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Escobedo FA. On the calculation of free energies over Hamiltonian and order parameters via perturbation and thermodynamic integration. J Chem Phys 2021; 155:114112. [PMID: 34551542 DOI: 10.1063/5.0061541] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, complementary formulas are presented to compute free-energy differences via perturbation (FEP) methods and thermodynamic integration (TI). These formulas are derived by selecting only the most statistically significant data from the information extractable from the simulated points involved. On the one hand, commonly used FEP techniques based on overlap sampling leverage the full information contained in the overlapping macrostate probability distributions. On the other hand, conventional TI methods only use information on the first moments of those distributions, as embodied by the first derivatives of the free energy. Since the accuracy of simulation data degrades considerably for high-order moments (for FEP) or free-energy derivatives (for TI), it is proposed to consider, consistently for both methods, data up to second-order moments/derivatives. This provides a compromise between the limiting strategies embodied by common FEP and TI and leads to simple, optimized expressions to evaluate free-energy differences. The proposed formulas are validated with an analytically solvable harmonic Hamiltonian (for assessing systematic errors), an atomistic system (for computing the potential of mean force with coordinate-dependent order parameters), and a binary-component coarse-grained model (for tracing a solid-liquid phase diagram in an ensemble sampled through alchemical transformations). It is shown that the proposed FEP and TI formulas are straightforward to implement, perform similarly well, and allow robust estimation of free-energy differences even when the spacing of successive points does not guarantee them to have proper overlapping in phase space.
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Affiliation(s)
- Fernando A Escobedo
- Robert Frederick Smith School of Chemistry and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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2
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Amsler J, Plessow PN, Studt F, Bučko T. Anharmonic Correction to Adsorption Free Energy from DFT-Based MD Using Thermodynamic Integration. J Chem Theory Comput 2021; 17:1155-1169. [PMID: 33482059 DOI: 10.1021/acs.jctc.0c01022] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Adsorption processes are often governed by weak interactions for which the estimation of entropy contributions by means of the harmonic approximation is prone to be inaccurate. Thermodynamic integration (TI) from the harmonic to the fully interacting system (λ-path integration) can be used to compute anharmonic corrections. Here, we combine TI with (curvilinear) internal coordinates in periodic systems to make the formalism available in computational studies. Our implementation of ab initio molecular dynamics in VASP is independent of the reaction path and can be thus applied to study adsorption processes relative to the gas phase and does hence provide a useful tool for computational catalysis. We discuss the application of the approach on three model systems for which exact semianalytical solutions exist and illustrate and quantify the importance of anharmonic vibrations, hindered rotations, and hindered translations (dissociation). Eventually, we apply the method to study the adsorption of small adsorbates in a zeolite (H-SSZ-13).
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Affiliation(s)
- Jonas Amsler
- Institute of Catalysis Research and Technology, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
| | - Philipp N Plessow
- Institute of Catalysis Research and Technology, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
| | - Felix Studt
- Institute of Catalysis Research and Technology, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany.,Institute for Chemical Technology and Polymer Chemistry, Karlsruhe Institute of Technology, Kaiserstr. 12, 76131 Karlsruhe, Germany
| | - Tomáš Bučko
- Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University in Bratislava, Ilkovičova 6, SK-84215 Bratislava, Slovakia.,Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84236 Bratislava, Slovakia
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3
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Bauer G, Gross J. Phase Equilibria of Solid and Fluid Phases from Molecular Dynamics Simulations with Equilibrium and Nonequilibrium Free Energy Methods. J Chem Theory Comput 2019; 15:3778-3792. [DOI: 10.1021/acs.jctc.8b01023] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gernot Bauer
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany,
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany,
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Shevkunov SV. Water Vapor Nucleation on a Surface with Nanoscopic Grooves. 2. Features of Thermodynamic Behavior. COLLOID JOURNAL 2019. [DOI: 10.1134/s1061933x19030141] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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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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Shevkunov SV. The Effect of Temperature on Nucleation of Condensed Water Phase on the Surface of a β-AgI Crystal. 1. Structure. COLLOID JOURNAL 2018. [DOI: 10.1134/s1061933x18020096] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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7
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Shevkunov SV. High-temperature stability of the hydrate shell of a Na+ cation in a flat nanopore with hydrophobic walls. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A 2017. [DOI: 10.1134/s0036024417150018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Abstract
Existing methods to compute free-energy differences between polymorphs use harmonic approximations, advanced non-Boltzmann bias sampling techniques, and/or multistage free-energy perturbations. This work demonstrates how Bennett's diabat interpolation method ( J. Comput. Phys. 1976, 22, 245 ) can be combined with energy gaps from lattice-switch Monte Carlo techniques ( Phys. Rev. E 2000, 61, 906 ) to swiftly estimate polymorph free-energy differences. The new method requires only two unbiased molecular dynamics simulations, one for each polymorph. To illustrate the new method, we compute the free-energy difference between face-centered cubic and body-centered cubic polymorphs for a Gaussian core solid. We discuss the justification for parabolic models of the free-energy diabats and similarities to methods that have been used in studies of electron transfer.
