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.

Intermolecular potential energy surface and thermophysical properties of the CH4-N2 system.

A five-dimensional potential energy surface (PES) for the interaction of a rigid methane molecule with a rigid nitrogen molecule was determined from quantum-chemical ab initio calculations. The counterpoise-corrected supermolecular approach at the CCSD(T) level of theory was utilized to compute a total of 743 points on the PES. The interaction energies were calculated using basis sets of up to quadruple-zeta quality with bond functions and were extrapolated to the complete basis set limit. An analytical site-site potential function with nine sites for methane and five sites for nitrogen was fitted to the interaction energies. The PES was validated by calculating the cross second virial coefficient as well as the shear viscosity and binary diffusion coefficient in the dilute-gas limit for CH4-N2 mixtures. An improved PES was obtained by adjusting a single parameter of the analytical potential function in such a way that quantitative agreement with the most accurate experimental values of the cross second virial coefficient was achieved. The transport property values obtained with the adjusted PES are in good agreement with the best experimental data.

Ab initio intermolecular potential energy surface and thermophysical properties of hydrogen sulfide.

A six-dimensional potential energy hypersurface (PES) for two interacting rigid hydrogen sulfide molecules was determined from high-level quantum-mechanical ab initio computations. A total of 4016 points for 405 different angular orientations of two molecules were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory and extrapolating the calculated interaction energies to the complete basis set limit. An analytical site-site potential function with eleven sites per hydrogen sulfide molecule was fitted to the interaction energies. The PES has been validated by computing the second pressure virial coefficient, shear viscosity, thermal conductivity and comparing with the available experimental data. The calculated values of volume viscosity were not used to validate the potential as the low accuracy of the available data precluded such an approach. The second pressure virial coefficient was evaluated by means of the Takahashi and Imada approach, while the transport properties, in the dilute limit, were evaluated by utilizing the classical trajectory method. In general, the agreement with the primary experimental data is within the experimental error for temperatures higher than 300 K. For lower temperatures the lack of reliable data indicates that the values of the second pressure virial coefficient and of the transport properties calculated in this work are currently the most accurate estimates for the thermophysical properties of hydrogen sulfide.

Ab initio virial equation of state for argon using a new nonadditive three-body potential.

An ab initio nonadditive three-body potential for argon has been developed using quantum-chemical calculations at the CCSD(T) and CCSDT levels of theory. Applying this potential together with a recent ab initio pair potential from the literature, the third and fourth to seventh pressure virial coefficients of argon were computed by standard numerical integration and the Mayer-sampling Monte Carlo method, respectively, for a wide temperature range. All calculated virial coefficients were fitted separately as polynomials in temperature. The results for the third virial coefficient agree with values evaluated directly from experimental data and with those computed for other nonadditive three-body potentials. We also redetermined the second and third virial coefficients from the best experimental pρT data utilizing the computed higher virial coefficients as constraints. Thus, a significantly closer agreement of the calculated third virial coefficients with the experimental data was achieved. For different orders of the virial expansion, pρT data have been calculated and compared with results from high quality measurements in the gaseous and supercritical region. The theoretically predicted pressures are within the very small experimental errors of ±0.02% for p ≤ 12 MPa in the supercritical region near room temperature, whereas for subcritical temperatures the deviations increase up to +0.3%. The computed pressure at the critical density and temperature is about 1.3% below the experimental value. At pressures between 200 MPa and 1000 MPa and at 373 K, the calculated values deviate by 1% to 9% from the experimental results.

Calculation of the transport and relaxation properties of methane. II. Thermal conductivity, thermomagnetic effects, volume viscosity, and nuclear-spin relaxation.

Transport properties of pure methane have been calculated in the rigid-rotor approximation using the recently proposed intermolecular potential energy hypersurface [R. Hellmann et al., J. Chem. Phys. 128, 214303 (2008)] and the classical-trajectory method. Results are reported in the dilute-gas limit for the temperature range of 80-1500 K. The calculated thermal conductivity values are in very good agreement with the measured data and correlations. In the temperature range of 310-480 K the calculated values underestimate the best experimental data by 0.5%-1.0%. We suggest that the calculated values are more accurate, especially at low and high temperatures, than the currently available correlations based on the experimental data. Our results also agree well with measurements of thermal transpiration and of the thermomagnetic coefficients. We have shown that although the dominant contribution to the thermomagnetic coefficients comes from the Wjj polarization in the spherical approximation, the contribution of a second polarization, Wj, cannot be neglected nor can a full description of the Wjj polarization. The majority of the volume viscosity measurements around room temperature are consistent with the calculated values but this is not the case at high and low temperatures. However, for nuclear-spin relaxation the calculated values consistently exceed the measurements, which are mutually consistent within a few percent.

Calculation of the transport and relaxation properties of dilute water vapor.

