1
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Kamat K, Guo R, Reutzel-Edens SM, Price SL, Peters B. Diabat method for polymorph free energies: Extension to molecular crystals. J Chem Phys 2020; 153:244105. [PMID: 33380078 DOI: 10.1063/5.0024727] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Lattice-switch Monte Carlo and the related diabat methods have emerged as efficient and accurate ways to compute free energy differences between polymorphs. In this work, we introduce a one-to-one mapping from the reference positions and displacements in one molecular crystal to the positions and displacements in another. Two features of the mapping facilitate lattice-switch Monte Carlo and related diabat methods for computing polymorph free energy differences. First, the mapping is unitary so that its Jacobian does not complicate the free energy calculations. Second, the mapping is easily implemented for molecular crystals of arbitrary complexity. We demonstrate the mapping by computing free energy differences between polymorphs of benzene and carbamazepine. Free energy calculations for thermodynamic cycles, each involving three independently computed polymorph free energy differences, all return to the starting free energy with a high degree of precision. The calculations thus provide a force field independent validation of the method and allow us to estimate the precision of the individual free energy differences.
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Affiliation(s)
- Kartik Kamat
- Department of Chemical Engineering, University of California-Santa Barbara, Santa Barbara, California 93106, USA
| | - Rui Guo
- Department of Chemistry, University College London, London WC1H 0AJ, United Kingdom
| | - Susan M Reutzel-Edens
- Small Molecule Design and Development, Eli Lilly and Company, Indianapolis, Indiana 46285, USA
| | - Sarah L Price
- Department of Chemistry, University College London, London WC1H 0AJ, United Kingdom
| | - Baron Peters
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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2
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Brukhno AV, Grant J, Underwood TL, Stratford K, Parker SC, Purton JA, Wilding NB. DL_MONTE: a multipurpose code for Monte Carlo simulation. MOLECULAR SIMULATION 2019. [DOI: 10.1080/08927022.2019.1569760] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- A. V. Brukhno
- Scientific Computing Department, STFC, Daresbury Laboratory, Warrington, UK
| | - J. Grant
- Department of Chemistry, University of Bath, Bath, UK
- Computing Services, University of Bath, Bath, UK
| | | | | | - S. C. Parker
- Department of Chemistry, University of Bath, Bath, UK
| | - J. A. Purton
- Scientific Computing Department, STFC, Daresbury Laboratory, Warrington, UK
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3
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Kamat K, Peters B. Gibbs free-energy differences between polymorphs via a diabat approach. J Chem Phys 2018; 149:214106. [PMID: 30525715 DOI: 10.1063/1.5051448] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Polymorph free-energy differences are critical to several applications. A recently proposed diabat interpolation framework estimated free-energy differences between polymorphs by quadratic interpolation of diabats. This work extends the Zwanzig-Bennett relation to the NPT ensemble so that the diabats directly give Gibbs free-energy differences. We also demonstrate how the approach can be used in cases where the diabats are not parabolic. We illustrate the diabat method for Gibbs free-energy difference of zirconium (BCC and HCP phases) and compare it with the conventional lattice switch Monte Carlo approach.
