. The resulting $B(T)$ have uncertainties similar to those of the best experimental data, but cover a much wider temperature range.

The cross second virial coefficients B_12 for interactions of molecular nitrogen (N2) with molecular hydrogen (H2), of molecular oxygen (O2) with H2, and of carbon dioxide (CO2) with H2 were obtained at temperatures ranging from 36 K to 2000 K for the former two systems and from 100 K to 2000 K for the latter system from new rigid-rotor intermolecular potential energy surfaces (PESs) for the three molecule pairs. Each PES is based on interaction energies calculated for a large number of pair configurations employing high-level quantum-chemical ab initio methods up to coupled cluster with single, double, triple, and perturbative quadruple excitations [CCSDT(Q)]. Core-core and core-valance correlation and relativistic effects were accounted for as well. B_12 values were extracted from the PESs classically and semiclassically using the Mayer-sampling Monte Carlo approach. The deficiencies of the semiclassical calculations at the lowest temperatures were partly remedied by a more rigorous treatment of translational quantum effects using the phase-shift method. The results for the N2–H2 and CO2–H2 systems are in excellent agreement with the most accurate experimental data. For the O2–H2 system, there are no experimental B_12 data because this mixture is highly explosive. There are, however, previous first-principles results for B_12 of this system by Van Tat and Deiters [Chem. Phys. 457, 171–179 (2015)], which were obtained at a much lower level of sophistication for both the PES and the method to extract B_12 and differ significantly from the present B_12 values.

We report comprehensive and accurate measurements of the speed of sound in neon. These measurements were carried out by a double-path-length pulse-echo technique and cover the temperature range between 200 K and 420 K with pressures up to 100 MPa. The standard uncertainties are 1.9 mK in temperature, 22 parts in 106 in pressure and 35 parts in 106 in speed of sound. The third and fourth acoustic virial coefficients of neon were derived from the speed of sound data in the temperature range of the measurements by fitting a fourth-order acoustic virial expansion in pressure with the second acoustic virial coefficient constrained from first-principles calculations. To support our claimed uncertainty, we determined the ratio M / γ 0 between the molar mass M and the ideal-gas heat capacity ratio γ 0 of the neon sample with a relative standard uncertainty of 7.7 parts in 106 by additional speed of sound measurements using a spherical resonator at 273.16 K.

Several thermophysical properties of gaseous mixtures of water (H2O) and argon (Ar) were obtained at temperatures up to 2000 K by applying state-of-the-art first-principles approaches. The H2O-Ar cross second and H2O-Ar-Ar cross third virial coefficients were calculated using statistical thermodynamics, and the dilute gas shear viscosity, thermal conductivity, and binary diffusion coefficient were obtained using the kinetic theory of gases. The required potential energy surfaces (PESs) describing H2O-Ar pair interactions and H2O-Ar-Ar nonadditive three-body interactions were developed in this work, while H2O-H2O and Ar-Ar pair interactions are described by PES models from the literature. All of these PESs are based on high-level quantum-chemical ab initio calculations. The predicted values for the investigated properties are in satisfying agreement with the few existing experimental data and are the most accurate estimates available to date. For the cross virial coefficients and the binary diffusion coefficient, the results are also provided in the form of practical correlations.

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.

The results of viscosity measurements at moderate densities on the two gaseous mixtures carbon dioxide–nitrogen and ethane–methane including the pure gases between 253.15 K and 473.15 K, originally performed by Humberg et al. at Ruhr University Bochum, Germany, using a rotating-cylinder viscometer between 0.1 MPa and 2.0 MPa, were employed to determine the interaction viscosity, η _12^(0) , and the product of molar density and diffusion coefficient, (ρ D_12)^(0) , each in the limit of zero density. The isothermal viscosity data were evaluated by those authors with density series restricted to the second order at most to derive the zero-density viscosities and initial density viscosity coefficients, η _mix^(0) and η _mix^(1) , for the mixtures, as well as, η _i^(0) and η _i^(1) ( i=1,2 ), respectively, for the pure gases. Humberg et al. have already compared their η _mix^(0) and η _i^(0) data for carbon dioxide–nitrogen and ethane–methane with corresponding viscosity values theoretically computed for the nonspherical potentials of the intermolecular interaction. Now we employed η _mix^(0) and η _mix^(1) as well as η _i^(0) and η _i^(1) in two procedures to derive η _12^(0) values. For this, we needed A_12^* values (ratio between effective cross-sections of viscosity and diffusion). But the second procedure applying the initial density viscosity coefficients η _mix^(1) and η _i^(1) failed to yield reasonable η _12^(0) values. The first procedure should provide the best results when it is possible to use A_12^* values computed for the nonspherical potential. The effect is comparatively small if η _12^(0) is determined. But if (ρ D_12)^(0) is calculated from η _12^(0) using A_12^* values for the nonspherical potential, the impact is several percent. Moreover, the experimentally based η _12^(0) and (ρ D_12)^(0) data agree with theoretically calculated values for the nonspherical potentials.

