Thermodynamik

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 cross second virial coefficients B₁₂ for the interactions of water (H₂O) with hydrogen sulfide (H₂S) and of water with sulfur dioxide (SO₂) were determined at temperatures from 200 to 2000 K employing new intermolecular potential energy surfaces (PESs) for the H₂O-H₂S and H₂O-SO₂ molecule pairs. The PESs were fitted to interaction energies calculated for more than 50 000 configurations of each molecule pair using quantum-chemical ab initio methods up to coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] with consideration of relativistic effects. The B₁₂ values were extracted from the PESs both classically and semiclassically using the Mayer-sampling Monte Carlo scheme. In addition, accurate correlations of the final B₁₂ values were used to derive the dilute gas cross isothermal Joule-Thomson coefficients, ϕ₁₂ = B₁₂ - T(dB₁₂/dT). For both investigated systems, Wormald provided the only experimentally based B₁₂ and ϕ₁₂ values available in the literature. While his B₁₂ values, which he obtained from the ϕ₁₂ data with the aid of model potentials, are not in satisfying agreement with the present B₁₂ values, his ϕ₁₂ data, after a reanalysis using more accurate pure-component ϕ values, agree very well with the calculated ϕ₁₂ values of this work.

The cross second virial coefficien 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.

In dieser Arbeit wurden Monte-Carlo-Simulationen für die Fluide Krypton, Argon, Stickstoff und Kohlendioxid durchgeführt, um ihre thermodynamischen Eigenschaften sehr genau zu bestimmen und dabei den Einfluss von nichtadditiven Dreikörperwechselwirkungen und Quanteneffekten auf die Ergebnisse zu untersuchen. In der statistischen Mechanik existieren acht grundlegende Ensembles, in denen Monte-Carlo-Simulationen durchgeführt werden können. Von Lustig wurde eine Methode entwickelt, mit der Ausdrücke zur Berechnung von Zustandsgrößen in einem Ensemble systematisch hergeleitet werden können, und von ihm genutzt, um Gleichungen zur Berechnung thermodynamischer Eigenschaften im mikrokanonischen und kanonischen Ensemble herzuleiten. Diese Methode wurde zuerst auf die anderen sechs Ensembles, darunter das häufig verwendete isotherm-isobare und das großkanonische Ensemble, angewendet. Anschließend wurde eine Software für Monte-Carlo-Simulationen in allen acht Ensembles entwickelt. Mit Simulationen für das gut untersuchte Lennard-Jones-Modellfluid wurden die hergeleiteten Gleichungen validiert. Zur Berechnung der Eigenschaften realer Fluide erweist sich das NpT-Ensemble als am besten geeignet. Da der Druck eine unabhängige Variable ist, treten in den Gleichungen keine Volumenableitungen der potentiellen Energie auf, deren Berechnung insbesondere bei der Berücksichtigung von nichtadditiven Dreikörperwechselwirkungen sehr aufwendig ist. Die Simulationsergebnisse für die vier realen Fluide zeigen, dass nichtadditive Dreikörperwechselwirkungen im gesamten fluiden Zustandsgebiet einen erheblichen Beitrag zu den Zustandsgrößen liefern, der im Flüssigkeitsgebiet in der Nähe der Siedelinie am stärksten ausgeprägt ist. Sie tragen dort bis zu ca. 15% zur Dichte und bis zu ca. 50% zu Zustandsgrößen zweiter Ordnung bei. Die Korrekturen für Quanteneffekte tragen je nach betrachtetem Fluid und Zustandspunkt bis zu 0,5% zur Dichte und bis zu 3,5% zu den thermodynamischen Eigenschaften zweiter Ordnung bei. Durch die Berücksichtigung beider Einflüsse gelingt es, eine sehr gute Übereinstimmung der Simulationsdaten mit experimentellen Daten und Zustandsgleichungen zu erzielen. Die genauesten Ergebnisse wurden für die Dichte von Argon generiert. Sie stimmen zwischen 0,002% im Flüssigkeitsgebiet und 0,05% im überkritischen Gebiet mit der Referenzzustandsgleichung überein. Darüber hinaus wurde die NpT + Testteilchenmethode zur Simulation von Verdampfungsgleichgewichten weiterentwickelt, um auch beliebige Zustandsgrößen auf der Siede- und Taulinie zu berechnen. Ergebnisse für den Dampfdruck, die Dichte und acht weitere Zustandsgrößen auf der Siede- und Taulinie für Krypton und Argon weisen eine hohe Übereinstimmung mit experimentellen Daten auf. Mit der Kombination von hochgenauen ab initio-Potentialen, sehr langen Simulationen im NpT-Ensemble mit verschiedenen Teilchenzahlen und anschließender Extrapolation ins thermodynamische Limit gelingt es, Ergebnisse für thermodynamische Eigenschaften zu generieren, die mit den genauesten experimentellen Daten und Referenzzustandsgleichungen nicht nur qualitativ, sondern auch quantitativ sehr genau übereinstimmen.

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.

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 International Association for the Properties of Water and Steam has adopted new formulations for the thermodynamic and transport properties of heavy water. This manuscript describes the development of a formulation for the thermal conductivity of heavy water that was adopted as an international standard in 2021. It is consistent with the equation of state adopted in 2017, revised slightly in 2018, and is valid for fluid states up to 825 K and 250 MPa with uncertainties ranging from 1.5% to 6% depending on the state point. Comparisons with experimental data and with an earlier thermal-conductivity formulation are presented. The 2021 formulation accounts for the critical enhancement of the thermal conductivity, which was not incorporated in the previous formulation. Furthermore, in the zero-density limit, the 2021 formulation is based on thermal conductivity values at temperatures from 250 to 2500 K obtained from the kinetic theory of polyatomic gases. In addition, the 2021 formulation is applicable in a larger range of pressures than the previous formulation.

The cross second virial coefficient B12 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 B12 was extracted from the PES using a semiclassical approach. An accurate correlation of the calculated B12 values was used to determine the dilute gas cross isothermal Joule–Thomson coefficient, ϕ12= B12- T(d B12/ d T). The predicted values for both B12 and ϕ12 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.

The static electric-dipole polarizability α 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, α=2.661067(77)a.u., is almost five times more accurate than the previous ab initio estimate, α=2.66080(36)a.u., by Lesiuk et al. [Phys. Rev. A 102, 052816 (2020)2469-992610.1103/PhysRevA.102.052816]. Similar to their work, we calculated α 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)0031-900710.1103/PhysRevLett.120.123203] with an uncertainty of only a few parts per million using dielectric-constant gas thermometry. Yet, our ab initio value agrees with their value, αexp=2.66057(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.