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Affiliation(s)
- Kartik Kamat
- Department of Chemical Engineering, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - Baron Peters
- Department of Chemical Engineering, University of California Santa Barbara, Santa Barbara, California 93106, USA
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4
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Singh SK. Corresponding states vapour–liquid phase equilibria of confined square–well fluid. MOLECULAR SIMULATION 2017. [DOI: 10.1080/08927022.2017.1304642] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Sudhir K. Singh
- Department of Chemical Engineering, Thapar University Patiala, Punjab, India
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5
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Evans R, Stewart MC, Wilding NB. Drying and wetting transitions of a Lennard-Jones fluid: Simulations and density functional theory. J Chem Phys 2017; 147:044701. [DOI: 10.1063/1.4993515] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Affiliation(s)
- Robert Evans
- H. H. Wills Physics Laboratory, University of Bristol, Royal Fort, Bristol BS8 1TL, United Kingdom
| | - Maria C. Stewart
- H. H. Wills Physics Laboratory, University of Bristol, Royal Fort, Bristol BS8 1TL, United Kingdom
| | - Nigel B. Wilding
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
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6
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Chakraborti T, Adhikari J. Phase Equilibria and Critical Point Predictions of Mixtures of Molecular Fluids Using Grand Canonical Transition Matrix Monte Carlo. Ind Eng Chem Res 2017. [DOI: 10.1021/acs.iecr.7b01114] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Affiliation(s)
- Tamaghna Chakraborti
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400476, India
| | - Jhumpa Adhikari
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400476, India
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7
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Wilding NB. Improved grand canonical sampling of vapour-liquid transitions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:414016. [PMID: 27546280 DOI: 10.1088/0953-8984/28/41/414016] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Simulation within the grand canonical ensemble is the method of choice for accurate studies of first order vapour-liquid phase transitions in model fluids. Such simulations typically employ sampling that is biased with respect to the overall number density in order to overcome the free energy barrier associated with mixed phase states. However, at low temperature and for large system size, this approach suffers a drastic slowing down in sampling efficiency. The culprits are geometrically induced transitions (stemming from the periodic boundary conditions) which involve changes in droplet shape from sphere to cylinder and cylinder to slab. Since the overall number density does not discriminate sufficiently between these shapes, it fails as an order parameter for biasing through the transitions. Here we report two approaches to ameliorating these difficulties. The first introduces a droplet shape based order parameter that generates a transition path from vapour to slab states for which spherical and cylindrical droplets are suppressed. The second simply biases with respect to the number density in a tetragonal subvolume of the system. Compared to the standard approach, both methods offer improved sampling, allowing estimates of coexistence parameters and vapor-liquid surface tension for larger system sizes and lower temperatures.
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8
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Lee YH, Yevick D. Renormalized multicanonical sampling in multiple dimensions. Phys Rev E 2016; 94:043323. [PMID: 27841523 DOI: 10.1103/physreve.94.043323] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2016] [Indexed: 11/07/2022]
Abstract
This paper extends to two and three dimensions the recently proposed renormalized multicanonical sampling procedure [D. Yevick, Int. J. Mod. Phys. C 27, 1650033 (2016)IJMPEO0129-183110.1142/S0129183116500339], which generates the density of states of a system from that of a smaller system. The accuracy and efficiency of the method is additionally enhanced through a transition matrix Monte Carlo method that incorporates multicanonical sampling. The performance of the resulting procedure is investigated through calculations of the specific heat of the standard Ising model for square lattices with up to 128^{2} spins and for cubic lattices with up to 24^{3} spins. A comparison of the scaling properties to those of other algorithms based on the transition matrix Monte Carlo method demonstrates that the relative advantage of the renormalized procedure increases rapidly with system size.
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Affiliation(s)
- Yong Hwan Lee
- Department of Physics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G7
| | - David Yevick
- Department of Physics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G7
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9
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Shi W, Maginn EJ. Continuous Fractional Component Monte Carlo: An Adaptive Biasing Method for Open System Atomistic Simulations. J Chem Theory Comput 2015; 3:1451-63. [PMID: 26633216 DOI: 10.1021/ct7000039] [Citation(s) in RCA: 130] [Impact Index Per Article: 14.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A new open system Monte Carlo procedure designed to overcome difficulties with insertion and deletion of molecules is introduced. The method utilizes gradual insertions and deletions of molecules through the use of a continuous coupling parameter and an adaptive bias potential. The method draws upon concepts from previous open system molecular dynamics and expanded ensemble Monte Carlo techniques and is applied to both the grand canonical and osmotic ensembles. It is shown to yield correct results for the volumetric properties of the Lennard-Jones fluid and water as well as the phase behavior of the CO2-ethanol binary system.
