1
|
Jorabchi MN, Ludwig R, Paschek D. Quasi-Universal Solubility Behavior of Light Gases in Imidazolium-Based Ionic Liquids with Varying Anions: A Molecular Dynamics Simulation Study. J Phys Chem B 2021; 125:1647-1659. [DOI: 10.1021/acs.jpcb.0c10721] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Majid Namayandeh Jorabchi
- Institut für Chemie, Physikalische und Theoretische Chemie, Universität Rostock, Albert-Einstein-Str. 21, D-18059 Rostock, Germany
| | - Ralf Ludwig
- Institut für Chemie, Physikalische und Theoretische Chemie, Universität Rostock, Dr.-Lorenz-Weg 2, D-18059 Rostock, Germany
- Department LL&M, Universität Rostock, Albert-Einstein-Str. 25, D-18059 Rostock, Germany
- Leibniz-Institut für Katalyse an der Universität Rostock, Albert-Einstein-Str. 29a, D-18059 Rostock, Germany
| | - Dietmar Paschek
- Institut für Chemie, Physikalische und Theoretische Chemie, Universität Rostock, Albert-Einstein-Str. 21, D-18059 Rostock, Germany
| |
Collapse
|
2
|
Rahbari A, Hens R, Moultos OA, Dubbeldam D, Vlugt TJH. Multiple Free Energy Calculations from Single State Point Continuous Fractional Component Monte Carlo Simulation Using Umbrella Sampling. J Chem Theory Comput 2020; 16:1757-1767. [PMID: 31999461 PMCID: PMC7066647 DOI: 10.1021/acs.jctc.9b01097] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
![]()
We introduce an alternative method
to perform free energy calculations
for mixtures at multiple temperatures and pressures from a single
simulation, by combining umbrella sampling and the continuous fractional
component Monte Carlo method. One can perform a simulation of a mixture
at a certain pressure and temperature and accurately compute the chemical
potential at other pressures and temperatures close to the simulation
conditions. This method has the following advantages: (1) Accurate
estimates of the chemical potential as a function of pressure and
temperature are obtained from a single state simulation without additional
postprocessing. This can potentially reduce the number of simulations
of a system for free energy calculations for a specific temperature
and/or pressure range. (2) Partial molar volumes and enthalpies are
obtained directly from the estimated chemical potentials. We tested
our method for a Lennard-Jones system, aqueous mixtures of methanol
at T = 298 K and P = 1 bar, and
a mixture of ammonia, nitrogen, and hydrogen at T = 573 K and P = 800 bar. For pure methanol (N = 410 molecules), we observed that the estimated chemical
potentials from umbrella sampling are in excellent agreement with
the reference values obtained from independent simulations, for ΔT = ±15 K and ΔP = 100 bar (with
respect to the simulated system). For larger systems, this range becomes
smaller because the relative fluctuations of energy and volume become
smaller. Without sufficient overlap, the performance of the method
will become poor especially for nonlinear variations of the chemical
potential.