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.

Recent advances regarding the interplay between ab initio calculations and metrology are reviewed, with particular emphasis on gas-based techniques used for temperature and pressure measurements. Since roughly 2010, several thermophysical quantities - in particular, virial and transport coefficients - can be computed from first principles without uncontrolled approximations and with rigorously propagated uncertainties. In the case of helium, computational results have accuracies that exceed the best experimental data by at least one order of magnitude and are suitable to be used in primary metrology. The availability of ab initio virial and transport coefficients contributed to the recent SI definition of temperature by facilitating measurements of the Boltzmann constant with unprecedented accuracy. Presently, they enable the development of primary standards of temperature in the range 2.5-552 K and pressure up to 7 MPa using acoustic gas thermometry, dielectric constant gas thermometry, and refractive index gas thermometry. These approaches will be reviewed, highlighting the effect of first-principles data on their accuracy. The recent advances in electronic structure calculations that enabled highly accurate solutions for the many-body interaction potentials and polarizabilities of atoms - particularly helium - will be described, together with the subsequent computational methods, most often based on quantum statistical mechanics and its path-integral formulation, that provide thermophysical properties and their uncertainties. Similar approaches for molecular systems, and their applications, are briefly discussed. Current limitations and expected future lines of research are assessed.

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.

The static electric-dipole polarizability a of the neon atom was determined with a relative uncertainty of only about 0.003% using state-of-the-art ab initio approaches. The new value, alpha = 2.661 067(77) a.u., is almost five times more accurate than the previous ab initio estimate, alpha = 2.660 80(36) a.u., by Lesiuk et al. [Phys. Rev. A 102, 052816 (2020)] Similar to their work, we calculated a using ab initio methods up to full configuration interaction and added corrections for finite nuclear mass and size, relativistic, and quantum electrodynamics (QED) effects. The uncertainty reduction of this work was achieved in particular by employing extremely large basis sets, including newly developed ones of 11Z, 12Z, and 13Z quality. Moreover, the finite nuclear mass effects and most of the relativistic contributions were calculated at much higher levels of theory than in the work of Lesiuk et al. However, we adopted their values for the orbit-orbit part of the relativistic correction and for the Bethe logarithm needed to compute the QED correction. The uncertainty of our final value is still an order of magnitude larger than that of the experimental value recently measured by Gaiser and Fellmuth [Phys. Rev. Lett. 120, 123203 (2018)] with an uncertainty of only a few parts per million using dielectric-constant gas thermometry. Yet, our ab initio value agrees with their value, alpha(exp) = 2.66 057(7) a.u., almost within the experimental uncertainty. This could indicate that the higher-order relativistic corrections and QED contributions, which dominate our uncertainty budget, are more accurate than expected considering the uncontrolled approximations involved in their calculation.

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.

The International Association for the Properties of Water and Steam (IAPWS) encouraged an extensive research effort to update the IAPS Formulation 1985 for the Thermal Conductivity of Ordinary Water Substance, leading to the adoption of a Release on the IAPWS Formulation 2011 for the Thermal Conductivity of Ordinary Water Substance. This paper describes the development and evaluation of the 2011 formulation, which provides a correlating equation for the thermal conductivity of water for fluid states from the melting temperature up to 1173 K and 1000 MPa with uncertainties from less than 1% to 6%, depending on the state point.

