1
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Pan C. A formula and numerical study on Ewald 1D summation. J Comput Chem 2023; 44:902-911. [PMID: 36479716 DOI: 10.1002/jcc.27051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2022] [Revised: 10/23/2022] [Accepted: 11/13/2022] [Indexed: 12/13/2022]
Abstract
Ewald summation is famous for its successful applications in molecular simulations for systems under 2 dimensional periodic boundary condition (2D PBC, e.g., planar interfaces) and systems under 3D PBC (e.g., bulk). However, the extension to systems under 1D PBC (like porous structures and tubes) is largely hindered by the special functions in the formula. In this work, a simple approximation of Ewald 1D sum is introduced with its error rigorously controlled. To investigate the impacts on the efficiency and accuracy by different parts, a pairwise potential is calculated for a series of screening parameters ( α ) and radial distances ( ρ ) between two point charges. A mapping between the sum of trigonometric functions in Ewald 1D method and the sum of specific vectors further reveals the different converging speeds of different Fourier parts. When choosing α = 0.2 Å-1 , it is appropriate to ignore the insignificant parts in the sum to accelerate the method.
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Affiliation(s)
- Cong Pan
- College of Data Science, Jiaxing University, Jiaxing, China
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2
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Hu Z. The symmetry-preserving mean field condition for electrostatic correlations in bulk. J Chem Phys 2022; 156:034111. [DOI: 10.1063/5.0078007] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Zhonghan Hu
- Qingdao Institute for Theoretical and Computational Sciences (QiTCS), Shandong University, Qingdao 266237, People’s Republic of China and Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, People’s Republic of China
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3
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Abstract
The dielectric nature of polar liquids underpins much of their ability to act as useful solvents, but its description is complicated by the long-ranged nature of dipolar interactions. This is particularly pronounced under the periodic boundary conditions commonly used in molecular simulations. In this article, the dielectric properties of a water model whose intermolecular electrostatic interactions are entirely short-ranged are investigated. This is done within the framework of local molecular-field theory (LMFT), which provides a well-controlled mean-field treatment of long-ranged electrostatics. This short-ranged model gives a remarkably good performance on a number of counts, and its apparent shortcomings are readily accounted for. These results not only lend support to LMFT as an approach for understanding solvation behavior, but also are relevant to those developing interaction potentials based on local descriptions of liquid structure.
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4
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Baker EB, Rodgers JM, Weeks JD. Local Molecular Field Theory for Nonequilibrium Systems. J Phys Chem B 2020; 124:5676-5684. [PMID: 32511933 DOI: 10.1021/acs.jpcb.0c03295] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
We provide a framework for extending equilibrium local molecular field (LMF) theory to a statistical ensemble evolving under a time-dependent applied field. In this context, the self-consistency of the original LMF equation is achieved dynamically, which provides an efficient method for computing the equilibrium LMF potential, in addition to providing the nonequilibrium generalization. As a concrete example, we investigate water confined between hydrophobic or charged walls, systems that are very sensitive to the treatment of long-ranged electrostatics. We then analyze confined water in the presence of a time-dependent applied electric field, generated by a sinusoidal or abrupt variation of the magnitudes of uniform charge densities on each wall. Very accurate results are found from the time-dependent LMF formalism even for strong static fields and for time-dependent systems that are driven far from equilibrium where linear response methods fail.
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Affiliation(s)
- Edward B Baker
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
| | | | - John D Weeks
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
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5
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Pan C, Yi S, Hu Z. Analytic theory of finite-size effects in supercell modeling of charged interfaces. Phys Chem Chem Phys 2019; 21:14858-14864. [PMID: 31232403 DOI: 10.1039/c9cp02518a] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
The Ewald3D sum with the tinfoil boundary condition (e3dtf) evaluates the electrostatic energy of a finite unit cell inside an infinitely periodic supercell. Although it has been used as a de facto standard treatment of electrostatics for simulations of extended polar or charged interfaces, the finite-size effect on simulated properties has yet to be fully understood. There is, however, an intuitive way to quantify the average effect arising from the difference between the e3dtf and Coulomb potentials on the response of mobile charges to contact surfaces with fixed charges and/or to an applied external electric field. Although any charged interface formed by mobile countercharges that compensate the fixed charges fluctuates upon a change in the acting electric field, the distance between a pair of oppositely charged interfaces is found to be nearly stationary, which allows an analytic finite-size correction to the amount of countercharges. Application of the theory to solvated electric double layers (insulator/electrolyte interfaces) predicts that the state of complete charge compensation is invariant with respect to solvent permittivities, which is confirmed by a proper analysis of simulation data in the literature.