Collapse
Affiliation(s)
- Ahmadreza Rahbari
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
| | - Remco Hens
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
| | - Othonas A Moultos
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
| | - David Dubbeldam
- Van't Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Thijs J H Vlugt
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
| |
Collapse
|
3
|
Zhuang L, Wang R, Lindberg GE, Hu H, Li XZ, Wang F. From a Liquid to a Crystal without Going through a First-Order Phase Transition: Determining the Free Energy of Melting with Glassy Intermediates. J Phys Chem B 2019; 123:7740-7747. [DOI: 10.1021/acs.jpcb.9b06840] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Lin Zhuang
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, and School of Physics, Peking University, Beijing 100871, People’s Republic of China
| | - Rui Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, People’s Republic of China
| | - Gerrick E. Lindberg
- Department of Chemistry and Biochemistry, and Department of Applied Physics and Materials Science, Northern Arizona University, 700 South Osborne Drive, Flagstaff, Arizona 86011, United States
| | - Hongyi Hu
- Department of Chemistry and Biochemistry, University of Arkansas, 119 Chemistry Building, Fayetteville, Arkansas 72701, United States
| | - Xin-Zheng Li
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, and School of Physics, Peking University, Beijing 100871, People’s Republic of China
- Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, People’s Republic of China
| | - Feng Wang
- Department of Chemistry and Biochemistry, University of Arkansas, 119 Chemistry Building, Fayetteville, Arkansas 72701, United States
| |
Collapse
|
4
|
Belloni L. Non-equilibrium hybrid insertion/extraction through the 4th dimension in grand-canonical simulation. J Chem Phys 2019; 151:021101. [DOI: 10.1063/1.5110478] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Luc Belloni
- LIONS, NIMBE, CEA, CNRS, Université Paris-Saclay, 91191-Gif-sur-Yvette, France
| |
Collapse
|
5
|
Rahbari A, Hens R, Dubbeldam D, Vlugt TJH. Improving the accuracy of computing chemical potentials in CFCMC simulations. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1631497] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- A. Rahbari
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft, Netherlands
| | - R. Hens
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft, Netherlands
| | - D. Dubbeldam
- Van't Hoff Institute for Molecular Sciences, University of Amsterdam, Amsterdam, Netherlands
| | - T. J. H. Vlugt
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft, Netherlands
| |
Collapse
|
6
|
Belloni L. Finite-size corrections in numerical simulation of liquid water. J Chem Phys 2018; 149:094111. [DOI: 10.1063/1.5046835] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Luc Belloni
- LIONS, NIMBE, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| |
Collapse
|
7
|
Rahbari A, Poursaeidesfahani A, Torres-Knoop A, Dubbeldam D, Vlugt TJH. Chemical potentials of water, methanol, carbon dioxide and hydrogen sulphide at low temperatures using continuous fractional component Gibbs ensemble Monte Carlo. MOLECULAR SIMULATION 2017. [DOI: 10.1080/08927022.2017.1391385] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Ahmadreza Rahbari
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The Netherlands
| | - Ali Poursaeidesfahani
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The Netherlands
| | - Ariana Torres-Knoop
- Van’t Hoff Institute for Molecular Sciences, University of Amsterdam, Amsterdam, The Netherlands
| | - David Dubbeldam
- Van’t Hoff Institute for Molecular Sciences, University of Amsterdam, Amsterdam, The Netherlands
| | - Thijs J. H. Vlugt
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The Netherlands
| |
Collapse
|
8
|
Kerlé D, Namayandeh Jorabchi M, Ludwig R, Wohlrab S, Paschek D. A simple guiding principle for the temperature dependence of the solubility of light gases in imidazolium-based ionic liquids derived from molecular simulations. Phys Chem Chem Phys 2017; 19:1770-1780. [PMID: 27886307 DOI: 10.1039/c6cp06792a] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We have determined the temperature dependence of the solvation behavior of a large collection of important light gases in imidazolium-based ionic liquids with the help of extensive molecular dynamics simulations. The motivation of our study is to unravel common features of the temperature dependent solvation under well controlled conditions, and to provide a guidance for cases, where experimental data from different sources disagree significantly. The solubility of molecular hydrogen, oxygen, nitrogen, methane, krypton, argon, neon and carbon dioxide in the imidazolium based ionic liquids of type 1-n-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([Cnmim][NTf2]) with varying alkyl side chain lengths n = 2, 4, 6, 8 is computed for a temperature range between 300 K and 500 K at 1 bar. By applying Widom's particle insertion technique and Bennet's overlapping distribution method, we are able to determine the temperature dependent solvation free energies of those selected light gases in simulated imidazolium based ionic liquids with high statistical accuracy. Our simulations demonstrate that the magnitude of the solvation free energy of a gas molecule at a chosen reference temperature and that of its temperature-derivatives are intimately related to one another. We conclude that this "universal" behavior is rooted in a solvation entropy-enthalpy compensation effect, which seems to be a defining feature of the solvation of small molecules in ionic liquids. The observations lead to simple analytical relations, determining the temperature dependence of the solubility data based on the absolute solubility at a certain reference temperature. By comparing our results with available experimental data from many sources, we can show that our approach is particularly helpful for providing reliable estimates for the solvation behavior of very light gases, such as hydrogen, where conflicting experimental data exist.
