Three-body potential and third virial coefficients for helium including relativistic and nuclear-motion effects

Lang, Jakub; Garberoglio, Giovanni; Przybytek, Michał; Jeziorska, Małgorzata; Jeziorski, Bogumił

doi:10.1039/d3cp01794j

Cited by 6 publications

(7 citation statements)

References 101 publications

(281 reference statements)

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“…Table 2 reports the values of the uncertainty of D ( T ) propagated from the uncertainties of the potentials. With respect to previous calculations, the use of an improved three-body potential 7 resulted in a reduction of the corresponding propagated uncertainty by a factor of approximately 4 across the whole temperature range investigated here. Nevertheless, the largest contribution to the uncertainty of D ( T ) comes from the propagated uncertainty from the four-body potential.…”

Section: Methodsmentioning

confidence: 66%

“… a u ( V 2 ): pair potential, 6 u ( V 3 ): three-body potential, 7 u ( V 4 ): four-body potential of this work. The numbers in parentheses are the standard uncertainties from the PIMC calculation.…”

Section: Methodsmentioning

confidence: 99%

“…Calculation of C ( T ) requires a three-body potential. With six electrons on which to perform computations, and three dimensions instead of one, the three-body potential cannot be calculated with the same accuracy as the pair potential, but recent work has produced a surface with uncertainties on the order of 1%. The values calculated for C ( T ) from this three-body potential and the state-of-the-art two-body potential similarly have uncertainties more than an order of magnitude smaller than those from experiment. , …”

Section: Introductionmentioning

confidence: 99%

“…The values calculated for C(T) from this three-body potential and the state-of-the-art two-body potential similarly have uncertainties more than an order of magnitude smaller than those from experiment. 7,8 At higher pressures, the fourth virial coefficient D(T) begins to become significant. Garberoglio and Harvey 9 available at the time, but they had to assume the four-body nonadditive contribution to be zero due to the lack of a fourbody potential.…”

Section: ■ Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Four-Body Nonadditive Potential Energy Surface and the Fourth Virial Coefficient of Helium

Wheatley,

Garberoglio,

Harvey

2023

J. Chem. Eng. Data

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The four-body nonadditive contribution to the energy of four helium atoms is calculated and fitted for all geometries for which the internuclear distances exceed a small minimum value. The interpolation uses an active learning approach based on Gaussian processes. Asymptotic functions are used to calculate the nonadditive energy when the four helium atoms form distinct subclusters. The resulting four-body potential is used to compute the fourth virial coefficient D ( T ) for helium, at temperatures from 10 to 2000 K, with a path-integral approach that fully accounts for quantum effects. The results are in reasonable agreement with the limited and scattered experimental data for D ( T ), but our calculated results have much smaller uncertainties.

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Section: Methodsmentioning

confidence: 66%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Four-Body Nonadditive Potential Energy Surface and the Fourth Virial Coefficient of Helium

Wheatley,

Garberoglio,

Harvey

2023

J. Chem. Eng. Data

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Ab Initio Calculation of Fluid Properties for Precision Metrology

Garberoglio,

Gaiser,

Gavioso

et al. 2023

Journal of Physical and Chemical Reference Data

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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 thermodynamic 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.

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Third density and acoustic virial coefficients of helium isotopologues from ab initio calculations

Binosi,

Garberoglio,

Harvey

2024

The Journal of Chemical Physics

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Improved two-body and three-body potentials for helium have been used to calculate from first principles the third density and acoustic virial coefficients for both 4He and 3He. For the third density virial coefficient C(T), uncertainties have been reduced by a factor of 4–5 compared to the previous state of the art; the accuracy of first-principles C(T) now exceeds that of the best experiments by more than two orders of magnitude. The range of calculations has been extended to temperatures as low as 0.5 K. For the third acoustic virial coefficient γa(T), we applied the Schlessinger point method, which can calculate γa and its uncertainty based on the C(T) data, overcoming some limitations of direct path-integral calculation. The resulting γa are calculated at temperatures down to 0.5 K; they are consistent with available experimental data but have much smaller uncertainties. The first-principles data presented here will enable improvement of primary temperature and pressure metrology based on gas properties.

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Three-body potential and third virial coefficients for helium including relativistic and nuclear-motion effects

Abstract: The non-additive three-body interaction potential for helium was computed using the coupled-cluster theory and the full configuration interaction method. The obtained potential comprises an improved nonrelativistic Born--Oppenheimer energy and the...

Cited by 6 publications

References 101 publications

Four-Body Nonadditive Potential Energy Surface and the Fourth Virial Coefficient of Helium

Four-Body Nonadditive Potential Energy Surface and the Fourth Virial Coefficient of Helium

Ab Initio Calculation of Fluid Properties for Precision Metrology

Third density and acoustic virial coefficients of helium isotopologues from ab initio calculations

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