An Analysis of the Accuracy of the Calculation of the Second Virial Coefficient of Helium from Interatomic Potential Functions

McConville, G. T.; Hurly, John J.

doi:10.1088/0026-1394/28/5/002

Cited by 13 publications

(9 citation statements)

References 26 publications

(22 reference statements)

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“…Numerical integration was performed using Simpson's method together with a cubic spline interpolator. 36,37 Integrated results were confirmed to be within 4-5 significant figures. …”

Section: The Quantum Scattering Calculationmentioning

confidence: 75%

Quantum second virial coefficient calculation for the 4He dimer on a recent potential

Costa¹,

Lemes²,

Alves³

et al. 2013

J. Braz. Chem. Soc.

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Este trabalho concentra-se no cálculo do segundo coeficiente virial quântico, a partir de um potencial desenvolvido recentemente. Este coeficiente foi determinado com 4-5 algarismos significativos na faixa de temperatura de 3 a 100 K. Nossos resultados estão dentro do erro experimental. Três contribuições para o valor total deste coeficiente são o espalhamento quântico (contribuição de estados no contínuo), o estado ligado (contribuição de estados discretos) e o gás ideal quântico; discutimos estas contribuições separadamente. A contribuição mais importante é do espalhamento quântico, enquanto que as contribuições menores são dos estados discretos. Uma análise da sensibilidade foi realizada em função da temperatura para um parâmetro na região de curto alcance do potencial e para três parâmetros na região de longo alcance do potencial. Para ambas as temperaturas consideradas, 10 e 100 K, o coeficiente de dispersão C 6 foi o mais significativo, e o termo dispersão C 10 foi o menos significativo para o resultado total. Em geral, a precisão exigida para descrever os potenciais diminui com o aumento da temperatura. A precisão total e a relação dos parâmetros com os erros experimentais são discutidas. This paper focuses on the calculation of the quantum second virial coefficient, under a recently developed potential. This coefficient was determined to within 4-5 significant figures in the temperature range from 3 to 100 K. Our results are within experimental error. The three contributions to the overall value of the coefficient are the quantum scattering (continuum state contribution), the bound state (discrete state contribution) and the quantum ideal gas; we discuss these contributions separately. The most significant contribution is from the scattering states, whereas the smaller contributions are from the discrete states. A sensitivity analysis was performed as a function of temperature for one parameter in the short-range region of the potential and for three parameters in the long-range regions of the potential. For both temperatures considered, 10 and 100 K, the C 6 dispersion coefficient was the most significant, and the C 10 dispersion term was the least significant to the overall result. In general, the precision required to describe the potential decays as the temperature increases. The overall accuracy and the relationship of the parameters to the experimental errors are discussed.

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“…Numerical integration was performed using Simpson's method together with a cubic spline interpolator. 36,37 Integrated results were confirmed to be within 4-5 significant figures. …”

Section: The Quantum Scattering Calculationmentioning

confidence: 75%

Quantum second virial coefficient calculation for the 4He dimer on a recent potential

Costa¹,

Lemes²,

Alves³

et al. 2013

J. Braz. Chem. Soc.

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“…For that purpose nodes of the outgoing waves located at R n of the nth zero far from the scattering centre have to be used. McConville and Hurly [14] discussed problems in the evaluation of the phase shifts in connection with two codes available in the literature [15,16] and recommended to determine the phase shifts using the relation…”

Section: Evaluation Of the Phase Shiftsmentioning

confidence: 99%

Ab initiopotential energy curve for the helium atom pair and thermophysical properties of the dilute helium gas. II. Thermophysical standard values for low-density helium

2007

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To cite this version:Eckhard Vogel, Eckard Bich, Robert Hellmann. Ab initio potential energy curve for the helium atom pair and thermophysical properties of the dilute helium gas. II. Thermophysical standard values for low-density helium. Molecular Physics, Taylor & Francis, 2007, 105 (23-24) A helium-helium interatomic potential energy curve determined from quantum-mechanical ab initio calculations and described with an analytical representation considering relativistic retardation effects (R. Hellmann, E. Bich, and E. Vogel, Mol. Phys. (submitted)) was used in the framework of the quantum-statistical mechanics and of the corresponding kinetic theory to calculate the most important thermophysical properties of helium governed by two-body and three-body interactions. The second pressure virial coefficient as well as the viscosity and thermal conductivity coefficients, the last two in the so-called limit of zero density, were calculated for 3 He and 4 He from 1 K to 10,000 K and the third pressure virial coefficient for 4 He from 20 K to 10,000 K. The transport property values can be applied as standard values for the complete temperature range of the calculations characterized by an uncertainty of ±0.02% for temperatures above 15 K. This uncertainty is superior to the best experimental measurements at ambient temperature.

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“…Figure 6 compares B exp ( T ) of 3 He, deduced from the measurements of Matacotta et al [ 47 ], with B 00 ( T ). There is an obvious trend in the deviations which is larger than the experimental uncertainties below 5 K. Probably, the trend would be removed if B exp ( T ) was corrected for the for effects of the third virial coefficient of 3 He [ 48 ] as discussed above for 4 He [ 42 ].…”

Section: Comparison With Measurementsmentioning

confidence: 99%

Ab initio values of the thermophysical properties of helium as standards

Hurly¹,

Moldover²

2000

J. Res. Natl. Inst. Stand. Technol.

146

136

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Recent quantum mechanical calculations of the interaction energy of pairs of helium atoms are accurate and some include reliable estimates of their uncertainty. We combined these ab initio results with earlier published results to obtain a helium-helium interatomic potential that includes relativistic retardation effects over all ranges of interaction. From this potential, we calculated the thermophysical properties of helium, i.e., the second virial coefficients, the dilute-gas viscosities, and the dilute-gas thermal conductivities of 3He, 4He, and their equimolar mixture from 1 K to 104 K. We also calculated the diffusion and thermal diffusion coefficients of mixtures of 3He and 4He. For the pure fluids, the uncertainties of the calculated values are dominated by the uncertainties of the potential; for the mixtures, the uncertainties of the transport properties also include contributions from approximations in the transport theory. In all cases, the uncertainties are smaller than the corresponding experimental uncertainties; therefore, we recommend the ab initio results be used as standards for calibrating instruments relying on these thermophysical properties. We present the calculated thermophysical properties in easy-to-use tabular form.

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An Analysis of the Accuracy of the Calculation of the Second Virial Coefficient of Helium from Interatomic Potential Functions

Cited by 13 publications

References 26 publications

Quantum second virial coefficient calculation for the 4He dimer on a recent potential

Quantum second virial coefficient calculation for the 4He dimer on a recent potential

Ab initiopotential energy curve for the helium atom pair and thermophysical properties of the dilute helium gas. II. Thermophysical standard values for low-density helium

Ab initio values of the thermophysical properties of helium as standards

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