arXiv subjects

Robert Hellmann

Publications and source records attributed to Robert Hellmann.

3 recordsLinked to original sources

arXiv2026

Recommended Second Virial Coefficients for Nitrogen and Oxygen

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.

physics.chem-ph↗

arXiv2026

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

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.

physics.chem-ph↗

arXiv2023

Ab initio Calculation of Fluid Properties for Precision Metrology

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.

cond-mat.stat-mech↗