The cross second virial coefficient $$B_{12}$$ for the interaction between water (H2O) and carbon monoxide (CO) was obtained with low uncertainty at temperatures from 200 K to 2000 K employing a new intermolecular potential energy surface (PES) for the H2O–CO system. This PES was fitted to interaction energies determined for about 58 000 H2O–CO configurations using high-level quantum-chemical ab initio methods up to coupled cluster with single, double, and perturbative triple excitations [CCSD(T)]. The cross second virial coefficient $$B_{12}$$ was extracted from the PES using a semiclassical approach. An accurate correlation of the calculated $$B_{12}$$ values was used to determine the dilute gas cross isothermal Joule–Thomson coefficient, $$\phi _{12}=B_{12}-T(\mathrm {d}B_{12}/\mathrm {d}T)$$ . The predicted values for both $$B_{12}$$ and $$\phi _{12}$$ agree reasonably well with the few existing experimental data and older calculated values and should be the most accurate estimates of these quantities to date.

For the diffusive contribution to fractionation in the Simple Water Isotope Model (SWIM), a temperature dependence was assumed for the quantity φdiff [Eq. (A5)] based on one of the sets of mutually inconsistent experimental data. Recent work (Hellmann, R. and Harvey, A. H.: First‐Principles Diffusivity Ratios for Kinetic Isotope Fractionation of Water in Air, Geophys. Res. Lett., 47, e2020GL089999, https://doi.org/10.1029/2020GL089999, 2020) has used molecular theory to determine a more physically correct temperature dependence. The new function differs significantly from what is assumed in this work, although it may not make a significant difference for the main results.

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.

15 Recent work used the kinetic theory of molecular gases, along with state-of-the-art in16 termolecular potentials, to calculate from first principles the diffusivity ratios necessary 17 for modeling kinetic fractionation of water isotopes in air. Here, we extend that work 18 to the Martian atmosphere, employing potential-energy surfaces for the interaction of 19 water with carbon dioxide and with nitrogen. We also derive diffusivity ratios for methane 20 isotopes in the atmosphere of Titan by using a high-quality potential for the methane21 nitrogen pair. The Mars calculations cover 100 K to 400 K, while the Titan calculations 22 cover 50 K to 200 K. Surprisingly, the simple hard-sphere theory that is inaccurate for 23 Earth’s atmosphere is in good agreement with the rigorous results for the diffusion of 24 water isotopes in the Martian atmosphere. A modest disagreement with the hard-sphere 25 results is observed for the diffusivity ratio of CH3D in the atmosphere of Titan. We present 26 temperature-dependent correlations, as well as estimates of uncertainty, for the diffusiv27 ity ratios involving HDO, H2 O, and H2 O in the Martian atmosphere, and for CH3D 28 and CH4 in the atmosphere of Titan, providing for the first time the necessary data 29 to be able to model kinetic isotope fractionation in these environments. 30 Plain Language Summary 31 Different isotopes distribute unevenly between the vapor phase and liquid or solid 32 phases during precipitation and evaporation, and the resulting changes in isotope ratios 33 are used in the study of climate and other geophysical processes. While equilibrium as34 pects of this fractionation are fairly well understood, in some circumstances there is also 35 a kinetic component that depends on the relative diffusivities of different isotopic species 36 in the atmosphere. We used rigorous molecular collision calculations to model this ef37 fect for water isotopes in the CO2-rich Martian atmosphere and for methane isotopes 38 in the nitrogen atmosphere of Titan. For the Martian atmosphere, the results are not 39 significantly different from those obtained by a simple theory that assumes the molecules 40 to be hard spheres; this is surprising since previous work showed that the hard-sphere 41 approach is significantly in error for water in Earth’s atmosphere. For methane in the 42 atmosphere of Titan, a small improvement is obtained for the diffusivity ratio of CH3D. 43 We provide simple correlations that allow these diffusivity ratios to be used in planetary 44 modeling. 45

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 100–400 K, while the Titan calculations cover 50–200 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 CH 3 D in the atmosphere of Titan. We present temperature‐dependent correlations, as well as estimates of uncertainty, for the diffusivity ratios involving HDO, H 2 17 O, and H 2 18 O in the Martian atmosphere, and for CH 3 D and 13 CH 4 in the atmosphere of Titan, providing for the first time the necessary data to be able to model kinetic isotope fractionation in these environments.

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.

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.