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Affiliation(s)
- Wei Shi
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, 182 Fitzpatrick Hall, Notre Dame, Indiana 46556-5637
| | - Edward J Maginn
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, 182 Fitzpatrick Hall, Notre Dame, Indiana 46556-5637
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10
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Evans R, Wilding NB. Quantifying Density Fluctuations in Water at a Hydrophobic Surface: Evidence for Critical Drying. PHYSICAL REVIEW LETTERS 2015; 115:016103. [PMID: 26182111 DOI: 10.1103/physrevlett.115.016103] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2015] [Indexed: 06/04/2023]
Abstract
Employing smart Monte Carlo sampling techniques within the grand canonical ensemble, we investigate the properties of water at a model hydrophobic substrate. By reducing the strength of substrate-water attraction, we find that fluctuations in the local number density, quantified by a rigorous definition of the local compressibility χ(z), increase rapidly for distances z within one or two molecular diameters from the substrate as the degree of hydrophobicity, measured by the macroscopic contact angle θ, increases. Our simulations provide evidence for a continuous (critical) drying transition as the substrate-water interaction becomes very weak: cos(θ)→-1. We speculate that the existence of such a transition might account for earlier simulation observations of strongly enhanced density fluctuations.
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Affiliation(s)
- Robert Evans
- H. H. Wills Physics Laboratory, University of Bristol, Royal Fort, Bristol BS8 1TL, United Kingdom
| | - Nigel B Wilding
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
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11
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Hemmen A, Panagiotopoulos AZ, Gross J. Grand Canonical Monte Carlo Simulations Guided by an Analytic Equation of State—Transferable Anisotropic Mie Potentials for Ethers. J Phys Chem B 2015; 119:7087-99. [DOI: 10.1021/acs.jpcb.5b01806] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- Andrea Hemmen
- Institute
of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | | | - Joachim Gross
- Institute
of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
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12
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Factorovich MH, Molinero V, Scherlis DA. A simple grand canonical approach to compute the vapor pressure of bulk and finite size systems. J Chem Phys 2014; 140:064111. [DOI: 10.1063/1.4865137] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Ashton DJ, Sánchez-Gil V, Wilding NB. Monte Carlo methods for estimating depletion potentials in highly size-asymmetrical hard sphere mixtures. J Chem Phys 2013; 139:144102. [DOI: 10.1063/1.4824137] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- D J Ashton
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
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14
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Hansen N, Allison JR, Hodel FH, van Gunsteren WF. Relative free enthalpies for point mutations in two proteins with highly similar sequences but different folds. Biochemistry 2013; 52:4962-70. [PMID: 23802564 DOI: 10.1021/bi400272q] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Enveloping distribution sampling was used to calculate free-enthalpy changes associated with single amino acid mutations for a pair of proteins, GA95 and GB95, that show 95% sequence identity yet fold into topologically different structures. Of the L → A, I → F, and L → Y mutations at positions 20, 30, and 45, respectively, of the 56-residue sequence, the first and the last contribute the most to the free-enthalpy difference between the native and non-native sequence-structure combinations, in agreement with the experimental findings for this protein pair. The individual free-enthalpy changes are almost sequence-independent in the four-strand/one-helix structure, the stable form of GB95, while in the three-helix bundle structure, the stable form of GA95, an interplay between residues 20 and 45 is observed.
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Affiliation(s)
- Niels Hansen
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology , ETH, CH-8093 Zürich, Switzerland
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15
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Rane KS, Murali S, Errington JR. Monte Carlo Simulation Methods for Computing Liquid–Vapor Saturation Properties of Model Systems. J Chem Theory Comput 2013; 9:2552-66. [DOI: 10.1021/ct400074p] [Citation(s) in RCA: 71] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Affiliation(s)
- Kaustubh S. Rane
- Department of Chemical
and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200,
United States
| | - Sabharish Murali
- Department of Chemical
and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200,
United States
| | - Jeffrey R. Errington
- Department of Chemical
and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200,
United States
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16
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Wilms D, Wilding NB, Binder K. Transitions between imperfectly ordered crystalline structures: a phase switch Monte Carlo study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:056703. [PMID: 23004899 DOI: 10.1103/physreve.85.056703] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2012] [Indexed: 06/01/2023]
Abstract
A model for two-dimensional colloids confined laterally by "structured boundaries" (i.e., ones that impose a periodicity along the slit) is studied by Monte Carlo simulations. When the distance D between the confining walls is reduced at constant particle number from an initial value D(0), for which a crystalline structure commensurate with the imposed periodicity fits, to smaller values, a succession of phase transitions to imperfectly ordered structures occur. These structures have a reduced number of rows parallel to the boundaries (from n to n-1 to n-2, etc.) and are accompanied by an almost periodic strain pattern, due to "soliton staircases" along the boundaries. Since standard simulation studies of such transitions are hampered by huge hysteresis effects, we apply the phase switch Monte Carlo method to estimate the free energy difference between the structures as a function of the misfit between D and D(0), thereby locating where the transitions occur in equilibrium. For comparison, we also obtain this free energy difference from a thermodynamic integration method: The results agree, but the effort required to obtain the same accuracy as provided by phase switch Monte Carlo would be at least three orders of magnitude larger. We also show for a situation where several "candidate structures" exist for a phase, that phase switch Monte Carlo can clearly distinguish the metastable structures from the stable one. Finally, applying the method in the conjugate statistical ensemble (where the normal pressure conjugate to D is taken as an independent control variable), we show that the standard equivalence between the conjugate ensembles of statistical mechanics is violated.