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Affiliation(s)
- Kartik Kamat
- Department of Chemical Engineering and ‡Department of Chemistry and Biochemistry, University of California , Santa Barbara, California 93106, United States
| | - Baron Peters
- Department of Chemical Engineering and ‡Department of Chemistry and Biochemistry, University of California , Santa Barbara, California 93106, United States
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Moustafa SG, Schultz AJ, Kofke DA. Harmonically Assisted Methods for Computing the Free Energy of Classical Crystals by Molecular Simulation: A Comparative Study. J Chem Theory Comput 2017; 13:825-834. [DOI: 10.1021/acs.jctc.6b01082] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sabry G. Moustafa
- Department of Chemical and
Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, United States
| | - Andrew J. Schultz
- Department of Chemical and
Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, United States
| | - David A. Kofke
- 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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Calero C, Knorowski C, Travesset A. Determination of anharmonic free energy contributions: Low temperature phases of the Lennard-Jones system. J Chem Phys 2016; 144:124102. [DOI: 10.1063/1.4944069] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- C. Calero
- Center for Polymer Studies and Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
- Departament de Física Fonamental, Universitat de Barcelona, Martí i Franqués 1, Barcelona 08028, Spain
| | - C. Knorowski
- Department of Physics and Astronomy and Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA
| | - A. Travesset
- Department of Physics and Astronomy and Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA
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Sesé LM. Path-integral and Ornstein-Zernike study of quantum fluid structures on the crystallization line. J Chem Phys 2016; 144:094505. [PMID: 26957169 DOI: 10.1063/1.4943005] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Liquid neon, liquid para-hydrogen, and the quantum hard-sphere fluid are studied with path integral Monte Carlo simulations and the Ornstein-Zernike pair equation on their respective crystallization lines. The results cover the whole sets of structures in the r-space and the k-space and, for completeness, the internal energies, pressures and isothermal compressibilities. Comparison with experiment is made wherever possible, and the possibilities of establishing k-space criteria for quantum crystallization based on the path-integral centroids are discussed. In this regard, the results show that the centroid structure factor contains two significant parameters related to its main peak features (amplitude and shape) that can be useful to characterize freezing.
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Affiliation(s)
- Luis M Sesé
- Departamento de Ciencias y Técnicas Fisicoquímicas, Universidad Nacional de Educación a Distancia, Paseo Senda del Rey 9, 28040 Madrid, Spain
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Zerbetto M, Frezzato D. Towards bulk thermodynamics via non-equilibrium methods: gaseous methane as a case study. Phys Chem Chem Phys 2015; 17:1966-79. [DOI: 10.1039/c4cp03815k] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
The equation of state of bulk materials is achieved via thermodynamic derivatives of the free energy yielded by nonequilibrium transformations and Jarzynski equality.
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Affiliation(s)
- Mirco Zerbetto
- Dipartimento di Scienze Chimiche
- Università degli Studi di Padova
- I-35131 Padova
- Italy
| | - Diego Frezzato
- Dipartimento di Scienze Chimiche
- Università degli Studi di Padova
- I-35131 Padova
- Italy
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Moustafa SG, Schultz AJ, Kofke DA. Effects of Finite Size and Proton Disorder on Lattice-Dynamics Estimates of the Free Energy of Clathrate Hydrates. Ind Eng Chem Res 2014. [DOI: 10.1021/ie504008h] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Sabry G. Moustafa
- Department
of Chemical and
Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, United States
| | - Andrew J. Schultz
- Department
of Chemical and
Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, United States
| | - David A. Kofke
- 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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Zerbetto M, Piserchia A, Frezzato D. Looking for some free energy? Call JEFREE (…). J Comput Chem 2014; 35:1865-81. [DOI: 10.1002/jcc.23701] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2013] [Revised: 04/09/2014] [Accepted: 07/13/2014] [Indexed: 11/09/2022]
Affiliation(s)
- Mirco Zerbetto
- Dipartimento di Scienze Chimiche; Università degli Studi di Padova; via Marzolo 1 I-35131 Padova Italy
| | - Andrea Piserchia
- Dipartimento di Scienze Chimiche; Università degli Studi di Padova; via Marzolo 1 I-35131 Padova Italy
| | - Diego Frezzato
- Dipartimento di Scienze Chimiche; Università degli Studi di Padova; via Marzolo 1 I-35131 Padova Italy
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Escobedo FA. Mapping coexistence lines via free-energy extrapolation: Application to order-disorder phase transitions of hard-core mixtures. J Chem Phys 2014; 140:094102. [DOI: 10.1063/1.4866764] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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