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Mahynski NA, Hatch HW, Witman M, Sheen DA, Errington JR, Shen VK. Flat-histogram extrapolation as a useful tool in the age of big data. MOLECULAR SIMULATION 2020. [DOI: 10.1080/08927022.2020.1747617] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Nathan A. Mahynski
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA
| | - Harold W. Hatch
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA
| | | | - David A. Sheen
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA
| | - Jeffrey R. Errington
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, NY, USA
| | - Vincent K. Shen
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA
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Mahynski NA, Jiao S, Hatch HW, Blanco MA, Shen VK. Predicting structural properties of fluids by thermodynamic extrapolation. J Chem Phys 2018; 148:194105. [PMID: 30307179 PMCID: PMC6183068 DOI: 10.1063/1.5026493] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We describe a methodology for extrapolating the structural properties of multicomponent fluids from one thermodynamic state to another. These properties generally include features of a system that may be computed from an individual configuration such as radial distribution functions, cluster size distributions, or a polymer's radius of gyration. This approach is based on the principle of using fluctuations in a system's extensive thermodynamic variables, such as energy, to construct an appropriate Taylor series expansion for these structural properties in terms of intensive conjugate variables, such as temperature. Thus, one may extrapolate these properties from one state to another when the series is truncated to some finite order. We demonstrate this extrapolation for simple and coarse-grained fluids in both the canonical and grand canonical ensembles, in terms of both temperatures and the chemical potentials of different components. The results show that this method is able to reasonably approximate structural properties of such fluids over a broad range of conditions. Consequently, this methodology may be employed to increase the computational efficiency of molecular simulations used to measure the structural properties of certain fluid systems, especially those used in high-throughput or data-driven investigations.
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Affiliation(s)
- Nathan A. Mahynski
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA
| | - Sally Jiao
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Harold W. Hatch
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA
| | - Marco A. Blanco
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA
- Institute for Bioscience and Biotechnology Research, University of Maryland, Rockville, Maryland 20850, USA
| | - Vincent K. Shen
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA
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Hatch HW, Jiao S, Mahynski NA, Blanco MA, Shen VK. Communication: Predicting virial coefficients and alchemical transformations by extrapolating Mayer-sampling Monte Carlo simulations. J Chem Phys 2017; 147:231102. [PMID: 29272929 PMCID: PMC5826560 DOI: 10.1063/1.5016165] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
Virial coefficients are predicted over a large range of both temperatures and model parameter values (i.e., alchemical transformation) from an individual Mayer-sampling Monte Carlo simulation by statistical mechanical extrapolation with minimal increase in computational cost. With this extrapolation method, a Mayer-sampling Monte Carlo simulation of the SPC/E (extended simple point charge) water model quantitatively predicted the second virial coefficient as a continuous function spanning over four orders of magnitude in value and over three orders of magnitude in temperature with less than a 2% deviation. In addition, the same simulation predicted the second virial coefficient if the site charges were scaled by a constant factor, from an increase of 40% down to zero charge. This method is also shown to perform well for the third virial coefficient and the exponential parameter for a Lennard-Jones fluid.
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Affiliation(s)
- Harold W. Hatch
- Chemical Informatics Research Group, Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8380, USA
| | - Sally Jiao
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Nathan A. Mahynski
- Chemical Informatics Research Group, Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8380, USA
| | - Marco A. Blanco
- Chemical Informatics Research Group, Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8380, USA
- Institute for Bioscience and Biotechnology Research, University of Maryland, Rockville, Maryland 20850, USA
| | - Vincent K. Shen
- Chemical Informatics Research Group, Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8380, USA
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Escobedo FA. Mapping coexistence lines via free-energy extrapolation: Application to order-disorder phase transitions of hard-core mixtures. J Chem Phys 2014; 140:094102. [DOI: 10.1063/1.4866764] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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Kristóf T, Liszi J, Szalai I. Determination of vapour-liquid equilibria of two-centre Lennard-Jones fluids in the canonical ensemble. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/bbpc.19961000815] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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Szalai I, Dietrich S. Magnetization and susceptibility of ferrofluids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2008; 20:204122. [PMID: 21694251 DOI: 10.1088/0953-8984/20/20/204122] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
A second-order Taylor series expansion of the free energy functional provides analytical expressions for the magnetic field dependence of the free energy and of the magnetization of ferrofluids, here modeled by dipolar Yukawa interaction potentials. The corresponding hard core dipolar Yukawa reference fluid is studied within the framework of the mean spherical approximation. Our findings for the magnetic and phase equilibrium properties are in quantitative agreement with previously published and new Monte Carlo simulation data.
