Third and fourth density and acoustic virial coefficients of neon from first-principles calculations

TL;DR

This study advances first-principles predictions of neon thermophysical properties by combining a high-accuracy ab initio pair potential with newly developed nonadditive three- and four-body potentials in path-integral Monte Carlo calculations. It delivers direct quantum estimates of the third and fourth density virial coefficients $C(T)$ and $D(T)$ and the third and fourth acoustic virial coefficients $RT\gamma_a(T)$ and $(RT)^2\delta_a(T)$ for temperatures from 10 to 5000 K, with rigorously propagated uncertainties. The work shows that nonadditive three-body effects are substantial for $C(T)$ and become increasingly important at higher temperatures, while four-body contributions are small; overall, the results agree with experimental data where available and provide improved benchmarks over previous semiclassical approaches. The authors supply analytical fits and Fortran codes to enable use of these coefficients in metrology and high-precision thermophysical modeling of neon as a working gas.

Abstract

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 $\textit{et al.}$ [J. Chem. Phys. 154, 164304 (2021)], which is based on supermolecular $\textit{ab initio}$ 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.

Figures (9)

• Figure 1: Ab initio neon pair potential as reported by Hellmann et al.Hellmann:2021
• Figure 2: The 156 triangular shapes considered for the quantum-chemical ab initio calculations of nonadditive three-body interaction energies, shown here by the respective positions of neon atom 3 relative to the positions of neon atoms 1 and 2, whose positions were arbitrarily chosen to be at the origin and on the positive $x$ axis, respectively.
• Figure 3: Nonadditive three-body interaction energies obtained with the fitted potential function versus the respective ab initio calculated values for different energy ranges [(a) to (f)].
• Figure 4: Nonadditive three-body interaction energies obtained from the quantum-chemical ab initio calculations, from the fitted potential function, and from the simple ATM potential for two of the 156 investigated triangular shapes: (a) equilateral triangles, (b) symmetric linear configurations.
• Figure 5: Nonadditive four-body interaction energies for regular tetrahedra of neon atoms obtained from the quantum-chemical ab initio calculations, from the fitted extended Bade potential function, and from the simple Bade potential.