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Affiliation(s)
- Dorothea Wilms
- Institut für Physik, Johannes Gutenberg Universität Mainz, Germany
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17
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Kumar V, Sridhar S, Errington JR. Monte Carlo simulation strategies for computing the wetting properties of fluids at geometrically rough surfaces. J Chem Phys 2011; 135:184702. [DOI: 10.1063/1.3655817] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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18
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Duncan PD, Masters AJ, Wilson MR. Thermodynamic stability of the cubatic phase of hard cut spheres evaluated by expanded ensemble simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011702. [PMID: 21867191 DOI: 10.1103/physreve.84.011702] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2011] [Revised: 05/23/2011] [Indexed: 05/31/2023]
Abstract
The system of hard cut spheres (disk-shaped particles formed by symmetrically truncating the end caps of a sphere) exhibits an intriguing "cubatic" phase with cubic orientational symmetry. However, it is unclear whether this phase is metastable with respect to the columnar phase. We attempt to provide an answer to this question by carrying out free energy calculations by the expanded ensemble Monte Carlo method. We conclude that there may be a very small region of cubatic stability in the vicinity of the isotropic-cubatic phase transition, but that that transition would need to be determined more accurately to obtain a definitive answer. We also comment on the efficacy of the expanded ensemble method for these kinds of calculations.
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Affiliation(s)
- Peter D Duncan
- Department of Chemistry, University of Durham, South Road, Durham DH1 3LE, UK
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19
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Chopra R, Truskett TM, Errington JR. Excess entropy scaling of dynamic quantities for fluids of dumbbell-shaped particles. J Chem Phys 2011; 133:104506. [PMID: 20849177 DOI: 10.1063/1.3477767] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
We use molecular simulation to study the ability of entropy scaling relationships to describe the kinetic properties of two Lennard-Jones dumbbell models. We begin by examining the excess entropy, the key quantity used to correlate dynamic properties within entropy scaling strategies. We compute the thermodynamic excess entropy as well as contributions to the two-body excess entropy stemming from translational and orientational intermolecular correlations. Our results indicate that the total two-body contribution accounts for more than 70% of the thermodynamic excess entropy at all state conditions explored. For the two dumbbell models studied here, the orientational component of the two-body excess entropy dominates at moderate and high fluid densities. We next investigate the relationships between kinetic properties and various contributions to the excess entropy. Four dynamic properties are considered: translational and rotational diffusivities, a characteristic relaxation time for rotational motion, and a collective relaxation time stemming from analysis of the coherent intermediate-scattering function. We find that the thermodynamic excess entropy provides the best metric for describing kinetic properties. For each of the dynamic properties considered, reduced data collapse onto a common curve when expressed as a function of the thermodynamic excess entropy. The likelihood of a two-body contribution to the excess entropy serving as a reliable scaling variable is linked to the extent to which it correlates with the thermodynamic excess entropy. The total two-body term contributes significantly to the excess entropy, and therefore this quantity generally serves as a suitable scaling variable.