Transport properties of dilute water vapor have been calculated in the rigid-rotor approximation using four different potential energy hypersurfaces and the classical-trajectory method. Results are reported for shear viscosity, self-diffusion, thermal conductivity, and volume viscosity in the dilute-gas limit for the temperature range of 250-2500 K. Of these four surfaces the CC-pol surface of Bukowski et al. [J. Chem. Phys. 128, 094314 (2008)] is in best accord with the available measurements. Very good agreement is found with the most accurate results for viscosity in the whole temperature range of the experiments. For thermal conductivity the deviations of the calculated values from the experimental data increase systematically with increasing temperature to around 5% at 1100 K. For both self-diffusion and volume viscosity, the much more limited number of available measurements are generally consistent with the calculated values, apart from the lower temperature isotopically labeled diffusion measurements.

Ab initio intermolecular potential energy surface and second pressure virial coefficients of methane.

A six-dimensional potential energy hypersurface (PES) for two interacting rigid methane molecules was determined from high-level quantum-mechanical ab initio computations. A total of 272 points for 17 different angular orientations on the PES were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory with basis sets of aug-cc-pVTZ and aug-cc-pVQZ qualities. The calculated interaction energies were extrapolated to the complete basis set limit. An analytical site-site potential function with nine sites per methane molecule was fitted to the interaction energies. In addition, a semiempirical correction to the analytical potential function was introduced to take into account the effects of zero-point vibrations. This correction includes adjustments of the dispersion coefficients and of a single-parameter within the fit to the measured values of the second virial coefficient B(T) at room temperature. Quantitative agreement was then obtained with the measured B values over the whole temperature range of the measurements. The calculated B values should definitely be more reliable at very low temperatures (T<150 K) than values extrapolated using the currently recommended equation of state.

Calculation of the transport and relaxation properties of methane. I. Shear viscosity, viscomagnetic effects, and self-diffusion.

Transport properties of pure methane gas have been calculated in the rigid-rotor approximation using the recently proposed intermolecular potential energy hypersurface [R. Hellmann et al., J. Chem. Phys. 128, 214303 (2008)] and the classical-trajectory method. Results are reported in the dilute-gas limit for shear viscosity, viscomagnetic coefficients, and self-diffusion in the temperature range of 80-1500 K. Compared with the best measurements, the calculated viscosity values are about 0.5% too high at room temperature, although the temperature dependence of the calculated values is in very good agreement with experiment between 210 and 390 K. For the shear viscosity, the calculations indicate that the corrections in the second-order approximation and those due to the angular-momentum polarization are small, less than 0.7%, in the temperature range considered. The very good agreement of the calculated values with the experimental viscosity data suggests that the rigid-rotor approximation should be very reasonable for the three properties considered. In general, the agreement for the other measured properties is within the experimental error.

Calculation of the transport properties of carbon dioxide. III. Volume viscosity, depolarized Rayleigh scattering, and nuclear spin relaxation.

Transport properties of pure carbon dioxide have been calculated from the intermolecular potential using the classical trajectory method. Results are reported in the dilute-gas limit for volume viscosity, depolarized Rayleigh scattering, and nuclear spin relaxation for temperatures ranging from 200 to 1000 K. Three recent carbon dioxide potential energy hypersurfaces have been investigated. Calculated values for the rotational collision number for all three intermolecular surfaces are consistent with the measurements and indicate that the temperature dependence of the Brau-Jonkman correlation is not applicable for carbon dioxide. The results for the depolarized Rayleigh scattering cross section and the nuclear spin relaxation cross section show that calculated values for the generally more successful potentials differ from the observations by 9% at about 290 K, although agreement is obtained for nuclear spin relaxation at about 400 K.

Calculation of the transport properties of carbon dioxide. II. Thermal conductivity and thermomagnetic effects.

The transport properties of pure carbon dioxide have been calculated from the intermolecular potential using the classical trajectory method. Results are reported in the dilute-gas limit for thermal conductivity and thermomagnetic coefficients for temperatures ranging from 200 K to 1000 K. Three recent carbon dioxide potential energy hypersurfaces have been investigated. Since thermal conductivity is influenced by vibrational degrees of freedom, not included in the rigid-rotor classical trajectory calculation, a correction for vibration has also been employed. The calculations indicate that the second-order thermal conductivity corrections due to the angular momentum polarization (< 2%) and velocity polarization (< 1%) are both small. Thermal conductivity values calculated using the potential energy hypersurface by Bukowski et al. (1999) are in good agreement with the available experimental data. They underestimate the best experimental data at room temperature by 1% and in the range up to 470 K by 1%-3%, depending on the data source. Outside this range the calculated values, we believe, may be more reliable than the currently available experimental data. Our results are consistent with measurements of the thermomagnetic effect at 300 K only when the vibrational degrees of freedom are considered fully. This excellent agreement for these properties indicates that particularly the potential surface of Bukowski et al. provides a realistic description of the anisotropy of the surface.