Thermophysical properties of krypton- helium gas mixtures from ab initio pair potentials Cite as: J. Chem. Phys. 146, 214302 (2017); https://doi.org/10.1063/1.4984100 Submitted: 28 February 2017 . Accepted: 11 May 2017 . Published Online: 05 June 2017 Benjamin Jäger , and Eckard Bich ARTICLES YOU MAY BE INTERESTED IN State-of-the-art ab initio potential energy curve for the xenon atom pair and related spectroscopic and thermophysical properties The Journal of Chemical Physics 147, 034304 (2017); https://doi.org/10.1063/1.4994267 Intermolecular potential energy surface and thermophysical properties of propane The Journal of Chemical Physics 146, 114304 (2017); https://doi.org/10.1063/1.4978412 Nonadditive three-body potential and third to eighth virial coefficients of carbon dioxide The Journal of Chemical Physics 146, 054302 (2017); https://doi.org/10.1063/1.4974995 J. Chem. Phys. 146, 214302 (2017); https://doi.org/10.1063/1.4984100 146, 214302 © 2017 Author(s). THE JOURNAL OF CHEMICAL PHYSICS 146, 214302 (2017) Thermophysical properties of krypton-helium gas mixtures from ab initio pair potentials Benjamin Jager¨ a) and Eckard Bichb) Institut fur¨ Chemie, Universitat¨ Rostock, D-18059 Rostock, Germany (Received 28 February 2017; accepted 11 May 2017; published online 5 June 2017) A new potential energy curve for the krypton-helium atom pair was developed using supermolecular ab initio computations for 34 interatomic distances. Values for the interaction energies at the complete basis set limit were obtained from calculations with the coupled-cluster method with single, double, and perturbative triple excitations and correlation consistent basis sets up to sextuple-zeta quality augmented with mid-bond functions. Higher-order coupled-cluster excitations up to the full quadru- ple level were accounted for in a scheme of successive correction terms. Core-core and core-valence correlation effects were included. Relativistic corrections were considered not only at the scalar relativistic level but also using full four-component Dirac–Coulomb and Dirac–Coulomb–Gaunt cal- culations. The fitted analytical pair potential function is characterized by a well depth of 31.42 K with an estimated standard uncertainty of 0.08 K. Statistical thermodynamics was applied to compute the krypton-helium cross second virial coefficients. The results show a very good agreement with the best experimental data. Kinetic theory calculations based on classical and quantum-mechanical approaches for the underlying collision dynamics were utilized to compute the transport properties of krypton-helium mixtures in the dilute-gas limit for a large temperature range. The results were analyzed with respect to the orders of approximation of kinetic theory and compared with experi- mental data. Especially the data for the binary diffusion coefficient confirm the predictive quality of the new potential. Furthermore, inconsistencies between two empirical pair potential functions for the krypton-helium system from the literature could be resolved. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4984100] I. INTRODUCTION included relativistic effects beyond the scalar relativistic level and a correction for the coupled-cluster method with up to For the pure monatomic gases helium through krypton, full iterative quadruple excitations, CCSDTQ.12,13 Unexpect- thermodynamic and transport properties at low densities can be edly, the ab initio pair potentials of Waldrop et al. and Jager¨ predicted from first principles with an accuracy that is superior et al. resulted in almost indistinguishable values for the low- or at least equal to that of the best experimental techniques.1 density transport properties of krypton. Jager¨ et al. showed Highly accurate ab initio pair potentials have been developed that the perfect agreement of the viscosity data computed for in the last years for helium by Hellmann et al.2 and Cencek the potential of Waldrop et al. with the most accurate exper- et al.,3 for neon by Hellmann et al.,4 and for argon by Jager¨ imental data was partly due to a fortuitous cancellation of et al.5,6 as well as by Patkowski and Szalewicz.7 Recently, errors. two ab initio pair potentials for krypton have been presented For interactions between unlike noble gas atoms, ab initio by Waldrop et al.8 and by Jager¨ et al.9 Waldrop et al. used pair potentials have not been developed at the same level of frozen-core (FC) explicitly correlated coupled-cluster calcu- accuracy as for the like interactions. Partridge et al.14 calcu- lations to obtain interaction energies for the krypton atom pair lated interaction energies for systems containing helium and at the complete basis set (CBS) limit. They applied a cor- different ground state atoms using the frozen-core CCSD(T) rection for electronic excitations beyond the coupled-cluster method and suitable quadruple order quintuple-zeta basis sets method with single, double, and