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Affiliation(s)
- Ravi Chopra
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA.
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20
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Chopra R, Truskett TM, Errington JR. On the Use of Excess Entropy Scaling To Describe Single-Molecule and Collective Dynamic Properties of Hydrocarbon Isomer Fluids. J Phys Chem B 2010; 114:16487-93. [DOI: 10.1021/jp107878u] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ravi Chopra
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States, and Department of Chemical Engineering and Institute for Theoretical Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
| | - Thomas M. Truskett
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States, and Department of Chemical Engineering and Institute for Theoretical Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
| | - Jeffrey R. Errington
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States, and Department of Chemical Engineering and Institute for Theoretical Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
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21
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Chopra R, Truskett TM, Errington JR. On the Use of Excess Entropy Scaling to Describe the Dynamic Properties of Water. J Phys Chem B 2010; 114:10558-66. [DOI: 10.1021/jp1049155] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ravi Chopra
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, and Department of Chemical Engineering and Institute for Theoretical Chemistry, University of Texas at Austin, Austin, Texas 78712
| | - Thomas M. Truskett
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, and Department of Chemical Engineering and Institute for Theoretical Chemistry, University of Texas at Austin, Austin, Texas 78712
| | - Jeffrey R. Errington
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, and Department of Chemical Engineering and Institute for Theoretical Chemistry, University of Texas at Austin, Austin, Texas 78712
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22
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Ashton DJ, Wilding NB. Grand canonical simulation of phase behaviour in highly size-asymmetrical binary fluids. Mol Phys 2010. [DOI: 10.1080/00268976.2010.482067] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
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23
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Affiliation(s)
- Doros N. Theodorou
- Department of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou Campus, Athens 15780, Greece
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24
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Hansen HS, Hünenberger PH. Using the local elevation method to construct optimized umbrella sampling potentials: Calculation of the relative free energies and interconversion barriers of glucopyranose ring conformers in water. J Comput Chem 2010; 31:1-23. [DOI: 10.1002/jcc.21253] [Citation(s) in RCA: 91] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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25
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Norizoe Y, Daoulas KC, Müller M. Measuring excess free energies of self-assembled membrane structures. Faraday Discuss 2010; 144:369-91; discussion 445-81. [DOI: 10.1039/b901657k] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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26
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Abreu CRA. Isochronal sampling in non-Boltzmann Monte Carlo methods. J Chem Phys 2009; 131:154113. [DOI: 10.1063/1.3245304] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Charlles R A Abreu
- School of Chemical Engineering, State University of Campinas, Campinas, Sao Paulo 13083-970, Brazil.
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27
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Christ CD, Van Gunsteren WF. Comparison of three enveloping distribution sampling Hamiltonians for the estimation of multiple free energy differences from a single simulation. J Comput Chem 2009; 30:1664-79. [DOI: 10.1002/jcc.21325] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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28
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Abstract
We present a new adaptation of umbrella sampling technique in studying nucleation, allowing for a large free energy barrier to be overcome within a time scale accessible to simulation. The method requires a set of order parameters that can distinguish a metastable state and a more stable state toward which the system relaxes, but does not demand that the order parameters be adequate for describing the process around the top of the free energy barrier. To illustrate its effectiveness, the method was implemented using Monte Carlo simulation and was applied to study bubble nucleation in single component truncated and shifted Lennard-Jones fluids. Under the conditions studied, the rate of nucleation, measured in Monte Carlo cycle, was enhanced by a factor ranging from 10(2) to 10(7). The simulation also yields various thermodynamic and structural information on the system during nucleation.
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Affiliation(s)
- Isamu Kusaka
- The William G. Lowrie Department of Chemical and Biomolecular Engineering, The Koffolt Laboratories, The Ohio State University, Columbus, Ohio 43210, USA.