Collapse
Affiliation(s)
- Daniela Kerlé
- Universität Bremen, Fachbereich Produktionstechnik, Technische Thermodynamik, Badgasteiner Str. 1, D-28359 Bremen, Germany.
| | - Majid Namayandeh Jorabchi
- Universität Rostock, Institut für Chemie, Physikalische und Theoretische Chemie, Dr.-Lorenz-Weg 1, D-18059 Rostock, Germany
| | - Ralf Ludwig
- Universität Rostock, Institut für Chemie, Physikalische und Theoretische Chemie, Dr.-Lorenz-Weg 1, D-18059 Rostock, Germany and Leibniz-Institut für Katalyse an der Universität Rostock, Albert-Einstein-Str. 29a, D-18059 Rostock, Germany
| | - Sebastian Wohlrab
- Leibniz-Institut für Katalyse an der Universität Rostock, Albert-Einstein-Str. 29a, D-18059 Rostock, Germany
| | - Dietmar Paschek
- Universität Rostock, Institut für Chemie, Physikalische und Theoretische Chemie, Dr.-Lorenz-Weg 1, D-18059 Rostock, Germany
| |
Collapse
|
9
|
Kim I, Allen TW. Bennett's acceptance ratio and histogram analysis methods enhanced by umbrella sampling along a reaction coordinate in configurational space. J Chem Phys 2012; 136:164103. [PMID: 22559466 DOI: 10.1063/1.3701766] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Free energy perturbation, a method for computing the free energy difference between two states, is often combined with non-Boltzmann biased sampling techniques in order to accelerate the convergence of free energy calculations. Here we present a new extension of the Bennett acceptance ratio (BAR) method by combining it with umbrella sampling (US) along a reaction coordinate in configurational space. In this approach, which we call Bennett acceptance ratio with umbrella sampling (BAR-US), the conditional histogram of energy difference (a mapping of the 3N-dimensional configurational space via a reaction coordinate onto 1D energy difference space) is weighted for marginalization with the associated population density along a reaction coordinate computed by US. This procedure produces marginal histograms of energy difference, from forward and backward simulations, with higher overlap in energy difference space, rendering free energy difference estimations using BAR statistically more reliable. In addition to BAR-US, two histogram analysis methods, termed Bennett overlapping histograms with US (BOH-US) and Bennett-Hummer (linear) least square with US (BHLS-US), are employed as consistency and convergence checks for free energy difference estimation by BAR-US. The proposed methods (BAR-US, BOH-US, and BHLS-US) are applied to a 1-dimensional asymmetric model potential, as has been used previously to test free energy calculations from non-equilibrium processes. We then consider the more stringent test of a 1-dimensional strongly (but linearly) shifted harmonic oscillator, which exhibits no overlap between two states when sampled using unbiased Brownian dynamics. We find that the efficiency of the proposed methods is enhanced over the original Bennett's methods (BAR, BOH, and BHLS) through fast uniform sampling of energy difference space via US in configurational space. We apply the proposed methods to the calculation of the electrostatic contribution to the absolute solvation free energy (excess chemical potential) of water. We then address the controversial issue of ion selectivity in the K(+) ion channel, KcsA. We have calculated the relative binding affinity of K(+) over Na(+) within a binding site of the KcsA channel for which different, though adjacent, K(+) and Na(+) configurations exist, ideally suited to these US-enhanced methods. Our studies demonstrate that the significant improvements in free energy calculations obtained using the proposed methods can have serious consequences for elucidating biological mechanisms and for the interpretation of experimental data.