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Affiliation(s)
- I Szalai
- Institute of Physics, University of Pannonia, H-8201 Veszprém, PO Box 158, Hungary
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Eslami H, Müller-Plathe F. Molecular Dynamics Simulation of Sorption of Gases in Polystyrene. Macromolecules 2007. [DOI: 10.1021/ma070697+] [Citation(s) in RCA: 62] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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10
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Methods for Examining Phase Equilibria. ACTA ACUST UNITED AC 2007. [DOI: 10.1007/978-3-540-38448-9_10] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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11
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Boda D, Winkelmann J, Liszi J, Szalai I. Vapour-liquid equilibrium of Stockmayer fluids in applied field. Mol Phys 2006. [DOI: 10.1080/00268979600100421] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Dezső Boda
- a Department of Physical Chemistry , University of Veszprém , H-8201 , Veszprém , PO Box 158, Hungary
| | - Jochen Winkelmann
- b Institut für Physikalische Chemie, Martin-Luther-Universität Halle-Wittenberg , D-06217 , Merseburg , Germany
| | - János Liszi
- a Department of Physical Chemistry , University of Veszprém , H-8201 , Veszprém , PO Box 158, Hungary
| | - István Szalai
- a Department of Physical Chemistry , University of Veszprém , H-8201 , Veszprém , PO Box 158, Hungary
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van 't Hof A, de Leeuw SW, Peters CJ. Computing the starting state for Gibbs-Duhem integration. J Chem Phys 2006; 124:054905. [PMID: 16468916 DOI: 10.1063/1.2137705] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Gibbs-Duhem integration implies the numerical integration of a Clapeyron equation. To start the numerical integration, an initial coexistence point and a corresponding initial slope of the Clapeyron equation are needed. In order to apply Gibbs-Duhem integration to all kinds of systems at diverse physical conditions, one has to investigate and assess the available methods that can be used to compute these initial values. This publication focuses on vapor-liquid equilibria in binary mixtures comprising chain molecules. The initial coexistence point is either computed with the NVbeta Gibbs ensemble or with the Npbeta+test molecule method with overlapping distributions, which is introduced in this publication. Although computationally demanding, the Npbeta+test molecule method with overlapping distributions is applicable at conditions where the NVbeta Gibbs ensemble fails. We investigated three methods that can be employed to compute the initial slope of the Clapeyron equation. The Widom method and the overlapping-distributions difference method provide correct values for the initial slope. The difference method does only provide the correct answer in special cases. The possibility to judge the reliability of the results makes the overlapping-distributions difference method the safest route to the initial slope. Gibbs-Duhem integration requires the frequent computation of the slope of the Clapeyron equation. This slope depends on ensemble averages of the composition. A new bias method for efficient sampling of the composition in a semigrand-canonical simulation of chain molecules is presented. This bias method considerably enhances the composition sampling in systems comprising chain molecules of different sizes.