perturbative triple excita- augmented by a small set of mid-bond functions. Later, Haley tions, CCSD(T),10 using the CCSDT(Q) method of Bomble and Cybulski15 studied various combinations of noble gas et al.,11 which accounts for full triple and perturbative quadru- atoms at the same level of theory employing correlation con- ple excitations. Furthermore, they included core-core and core- sistent basis sets (aug-cc-pVXZ,16–18 abbreviated as aVXZ) valence correlation as well as scalar relativistic effects. Using of up to quintuple-zeta quality and mid-bond functions. We a new basis set of sextuple-zeta quality and standard orbital chose krypton-helium as a model system because of its large CCSD(T) computations, Jager¨ et al. calculated CBS limiting mass difference, which causes a rather strong composition values for the Kr–Kr interaction energy that are somewhat dif- dependence of the binary and thermal diffusion coefficients ferent from the results of Waldrop et al. Furthermore, they compared to the neon-helium and argon-helium systems. Thus, a meaningful test of the higher orders of approxima- a)Electronic mail: [email protected] tion to the kinetic theory can be conducted. Calculations for b)Electronic mail: [email protected] xenon-helium are not feasible at the same level of accuracy 0021-9606/2017/146(21)/214302/15/$30.00 146, 214302-1 Published by AIP Publishing. 214302-2 B. Jager¨ and E. Bich J. Chem. Phys. 146, 214302 (2017) due to the lack of suitable correlation consistent basis sets. In Sec.II, we present the details of the new ab initio Moreover, the available ab initio and empirical pair poten- pair potential for the krypton-helium atom pair. Section III tials for krypton-helium exhibit a significant disagreement is concerned with the assessment of the analytical potential with respect to their well depths. The ab initio potentials energy curve by the comparison of calculated and experimen- of Partridge et al. and Haley and Cybulski as well as the tally based values of the cross second virial coefficient. In empirical potential of Keil et al.19 are characterized by sim- Sec.IV, the kinetic theory methodology is explained, and the ilar well depths of 29.56 K, 29.84 K, and 29.45 K, respec- computed results for the coefficients of viscosity and thermal tively, whereas the earlier empirical potential of Danielson conductivity as well as of binary and thermal diffusion are 20 and Keil is considerably deeper with "=kB = 30.95 K (kB is compared with experimental data. Boltzmann’s constant). Note that Keil et al. already observed that their new potential shows, compared to the older version II. KRYPTON-HELIUM PAIR POTENTIAL of Danielson and Keil, a worse agreement of the computed values for the cross second virial coefficient with the best We computed interaction energies for 34 interatomic experimental data. A later ab initio potential of Bouazza and distances from 1.3 Å to 9.0 Å using the supermolecular Bouledroua21 is not based on any improved quantum-chemical approach including the full counterpoise correction by Boys 27 interaction energies but on the results from the two earlier and Bernardi. For helium, the correlation consistent basis studies (Refs. 14 and 15) and is therefore not considered any sets [aVXZ, X = D(2), T(3), Q(4), 5, 6] developed by Dun- 16 17 further. ning as well as by Woon and Dunning were employed. Transport property calculations for noble gas mixtures by The corresponding basis sets for krypton were introduced by 18 means of the kinetic theory of gases were limited to Lennard- Wilson et al. (aVXZ with X = D, T, Q, 5) and by Jager¨ 9 Jones-type or other simple potential models (see, for example, et al. (aV6Z). Basis sets for calculations that incorporate core- Refs. 22–24) for a long time. In the late 1980s, such computa- core and core-valence correlation effects were developed by 28 tions were performed for the more realistic but still empir- DeYonker et al. (wCVXZ with X = D, T, Q, 5; augmenting ical Hartree–Fock-dispersion-type (HFD) potentials.19,20 diffuse functions were taken from the standard aVXZ basis Partridge et al.14 were the first to use ab initio pair poten- sets). The exponents of additional diffuse functions leading tials for the interactions between unlike atoms. They computed to doubly augmented basis sets (daVXZ) were obtained in the necessary collision integrals quantum-mechanically for all an even-tempered manner from the two most diffuse basis atom pairs that include helium and applied up to fourth-order functions of each type of the corresponding aVXZ basis kinetic theory expressions for the transport properties taken sets. from the work of Mason.23,24 Unfortunately, they analyzed At the center between the krypton and the helium atom, their results only marginally regarding the influence of differ- additional bond functions were placed to improve the conver- ent orders of approximation to the kinetic theory solutions.