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Affiliation(s)
- Cong Pan
- State Key Laboratory of Supramolecular Structure and Materials, Jilin University, Changchun, 130012, P. R. China.
| | - Shasha Yi
- State Key Laboratory of Supramolecular Structure and Materials, Jilin University, Changchun, 130012, P. R. China.
| | - Zhonghan Hu
- State Key Laboratory of Supramolecular Structure and Materials, Jilin University, Changchun, 130012, P. R. China.
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6
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Remsing RC, Weeks JD. Alchemical free energy calculations and umbrella sampling with local molecular field theory. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2018. [DOI: 10.1142/s0219633618400035] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Understanding the thermodynamic driving forces underlying any chemical process requires a description of the underlying free energy surface. However, computation of free energies is difficult, often requiring advanced sampling techniques. Moreover, these computations can be further complicated by the evaluation of any long-ranged interactions in the system of interest, such as Coulomb interactions in charged and polar media. Local molecular field theory is a promising approach to avoid many of the conceptual and computational difficulties associated with long-ranged interactions. We present frameworks for performing alchemical free energy calculations and non-Boltzmann sampling with local molecular field theory. We demonstrate that local molecular field theory can be used to perform these free energy calculations with accuracy comparable to traditional methodologies while eliminating the need for explicit treatment of long-ranged interactions in simulations.
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Affiliation(s)
- Richard C. Remsing
- Institute for Computational Molecular Science, Department of Chemistry, Temple University, Philadelphia, PA 19122, USA
| | - John D. Weeks
- Institute for Physical Science and Technology, Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742, USA
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7
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Gao A, Tan L, Chaudhari MI, Asthagiri D, Pratt LR, Rempe SB, Weeks JD. Role of Solute Attractive Forces in the Atomic-Scale Theory of Hydrophobic Effects. J Phys Chem B 2018; 122:6272-6276. [DOI: 10.1021/acs.jpcb.8b01711] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Ang Gao
- Institute for Physical Science and Technology, and Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, United States
| | - Liang Tan
- Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, United States
| | - Mangesh I. Chaudhari
- Center for Biological and Engineering Sciences, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - D. Asthagiri
- Chemical and Biomolecular Engineering Rice University, Houston, Texas 77005, United States
| | - Lawrence R. Pratt
- Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, United States
| | - Susan B. Rempe
- Center for Biological and Engineering Sciences, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - John D. Weeks
- Institute for Physical Science and Technology, and Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, United States
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8
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Cao S, Zhu L, Huang X. 3DRISM-HI-D2MSA: an improved analytic theory to compute solvent structure around hydrophobic solutes with proper treatment of solute–solvent electrostatic interactions. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1416195] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Siqin Cao
- Department of Chemistry, Center of Systems Biology and Human Health, State Key Laboratory of Molecular Neuroscience, Hong Kong Branch of Chinese National Engineering Research Center for Tissue Restoration and Reconstruction, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Lizhe Zhu
- Department of Chemistry, Center of Systems Biology and Human Health, State Key Laboratory of Molecular Neuroscience, Hong Kong Branch of Chinese National Engineering Research Center for Tissue Restoration and Reconstruction, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Xuhui Huang
- Department of Chemistry, Center of Systems Biology and Human Health, State Key Laboratory of Molecular Neuroscience, Hong Kong Branch of Chinese National Engineering Research Center for Tissue Restoration and Reconstruction, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen, China
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9
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Yi S, Pan C, Hu Z. Note: A pairwise form of the Ewald sum for non-neutral systems. J Chem Phys 2017; 147:126101. [DOI: 10.1063/1.4998320] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Affiliation(s)
- Shasha Yi
- State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun 130012, People’s Republic of China
| | - Cong Pan
- State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun 130012, People’s Republic of China
| | - Zhonghan Hu
- State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun 130012, People’s Republic of China
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10
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Yi S, Pan C, Hu L, Hu Z. On the connections and differences among three mean-field approximations: a stringent test. Phys Chem Chem Phys 2017; 19:18514-18518. [PMID: 28682374 DOI: 10.1039/c7cp02338c] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
This letter attempts to clarify the meaning of three closely related mean-field approximations: random phase approximation (RPA), local molecular field (LMF) approximation, and symmetry-preserving mean-field (SPMF) approximation, and their use of reliability and validity in the field of theory and simulation of liquids when the long-ranged component of the intermolecular interaction plays an important role in determining density fluctuations and correlations. The RPA in the framework of classical density functional theory (DFT) neglects the higher order correlations in the bulk and directly applies the long-ranged part of the potential to correct the pair direct correlation function of the short-ranged system while the LMF approach introduces a nonuniform mimic system under a reconstructed static external potential that accounts for the average effect arising from the long-ranged component of the interaction. Furthermore, the SPMF approximation takes the viewpoint of LMF but instead instantaneously averages the long-ranged component of the potential over the degrees of freedom in the direction with preserved symmetry. The formal connections and the particular differences of the viewpoint among the three approximations are explained and their performances in producing structural properties of liquids are stringently tested using an exactly solvable model. We demonstrate that the RPA treatment often yields uncontrolled poor results for pair distribution functions of the bulk system. On the other hand, the LMF theory produces quite reasonably structural correlations when the pair distribution in the bulk is converted to the singlet particle distribution in the nonuniform system. It turns out that the SPMF approach outperforms the other two at all densities and under extreme conditions where the long-ranged component significantly contributes to the structural correlations.
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Affiliation(s)
- Shasha Yi
- State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun, 130012, P. R. China.
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11
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Remsing RC, Liu S, Weeks JD. Long-ranged contributions to solvation free energies from theory and short-ranged models. Proc Natl Acad Sci U S A 2016; 113:2819-26. [PMID: 26929375 PMCID: PMC4801310 DOI: 10.1073/pnas.1521570113] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Long-standing problems associated with long-ranged electrostatic interactions have plagued theory and simulation alike. Traditional lattice sum (Ewald-like) treatments of Coulomb interactions add significant overhead to computer simulations and can produce artifacts from spurious interactions between simulation cell images. These subtle issues become particularly apparent when estimating thermodynamic quantities, such as free energies of solvation in charged and polar systems, to which long-ranged Coulomb interactions typically make a large contribution. In this paper, we develop a framework for determining very accurate solvation free energies of systems with long-ranged interactions from models that interact with purely short-ranged potentials. Our approach is generally applicable and can be combined with existing computational and theoretical techniques for estimating solvation thermodynamics. We demonstrate the utility of our approach by examining the hydration thermodynamics of hydrophobic and ionic solutes and the solvation of a large, highly charged colloid that exhibits overcharging, a complex nonlinear electrostatic phenomenon whereby counterions from the solvent effectively overscreen and locally invert the integrated charge of the solvated object.
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Affiliation(s)
- Richard C Remsing
- Institute for Physical Science and Technology and Chemical Physics Program, University of Maryland, College Park, MD 20742; Institute for Computational Molecular Science, Temple University, Philadelphia, PA 19122
| | - Shule Liu
- Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742; Department of Chemistry, James Franck Institute and Computation Institute, University of Chicago, Chicago, IL 60637
| | - John D Weeks
- Institute for Physical Science and Technology and Chemical Physics Program, University of Maryland, College Park, MD 20742; Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742;
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12
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Cao S, Sheong FK, Huang X. Reference interaction site model with hydrophobicity induced density inhomogeneity: An analytical theory to compute solvation properties of large hydrophobic solutes in the mixture of polyatomic solvent molecules. J Chem Phys 2015; 143:054110. [DOI: 10.1063/1.4928051] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Siqin Cao
- The HKUST Shenzhen Research Institute, Shenzhen, China
- Department of Chemistry, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Fu Kit Sheong
- Department of Chemistry, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Xuhui Huang
- The HKUST Shenzhen Research Institute, Shenzhen, China
- Department of Chemistry, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Division of Biomedical Engineering, Center of Systems Biology and Human Health, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
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13
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Pan C, Hu Z. Optimized Ewald sum for electrostatics in molecular self-assembly systems at interfaces. Sci China Chem 2015. [DOI: 10.1007/s11426-014-5303-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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14
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Zhang J, Zhong J, Li W, Wang M, Liu B, Li Z, Yan Y. Molecular insight into the dynamical adsorption behavior of nanoscale water droplets on a heterogeneous surface. RSC Adv 2015. [DOI: 10.1039/c5ra09296e] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
A heterogeneous surface is constructed by adding one hydrophilic patch at the center of a hydrophobic surface, and the dynamical adsorption process of nanoscale water droplets is investigated adopting molecular dynamics simulations.
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Affiliation(s)
- Jun Zhang
- College of Science
- China University of Petroleum
- 266580 Qingdao
- People’s Republic of China
- Key Laboratory of New Energy Physics & Materials Science in Universities of Shandong
| | - Jie Zhong
- College of Science
- China University of Petroleum
- 266580 Qingdao
- People’s Republic of China
- Key Laboratory of New Energy Physics & Materials Science in Universities of Shandong
| | - Wen Li
- College of Science
- China University of Petroleum
- 266580 Qingdao
- People’s Republic of China
- Key Laboratory of New Energy Physics & Materials Science in Universities of Shandong
| | - Muhan Wang
- College of Science
- China University of Petroleum
- 266580 Qingdao
- People’s Republic of China
- Key Laboratory of New Energy Physics & Materials Science in Universities of Shandong
| | - Bing Liu
- College of Science
- China University of Petroleum
- 266580 Qingdao
- People’s Republic of China
- Key Laboratory of New Energy Physics & Materials Science in Universities of Shandong
| | - Zhen Li
- College of Science
- China University of Petroleum
- 266580 Qingdao
- People’s Republic of China
- Key Laboratory of New Energy Physics & Materials Science in Universities of Shandong
| | - Youguo Yan
- College of Science
- China University of Petroleum
- 266580 Qingdao
- People’s Republic of China
- Key Laboratory of New Energy Physics & Materials Science in Universities of Shandong
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15
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Hu Z. Infinite Boundary Terms of Ewald Sums and Pairwise Interactions for Electrostatics in Bulk and at Interfaces. J Chem Theory Comput 2014; 10:5254-64. [DOI: 10.1021/ct500704m] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Zhonghan Hu
- State Key Laboratory
of Supramolecular Structure and Materials and Institute of Theoretical Chemistry, Jilin University, Changchun 130012, P. R. China
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16
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Pan C, Hu Z. Rigorous Error Bounds for Ewald Summation of Electrostatics at Planar Interfaces. J Chem Theory Comput 2014; 10:534-42. [DOI: 10.1021/ct400839x] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Cong Pan
- State
Key Laboratory of Supramolecular Structure and Materials, Jilin University, Changchun, 130012, P. R. China
- Institute
of Theoretical Chemistry, Jilin University, Changchun, 130012, P. R. China
| | - Zhonghan Hu
- State
Key Laboratory of Supramolecular Structure and Materials, Jilin University, Changchun, 130012, P. R. China
- Institute
of Theoretical Chemistry, Jilin University, Changchun, 130012, P. R. China
- Kavli
Institute for Theoretical Physics China, CAS, Beijing 100190, P. R. China
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17
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Jiang J, Cao D, Henderson D, Wu J. Revisiting density functionals for the primitive model of electric double layers. J Chem Phys 2014; 140:044714. [DOI: 10.1063/1.4862990] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.7] [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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Hu Z. Symmetry-preserving mean field theory for electrostatics at interfaces. Chem Commun (Camb) 2014; 50:14397-400. [DOI: 10.1039/c4cc06618a] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A novel method is developed for complex nonuniform electrostatics in computer simulations of molecular liquids at interfaces.
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Affiliation(s)
- Zhonghan Hu
- State Key Laboratory of Supramolecular Structure and Materials
- Institute of Theoretical Chemistry
- Jilin University
- Changchun, P. R. China
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19
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Archer AJ, Evans R. