Cluster integrals and virial coefficients for realistic molecular models

Wheatley, Richard J.; Schultz, Andrew J.; Do, Hainam; Gokul, Navneeth; Kofke, David A.

doi:10.1103/physreve.101.051301

Cited by 12 publications

(16 citation statements)

References 49 publications

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“…Rather than direct evaluation of the sum as suggested in Equation ), a more efficient recursive algorithm due to Wheatley 15 is available to compute the integrand, f B . This algorithm can be modified to evaluate temperature derivatives of virial coefficients in the same Mayer‐sampling calculation 5 . A general framework for evaluating virial coefficients and their derivatives via Mayer sampling and Wheatley recursion is implemented in etomica 16 …”

Section: Models and Methodsmentioning

confidence: 99%

“…The product is over all pairs of molecules ij in a single biconnected graph. Hence, B klmn can be evaluated directly as sum of "diagram integrals" using Equation (5). There are 2 N(N − 1)/2 possible graphs, and for large N, most of them are biconnected.…”

Section: Virial Coefficientsmentioning

confidence: 99%

“…Figure 10 (a) compares B 0011 computed according to Equation (5) against experimental values for the same from Wormald and Wurzberger. 30 Consistent with previous observations, B 0011 is overestimated by the TraPPE model.…”

Section: Co 2 −Nhmentioning

confidence: 99%

“…In particular, for a four-component mixture, the dependence for the Nth virial coefficient is The VEOS is appealing because it has a direct connection to molecular behavior, in that the coefficients can be computed rigorously given a force-field model for the intermolecular interactions. [1][2][3][4][5] Hence, starting with a good molecular model, we can develop an accurate thermodynamic model that has all the correct dependencies on temperature, mole fractions, and density. The key limitation of the VEOS is that it is restricted to non-condensed phases, and that it fails at sufficiently high density.…”

Section: Introductionmentioning

confidence: 99%

“…The VEOS is appealing because it has a direct connection to molecular behavior, in that the coefficients can be computed rigorously given a force‐field model for the intermolecular interactions 1‐5 . Hence, starting with a good molecular model, we can develop an accurate thermodynamic model that has all the correct dependencies on temperature, mole fractions, and density.…”

Section: Introductionmentioning

confidence: 99%

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Properties of supercritical N₂, O₂, CO₂, and NH₃ mixtures from the virial equation of state

2020

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We report virial coefficients up to sixth order in density for N 2 , O 2 , NH 3 , and CO 2 , covering temperatures from 50 to 1,000 K. The reported values include coefficients and their first three temperature derivatives, for the pure species as well as all of those needed to evaluate full composition dependence of mixtures formed from any or all of these compounds. The values are obtained by calculation of appropriate cluster integrals using Mayer sampling Monte Carlo, with intermolecular interactions described by the Transferable Potential for Phase Equilibria (TraPPE) force field. All coefficients are fit as a function of temperature, yielding a thermodynamic model with analytic dependence on temperature, density, and composition. The coefficients and properties computed from them are compared to experimental data where available.

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Section: Models and Methodsmentioning

confidence: 99%

Section: Virial Coefficientsmentioning

confidence: 99%

Section: Co 2 −Nhmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Properties of supercritical N₂, O₂, CO₂, and NH₃ mixtures from the virial equation of state

2020

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Speed of Sound in Helium-4 from Ab Initio Acoustic Virial Coefficients

2021

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We present values for 4He of temperature-dependent acoustic virial coefficients that appear in series expansions for the speed of sound in the gas (AVEOS). Coefficients are computed from first-principles molecular models from the literature and are presented for expansions both in density and in pressure. These coefficients, labeled here as Ω n and ω n , respectively, are determined from previously reported values of the pressure virials B n as a function of temperature T. Data are provided for T from 2.6 to 1000 K and for n from 2 to 7; those for n = 2–5 include nuclear quantum effects but not exchange, and those for n = 6 and 7 are semiclassical. Analysis of experimental data for the speed of sound from the literature is performed to estimate thermodynamic temperatures, to regress coefficient values to compare to ab initio results, and to evaluate the performance of the AVEOS for pressures up to 1000 MPa. A study of the convergence of the series shows that the pressure-expanded AVEOS diverges at about 100 MPa, while the density-expanded series appears to remain convergent over the entire pressure range; at the highest pressures, the seventh-order series still yields results that are within 1% of the correct value of the speed of sound, at least when applied at temperatures above 200 K.

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Virial Coefficients of Helium-4 from Ab Initio-Based Molecular Models

Schultz

Kofke

2019

J. Chem. Eng. Data

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We examine the accuracy of virial coefficients B n (T) for 4He for n = 2–7 and temperatures T from 20 to 1000 K while reporting new values from semiclassical and (for n = 5) path-integral Monte Carlo (PIMC) calculations. All coefficients are based on first-principles two- and three-body molecular models from the literature and have estimated stochastic and systematic uncertainty between 0.005 and 20%, depending on n and T (almost all of this due to estimated inaccuracy in the three-body model). The calculated B n (T) are used to examine the virial equation of state (VEOS) against experimental data from the literature, from 223.15 to 500 K and pressures up to 38 MPa. First, the VEOS is used to calibrate the data, providing adjustments not exceeding the data’s estimated systematic uncertainty. Then, findings from the comparison include the following: (1) the VEOS based on the ab initio B n (T) is fully consistent with the experimental data; (2) the series requires coefficients up to n = 5 in order to agree with experiment within all relevant uncertainties; (3) individual values B k (T) can be regressed accurately from the experimental data if other coefficients B n (T), n ≠ k, are given from the ab initio calculations; however, the uncertainty of these values is less than the coefficient magnitude only for k ≤ 5.

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Cluster integrals and virial coefficients for realistic molecular models

Cited by 12 publications

References 49 publications

Properties of supercritical N₂, O₂, CO₂, and NH₃ mixtures from the virial equation of state

Properties of supercritical N₂, O₂, CO₂, and NH₃ mixtures from the virial equation of state

Speed of Sound in Helium-4 from Ab Initio Acoustic Virial Coefficients

Virial Coefficients of Helium-4 from Ab Initio-Based Molecular Models

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Cluster integrals and virial coefficients for realistic molecular models

Cited by 12 publications

References 49 publications

Properties of supercritical N2, O2, CO2, and NH3 mixtures from the virial equation of state

Properties of supercritical N2, O2, CO2, and NH3 mixtures from the virial equation of state

Speed of Sound in Helium-4 from Ab Initio Acoustic Virial Coefficients

Virial Coefficients of Helium-4 from Ab Initio-Based Molecular Models

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Product

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Properties of supercritical N₂, O₂, CO₂, and NH₃ mixtures from the virial equation of state

Properties of supercritical N₂, O₂, CO₂, and NH₃ mixtures from the virial equation of state