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29
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Wilding NB. Solid-liquid coexistence of polydisperse fluids via simulation. J Chem Phys 2009; 130:104103. [DOI: 10.1063/1.3081141] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Christ CD, van Gunsteren WF. Simple, Efficient, and Reliable Computation of Multiple Free Energy Differences from a Single Simulation: A Reference Hamiltonian Parameter Update Scheme for Enveloping Distribution Sampling (EDS). J Chem Theory Comput 2009; 5:276-86. [DOI: 10.1021/ct800424v] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Clara D. Christ
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH, 8093 Zürich, Switzerland
| | - Wilfred F. van Gunsteren
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH, 8093 Zürich, Switzerland
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31
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Müller M, Daoulas KC, Norizoe Y. Computing free energies of interfaces in self-assembling systems. Phys Chem Chem Phys 2009; 11:2087-97. [DOI: 10.1039/b818111j] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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32
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Christ CD, Mark AE, van Gunsteren WF. Basic ingredients of free energy calculations: A review. J Comput Chem 2009; 31:1569-82. [DOI: 10.1002/jcc.21450] [Citation(s) in RCA: 150] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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33
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Fenwick MK. A direct multiple histogram reweighting method for optimal computation of the density of states. J Chem Phys 2008; 129:125106. [DOI: 10.1063/1.2981800] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
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34
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Paluch AS, Shen VK, Errington JR. Comparing the Use of Gibbs Ensemble and Grand-Canonical Transition-Matrix Monte Carlo Methods to Determine Phase Equilibria. Ind Eng Chem Res 2008. [DOI: 10.1021/ie800143n] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Andrew S. Paluch
- Department of Chemical and Biological Engineering, The State University of New York at Buffalo, Buffalo, New York 14260-4200, and Physical and Chemical Properties Division, National Institute of Standards and Technology, 100 Bureau Drive MS 8380, Gaithersburg, Maryland 20899-8380
| | - Vincent K. Shen
- Department of Chemical and Biological Engineering, The State University of New York at Buffalo, Buffalo, New York 14260-4200, and Physical and Chemical Properties Division, National Institute of Standards and Technology, 100 Bureau Drive MS 8380, Gaithersburg, Maryland 20899-8380
| | - Jeffrey R. Errington
- Department of Chemical and Biological Engineering, The State University of New York at Buffalo, Buffalo, New York 14260-4200, and Physical and Chemical Properties Division, National Institute of Standards and Technology, 100 Bureau Drive MS 8380, Gaithersburg, Maryland 20899-8380
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35
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Christ CD, van Gunsteren WF. Multiple free energies from a single simulation: Extending enveloping distribution sampling to nonoverlapping phase-space distributions. J Chem Phys 2008; 128:174112. [DOI: 10.1063/1.2913050] [Citation(s) in RCA: 80] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Shi W, Maginn EJ. Atomistic Simulation of the Absorption of Carbon Dioxide and Water in the Ionic Liquid 1-n-Hexyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide ([hmim][Tf2N]. J Phys Chem B 2008; 112:2045-55. [DOI: 10.1021/jp077223x] [Citation(s) in RCA: 165] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Wei Shi
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, 182 Fitzpatrick Hall, Notre Dame, Indiana 46556-5637
| | - Edward J. Maginn
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, 182 Fitzpatrick Hall, Notre Dame, Indiana 46556-5637
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37
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Grzelak EM, Errington JR. Computation of interfacial properties via grand canonical transition matrix Monte Carlo simulation. J Chem Phys 2008; 128:014710. [DOI: 10.1063/1.2812285] [Citation(s) in RCA: 86] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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38
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Errington JR, Kofke DA. Calculation of surface tension via area sampling. J Chem Phys 2007; 127:174709. [DOI: 10.1063/1.2795698] [Citation(s) in RCA: 95] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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39
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Reimer M, Awadalla A, Yevick D, Lu T. Alignment methods for biased multicanonical sampling. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2007; 24:2474-9. [PMID: 17621352 DOI: 10.1364/josaa.24.002474] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
The efficiency of the multicanonical procedure can be significantly improved by applying an additional bias to the numerically generated sample space. However, results obtained by biasing in different sampling regions cannot in general be accurately combined, since their relative normalization coefficient is not known precisely. We demonstrate that for overlapping biasing regions a simple iterative procedure can be employed to determine the required coefficients.
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Affiliation(s)
- Michael Reimer
- Department of Physics, University of Waterloo, Waterloo Ontario, Canada.