Collapse
Affiliation(s)
- Ilsoo Kim
- Department of Chemistry, University of California, One Shields Avenue, Davis, California 95616, USA.
| | | |
Collapse
|
10
|
Lai PK, Hsieh CM, Lin ST. Rapid determination of entropy and free energy of mixtures from molecular dynamics simulations with the two-phase thermodynamic model. Phys Chem Chem Phys 2012; 14:15206-13. [DOI: 10.1039/c2cp42011b] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
|
11
|
Lu J, Han B, Yan H. UV-Vis spectroscopic study of molecular clustering in supercritical CO2-acetone mixtures. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/bbpc.19981020414] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
|
12
|
CUMMINGS PETERT, JACKSON GEORGE, ROWLINSON JOHNS. Keith E. Gubbins: A celebration of statistical mechanics. Mol Phys 2009. [DOI: 10.1080/00268970210142666] [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]
|
13
|
Kerlé D, Ludwig R, Geiger A, Paschek D. Temperature Dependence of the Solubility of Carbon Dioxide in Imidazolium-Based Ionic Liquids. J Phys Chem B 2009; 113:12727-35. [DOI: 10.1021/jp9055285] [Citation(s) in RCA: 94] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Daniela Kerlé
- Institut für Chemie, Abteilung Physikalische Chemie, Universität Rostock, Dr.-Lorenz-Weg 1, D-18051 Rostock, Germany, Leibniz-Institut für Katalyse an der Universität Rostock, A.-Einstein-Strasse 29a, D-18059 Rostock, Germany, Fakultät Chemie, Physikalische Chemie, TU Dortmund, Otto-Hahn-Strasse 6, D-44221 Dortmund, Germany, and Department of Physics, Applied Physics & Astronomy, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180
| | - Ralf Ludwig
- Institut für Chemie, Abteilung Physikalische Chemie, Universität Rostock, Dr.-Lorenz-Weg 1, D-18051 Rostock, Germany, Leibniz-Institut für Katalyse an der Universität Rostock, A.-Einstein-Strasse 29a, D-18059 Rostock, Germany, Fakultät Chemie, Physikalische Chemie, TU Dortmund, Otto-Hahn-Strasse 6, D-44221 Dortmund, Germany, and Department of Physics, Applied Physics & Astronomy, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180
| | - Alfons Geiger
- Institut für Chemie, Abteilung Physikalische Chemie, Universität Rostock, Dr.-Lorenz-Weg 1, D-18051 Rostock, Germany, Leibniz-Institut für Katalyse an der Universität Rostock, A.-Einstein-Strasse 29a, D-18059 Rostock, Germany, Fakultät Chemie, Physikalische Chemie, TU Dortmund, Otto-Hahn-Strasse 6, D-44221 Dortmund, Germany, and Department of Physics, Applied Physics & Astronomy, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180
| | - Dietmar Paschek
- Institut für Chemie, Abteilung Physikalische Chemie, Universität Rostock, Dr.-Lorenz-Weg 1, D-18051 Rostock, Germany, Leibniz-Institut für Katalyse an der Universität Rostock, A.-Einstein-Strasse 29a, D-18059 Rostock, Germany, Fakultät Chemie, Physikalische Chemie, TU Dortmund, Otto-Hahn-Strasse 6, D-44221 Dortmund, Germany, and Department of Physics, Applied Physics & Astronomy, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180
| |
Collapse
|
14
|
Holzmann J, Ludwig R, Geiger A, Paschek D. Temperature and Concentration Effects on the Solvophobic Solvation of Methane in Aqueous Salt Solutions. Chemphyschem 2008; 9:2722-30. [DOI: 10.1002/cphc.200800544] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
|
15
|
Malasics A, Gillespie D, Boda D. Simulating prescribed particle densities in the grand canonical ensemble using iterative algorithms. J Chem Phys 2008; 128:124102. [PMID: 18376903 DOI: 10.1063/1.2839302] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present two efficient iterative Monte Carlo algorithms in the grand canonical ensemble with which the chemical potentials corresponding to prescribed (targeted) partial densities can be determined. The first algorithm works by always using the targeted densities in the kT log(rho(i)) (ideal gas) terms and updating the excess chemical potentials from the previous iteration. The second algorithm extrapolates the chemical potentials in the next iteration from the results of the previous iteration using a first order series expansion of the densities. The coefficients of the series, the derivatives of the densities with respect to the chemical potentials, are obtained from the simulations by fluctuation formulas. The convergence of this procedure is shown for the examples of a homogeneous Lennard-Jones mixture and a NaCl-CaCl(2) electrolyte mixture in the primitive model. The methods are quite robust under the conditions investigated. The first algorithm is less sensitive to initial conditions.