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Affiliation(s)
- A van 't Hof
- Physical Chemistry and Molecular Thermodynamics, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands
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Merényi L, Kristóf T. The Extrapolation of Vapour–liquid Equilibrium Curves of Pure Fluids in Alternative Gibbs Ensemble Monte Carlo Implementations. MOLECULAR SIMULATION 2004. [DOI: 10.1080/08927020410001715373] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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15
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Van 'T Hof A, De Leeuw SW, Hall CK, Peters CJ. Molecular simulation of binary vapour–liquid equilibria with components differing largely in volatility. Mol Phys 2004. [DOI: 10.1080/00268970410001668462] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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VRABEC JADRAN, HASSE HANS. Grand Equilibrium: vapour-liquid equilibria by a new molecular simulation method. Mol Phys 2002. [DOI: 10.1080/00268970210153772] [Citation(s) in RCA: 98] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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KRISTÓF TAMÁS, LISZI JÁNOS, BODA DEZSŐ. The extrapolation of phase equilibrium curves of mixtures in the isobaric—isothermal Gibbs ensemble. Mol Phys 2002. [DOI: 10.1080/00268970210158641] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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BODA DEZSŐ, KRISTÓF TAMÁS, LISZI JÁNOS, SZALAI ISTVÁN. The extrapolation of the vapour—liquid equilibrium curves of pure fluids in the isothermal Gibbs ensemble. Mol Phys 2002. [DOI: 10.1080/00268970210130966] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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BODA DEZSÖ, KRISTÓF TAMÁS, LISZI JÁNOS, SZALAI ISTVÁN. A new simulation method for the determination of phase equilibria in mixtures in the grand canonical ensemble. Mol Phys 2001. [DOI: 10.1080/00268970110090494] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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Kronome G, Szalai I, Wendland M, Fischer J. Extension of the NpT + test particle method for the calculation of phase equilibria of nitrogen + ethane. J Mol Liq 2000. [DOI: 10.1016/s0167-7322(99)00183-x] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Szalai I, Henderson D, Boda D, Chan KY. Thermodynamics and structural properties of the dipolar Yukawa fluid. J Chem Phys 1999. [DOI: 10.1063/1.479275] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Henderson D, Boda D, Szalai I, Chan KY. The mean spherical approximation for a dipolar Yukawa fluid. J Chem Phys 1999. [DOI: 10.1063/1.478636] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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GERGELY KRONOME JANOS LISZI ISTVAN. Monte Carlo simulation of some thermophysical properties of two-centre Lennard-Jones fluids along the vapour–liquid equilibrium curve. Mol Phys 1998. [DOI: 10.1080/002689798169285] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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BODA BDEZSO, CHAN KWONGYU, SZALAI ISTVAN. Determination of vapour-liquid equilibrium using cavity-biased grand canonical Monte Carlo method. Mol Phys 1997. [DOI: 10.1080/002689797169691] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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Kristóf T, Liszi J. A New Computer Simulation Method for the Determination of the Vapour-Liquid Phase Equilibria in an Adiabatic Ensemble. Z PHYS CHEM 1997. [DOI: 10.1524/zpch.1997.199.part_1.061] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Kristóf T, Liszi J. Alternative implementations of the Gibbs ensemble Monte Carlo calculation. Chem Phys Lett 1996. [DOI: 10.1016/0009-2614(96)01012-3] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Boda D, Liszi J, Szalai I. A new simulation method for the determination of the vapour-liquid equilibria in the grand canonical ensemble. Chem Phys Lett 1996. [DOI: 10.1016/0009-2614(96)00423-x] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Kristóf T, Liszi J. Sensitivity Analysis of the Vapour-Liquid Phase Equilibria of a Model of Liquid Carbon Disulphide. Z PHYS CHEM 1996. [DOI: 10.1524/zpch.1996.194.part_2.263] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Boda D, Kalmár B, Liszi J, Szalai I. Fluid–fluid equilibrium of a mixture of non-polar and dipolar hard spheres in an applied field. ACTA ACUST UNITED AC 1996. [DOI: 10.1039/ft9969202709] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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30
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Szalai I, Liszi J, Boda D. The NVT plus test particle method for the determination of the vapour-liquid equilibria of pure fluids. Chem Phys Lett 1995. [DOI: 10.1016/0009-2614(95)01100-n] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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31
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Boda D, Liszi J, Szalai I. Dielectric constant of a Stockmayer fluid along the vapour-liquid coexistence curve. Mol Phys 1995. [DOI: 10.1080/00268979500101221] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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