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40
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Chen H, Sholl DS. Examining the accuracy of ideal adsorbed solution theory without curve-fitting using transition matrix Monte Carlo simulations. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2007; 23:6431-7. [PMID: 17441746 DOI: 10.1021/la700351c] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
Ideal adsorbed solution theory (IAST) is a well-known approach to predicting multicomponent adsorption isotherms in microporous materials from experimental or simulation data for single-component adsorption. A limitation in practical applications of IAST is that useful calculations often require extrapolation of fitted single-component isotherms beyond the range for which data are available. We introduce a molecular simulation approach in which the intrinsic accuracy of IAST can be examined in a context that avoids any need to perform curve fitting with single-component data. Our approach is based on using transition matrix Monte Carlo to define single-component adsorption isotherms for arbitrary bulk-phase pressures from a single simulation. We apply our approach to several light gas mixtures in silica zeolites and a carbon nanotube to examine the intrinsic accuracy of IAST for these model systems.
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Affiliation(s)
- Haibin Chen
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
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41
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Thermodynamic-Scaling Methods in Monte Carlo and their Application to Phase Equilibria. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141649.ch12] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register]
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42
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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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43
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44
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45
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Park S, Ensign DL, Pande VS. Bayesian update method for adaptive weighted sampling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:066703. [PMID: 17280173 DOI: 10.1103/physreve.74.066703] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2006] [Revised: 11/08/2006] [Indexed: 05/13/2023]
Abstract
Exploring conformational spaces is still a challenging task for simulations of complex systems. One way to enhance such a task is weighted sampling, e.g., by assigning high weights to regions that are rarely sampled. It is, however, difficult to estimate adequate weights beforehand, and therefore adaptive methods are desired. Here we present a method for adaptive weighted sampling based on Bayesian inference. Within the framework of Bayesian inference, we develop an update scheme in which the information from previous data is stored in a prior distribution which is then updated to a posterior distribution according to new data. The method proposed here is particularly well suited for distributed computing, in which one must deal with rapid influxes of large amounts of data.
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Affiliation(s)
- Sanghyun Park
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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46
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Fenwick MK. Accurate estimation of the density of states from Monte Carlo transition probability data. J Chem Phys 2006; 125:144905. [PMID: 17042648 DOI: 10.1063/1.2358345] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
This study develops an efficient approach for calculating the density of states from energy transition probability matrices generated from extended sampling Monte Carlo simulations. Direct and iterative variants of the method are shown to achieve high accuracy when applied to the two-dimensional Ising model for which the density of states function can be determined exactly. They are also used to calculate the density of states of lattice protein and Lennard-Jones models which generate more complex nonzero matrix structures. Whereas the protein simulations test the method on a system exhibiting a rugged free energy landscape, the Lennard-Jones calculations highlight implementation details that arise in applications to continuous energy systems. Density of states results for these two systems agree with estimates from multiple histogram reweighting, demonstrating that the new method provides an alternative approach for computing the thermodynamic properties of complex systems.
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Affiliation(s)
- Michael K Fenwick
- Department of Molecular Medicine, College of Veterinary Medicine, Cornell University, Ithaca, New York 14853-6401, USA.
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47
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Fenwick MK, Escobedo FA. On the use of Bennett's acceptance ratio method in multi-canonical-type simulations. J Chem Phys 2006; 120:3066-74. [PMID: 15268459 DOI: 10.1063/1.1641000] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
A common strategy for mapping coexistence curves is to employ multi-canonical (MUCA) sampling to simulate along a macrostate path connecting two phases. Central to this approach is the task of accurately calculating the importance weights used in the MUCA procedure, which are needed for both effective sampling and accurate determination of phase boundaries. The purpose of this study is to develop a strategy for determining the importance weights that is built upon Bennett's optimized acceptance ratio method. This approach is shown to be closely related to transition matrix schemes, and is used to compute the vapor-liquid equilibrium of a Lennard-Jones fluid and the liquid-liquid equilibrium of a n-hexane/n-perfluorohexane mixture. For the Lennard-Jones system, the importance weights as a function of the number of particles "N" (at fixed temperature and volume) are obtained by using Bennett's method to estimate free energy differences between N and N+1 particle systems over the desired range of N values. In this application, the method is found to perform slightly better than a related transition matrix scheme. For the n-hexane/n-perfluorohexane liquid mixture, the method is designed to obtain weights as a function of composition (for fixed temperature, pressure, and total number of particles); in this case, the method is found to outperform the Gibbs ensemble approach.