Collapse
Affiliation(s)
- Attila Malasics
- Department of Physical Chemistry, University of Pannonia, P.O. Box 158, H-8201 Veszprém, Hungary
| | | | | |
Collapse
|
16
|
Shinoda K, Shinoda W, Mikami M. Efficient free energy calculation of water across lipid membranes. J Comput Chem 2008; 29:1912-8. [DOI: 10.1002/jcc.20956] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
17
|
Theodorou DN. A reversible minimum-to-minimum mapping method for the calculation of free-energy differences. J Chem Phys 2007; 124:034109. [PMID: 16438569 DOI: 10.1063/1.2138701] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A general method is introduced for the calculation of the free-energy difference between two systems, 0 and 1, with configuration spaces omega(0), omega(1) of the same dimensionality. The method relies upon establishing a objective mapping between disjoint subsets gamma(i)(0) of omega(0) and corresponding disjoint subsets gamma(i)(1) of omega(1), and averaging a function of the ratio of configurational integrals over gamma(i)(0) and gamma(i)(1) with respect to the probability densities of the two systems. The mapped subsets gamma(i)(0) and gamma(i)(1) need not span the entire configuration spaces omega(0) and omega(1). The method is applied for the calculation of the excess chemical potential mu(ex) in a Lennard-Jones (LJ) fluid. In this case, omega(0) is the configuration space of a (N-1) real molecule plus one ideal-gas molecule system, while omega(1) is the configuration space of a N real molecule system occupying the same volume. Gamma(i)(0) and gamma(i)(1) are constructed from hyperspheres of the same radius centered at minimum-energy configurations of a set of "active" molecules lying within distance a from the ideal-gas molecule and the last real molecule, respectively. An algorithm is described for sampling gamma(i)(0) and gamma(i)(1) given a point in omega(0) or in omega(1). The algorithm encompasses three steps: "quenching" (minimization with respect to the active-molecule degrees of freedom), "mutation" (gradual conversion of the ideal-gas molecule into a real molecule, with simultaneous minimization of the energy with respect to the active-molecule degrees of freedom), and "excitation" (generation of points on a hypersphere centered at the active-molecule energy minimum). These steps are also carried out in reverse, as required by the bijective nature of the mapping. The mutation step, which establishes a reversible mapping between energy minima with respect to the active degrees of freedom of systems 0 and 1, ensures that excluded volume interactions emerging in the process of converting the ideal-gas molecule into a real molecule are relieved through appropriate rearrangement of the surrounding active molecules. Thus, the insertion problem plaguing traditional methods for the calculation of chemical potential at high densities is alleviated. Results are presented at two state points of the LJ system for a variety of radii a of the active domain. It is shown that the estimated values of mu(ex) are correct in all cases and subject to an order of magnitude lower statistical uncertainty than values based on the same number of Widom [J. Chem. Phys. 39, 2808 (1963)] insertions at high fluid densities. Optimal settings for the new algorithm are identified and distributions of the quantities involved in it [number of active molecules, energy at the sampled minima of systems 0 and 1, and free-energy differences between subsets gamma(i)(0) and gamma(i)(1) that are mapped onto each other] are explored.
Collapse
Affiliation(s)
- Doros N Theodorou
- School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou Campus, 157 80 Athens, Greece.
| |
Collapse
|
18
|
WONG J, PRAUSNITZ J. COMMENTS CONCERNING A SIMPLE EQUATION OF STATE OF THE VAN DER WAALS FORM. CHEM ENG COMMUN 2007. [DOI: 10.1080/00986448508911271] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- J.O. WONG
- a Chemical Engineering Department , Materials and Molecular Research Division Lawrence Berkeley Laboratory University of California , Berkeley, 94720
| | - J.M. PRAUSNITZ
- a Chemical Engineering Department , Materials and Molecular Research Division Lawrence Berkeley Laboratory University of California , Berkeley, 94720
| |
Collapse
|
19
|
Monte Carlo Methods for Simulating Phase Equilibria of Complex Fluids. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141649.ch14] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
|
20
|
Panagiotopoulos AZ. Direct Determination of Fluid Phase Equilibria by Simulation in the Gibbs Ensemble: A Review. MOLECULAR SIMULATION 2006. [DOI: 10.1080/08927029208048258] [Citation(s) in RCA: 259] [Impact Index Per Article: 14.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
21
|
Guillot B, Guissani Y. Investigation of the chemical potential by molecular dynamics simulation. Mol Phys 2006. [DOI: 10.1080/00268978500100361] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
22
|
Schoen M, Hoheisel C. Static and dynamic cross correlation in thermodynamically stable and unstable mixtures. Mol Phys 2006. [DOI: 10.1080/00268978400103061] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
23
|
Reliable computation of solid solubility in dense gases through homotopy continuation approach. Chem Eng Sci 2006. [DOI: 10.1016/j.ces.2005.11.067] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
|
24
|
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.
Collapse
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
| | | | | |
Collapse
|
25
|
Das C, Frenkel D. Numerical calculation of the melting phase diagram of low molecular-weight polyethylene. J Chem Phys 2003. [DOI: 10.1063/1.1568934] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
26
|
Krakoviack V, Hansen JP, Louis AA. Influence of solvent quality on effective pair potentials between polymers in solution. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:041801. [PMID: 12786388 DOI: 10.1103/physreve.67.041801] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2002] [Indexed: 05/24/2023]
Abstract
Solutions of interacting linear polymers are mapped onto a system of "soft" spherical particles interacting via an effective pair potential. This coarse-graining reduces the individual monomer-level description to a problem involving only the center of mass (c.m.) of the polymer coils. The effective pair potentials are derived by inverting the c.m. pair distribution function, generated in Monte Carlo simulations, using the hypernetted chain closure. The method, previously devised for the self-avoiding walk model of polymers in good solvent, is extended to the case of polymers in solvents of variable quality by adding a finite nearest-neighbor monomer-monomer attraction to the previous model and varying the temperature. The resulting effective pair potential is found to depend strongly on temperature and polymer concentration. At low concentration the effective interaction becomes increasingly attractive as the temperature decreases, eventually violating thermodynamic stability criteria. However, as polymer concentration is increased at fixed temperature, the effective interaction reverts to mostly repulsive behavior. These issues help to illustrate some fundamental difficulties encountered when coarse-graining complex systems via effective pair potentials.
Collapse
Affiliation(s)
- V Krakoviack
- Department of Chemistry, University of Cambridge, Lensfield Road, United Kingdom
| | | | | |
Collapse
|
27
|
Nada H, van der Eerden JPJM. An intermolecular potential model for the simulation of ice and water near the melting point: A six-site model of H[sub 2]O. J Chem Phys 2003. [DOI: 10.1063/1.1562610] [Citation(s) in RCA: 200] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
|
28
|
Juranek H, Redmer R, Rosenfeld Y. Fluid variational theory for pressure dissociation in dense hydrogen: Multicomponent reference system and nonadditivity effects. J Chem Phys 2002. [DOI: 10.1063/1.1486210] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
29
|
PANAGIOTOPOULOS ATHANASSIOSZ. Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble. Mol Phys 2002. [DOI: 10.1080/00268970110097866] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
|
30
|
Zervopoulou E, Mavrantzas VG, Theodorou DN. A new Monte Carlo simulation approach for the prediction of sorption equilibria of oligomers in polymer melts: Solubility of long alkanes in linear polyethylene. J Chem Phys 2001. [DOI: 10.1063/1.1383050] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
31
|
Vlot MJ, Huinink J, van der Eerden JP. Free energy calculations on systems of rigid molecules: An application to the TIP4P model of H2O. J Chem Phys 1999. [DOI: 10.1063/1.478084] [Citation(s) in RCA: 80] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
32
|
Vlot MJ, van der Eerden JP. Symmetric Lennard-Jones mixtures in two dimensions. J Chem Phys 1998. [DOI: 10.1063/1.477229] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
33
|
Schultze C, Donohue MD. Lattice Theory Predictions of Nonrandom Behavior in Square-Well Fluids. Ind Eng Chem Res 1998. [DOI: 10.1021/ie970901p] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Claudia Schultze
- Department of Chemical Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218
| | - Marc D. Donohue
- Department of Chemical Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218
| |
Collapse
|
34
|
Vlot MJ, van Miltenburg JC, Oonk HAJ, van der Eerden JP. Phase diagrams of scalemic mixtures: A Monte Carlo simulation study. J Chem Phys 1997. [DOI: 10.1063/1.474147] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
35
|
Sadus RJ. Molecular Simulation of Henry's Constant at Vapor−Liquid and Liquid−Liquid Phase Boundaries. J Phys Chem B 1997. [DOI: 10.1021/jp963793d] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Richard J. Sadus
- Computer Simulation and Physical Applications Group, School of Computer Science and Software Engineering, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
| |
Collapse
|
36
|
VLOT BMJ, CLAASSEN S, HUITEMA HEA, VAN DER EERDEN JP. Monte Carlo simulations of racemic liquid mixtures: thermodynamic properties and local structure. Mol Phys 1997. [DOI: 10.1080/002689797171706] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
|
37
|
|
38
|
GAO GT, WOLLER JB, ZENG XC, WANG WENCHUAN. Solute-solvent size ratio dependence of the solute residual chemical RESEARCH NOTE potential in subcritical solvents. Mol Phys 1997. [DOI: 10.1080/002689797172958] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
|
39
|
|
40
|
Ghonasgi D, Llano‐Restrepo M, Chapman WG. Henry’s law constant for diatomic and polyatomic Lennard‐Jones molecules. J Chem Phys 1993. [DOI: 10.1063/1.464915] [Citation(s) in RCA: 52] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
41
|
Tříska B, Boublík T. The chemical potential of non-spherical solute in the infinitely diluted mixture. Mol Phys 1992. [DOI: 10.1080/00268979200101201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
42
|
Miyano Y. Monte Carlo calculation of compressibility factors and internal energies of homonuclear diatomic molecules. JOURNAL OF CHEMICAL ENGINEERING OF JAPAN 1992. [DOI: 10.1252/jcej.25.95] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
43
|
Wakayama SI, Koshi M, Matsui H. Equations of State for the Lennard–Jones Mixtures at High Temperatures. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 1991. [DOI: 10.1246/bcsj.64.3329] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
44
|
Arrieta E, Jedrzejek C, Marsh KN. Mean spherical approximation algorithm for multicomponent multi‐Yukawa fluid mixtures: Study of vapor–liquid, liquid–liquid, and fluid–glass transitions. J Chem Phys 1991. [DOI: 10.1063/1.461493] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
45
|
Gubbins KE. The Role of Computer Simulation in Studying Fluid Phase Equilibria. MOLECULAR SIMULATION 1989. [DOI: 10.1080/08927028908034604] [Citation(s) in RCA: 65] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
46
|
Lotfi A, Fischer J. Chemical potentials of model and real dense fluid mixtures from perturbation theory and simulations. Mol Phys 1989. [DOI: 10.1080/00268978900100101] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
47
|
Migliore M, Corongiu G, Clementi E, Lie GC. Monte Carlo study of free energy of hydration for Li+, Na+, K+, F−, and Cl− with ab initio potentials. J Chem Phys 1988. [DOI: 10.1063/1.454289] [Citation(s) in RCA: 75] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
48
|
|
49
|
McGuigan D, Monson P. Vapour-liquid critical lines predicted by distribution function theories. Mol Phys 1987. [DOI: 10.1080/00268978700102021] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
50
|
Panagiotopoulos AZ. Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble. Mol Phys 1987. [DOI: 10.1080/00268978700101491] [Citation(s) in RCA: 1471] [Impact Index Per Article: 39.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|