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Affiliation(s)
- Michael K Fenwick
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14850-5201, USA
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48
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Malakis A, Fytas NG. Universal features and tail analysis of the order-parameter distribution of the two-dimensional Ising model: an entropic sampling Monte Carlo study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:056114. [PMID: 16803005 DOI: 10.1103/physreve.73.056114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2005] [Indexed: 05/10/2023]
Abstract
We present a numerical study of the order-parameter probability density function (PDF) of the square Ising model for lattices with linear sizes L = 80 - 140. A recent efficient entropic sampling scheme, combining the Wang-Landau and broad histogram methods and based on the high levels of the Wang-Landau process in dominant energy subspaces is employed. We find that for large lattices there exists a stable window of the scaled order-parameter in which the full ansatz including the pre-exponential factor for the tail regime of the universal PDF is well obeyed. This window is used to estimate the equation of state exponent and to observe the behavior of the universal constants implicit in the functional form of the universal PDF. The probability densities are used to estimate the universal Privman-Fisher coefficient and to investigate whether one could obtain reliable estimates of the universal constants controlling the asymptotic behavior of the tail regime.
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Affiliation(s)
- Anastasios Malakis
- Department of Physics, Section of Solid State Physics, University of Athens, Zografos, Greece.
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49
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Escobedo FA. Simulation of the density of states in isothermal and adiabatic ensembles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:056701. [PMID: 16803068 DOI: 10.1103/physreve.73.056701] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2006] [Indexed: 05/10/2023]
Abstract
This paper provides a unified treatment of the fundamental methods used to obtain the density of states via molecular simulations with isothermal ensembles (IEs) and adiabatic ensembles (AEs). Our analysis and results show that provides a natural bridge to go back and forth between IE and AE simulation data. They also underline the difference between the density of states of potential energy macrostates and that of total energy macrostates Omega, even though both provide access to the thermodynamic properties of the system. Visited-states approaches and transition matrix methods are described and applied to the Lennard-Jones fluid to target omega and Omega as functions of energy and volume macrostates. It is shown that one can obtain omega via a generalized acceptance-ratio formula that is applicable regardless of the conditions at which the ensemble is simulated. In this way, one can obtain while performing conventional IE or AE simulations, and do it at no extra cost and with a higher accuracy than is achievable with histogram methods.
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Affiliation(s)
- Fernando A Escobedo
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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50
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Escobedo FA, Abreu CRA. On the use of transition matrix methods with extended ensembles. J Chem Phys 2006; 124:104110. [PMID: 16542071 DOI: 10.1063/1.2174010] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
Different extended ensemble schemes for non-Boltzmann sampling (NBS) of a selected reaction coordinate lambda were formulated so that they employ (i) "variable" sampling window schemes (that include the "successive umbrella sampling" method) to comprehensibly explore the lambda domain and (ii) transition matrix methods to iteratively obtain the underlying free-energy eta landscape (or "importance" weights) associated with lambda. The connection between "acceptance ratio" and transition matrix methods was first established to form the basis of the approach for estimating eta(lambda). The validity and performance of the different NBS schemes were then assessed using as lambda coordinate the configurational energy of the Lennard-Jones fluid. For the cases studied, it was found that the convergence rate in the estimation of eta is little affected by the use of data from high-order transitions, while it is noticeably improved by the use of a broader window of sampling in the variable window methods. Finally, it is shown how an "elastic" window of sampling can be used to effectively enact (nonuniform) preferential sampling over the lambda domain, and how to stitch the weights from separate one-dimensional NBS runs to produce a eta surface over a two-dimensional domain.
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Affiliation(s)
- Fernando A Escobedo
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA.
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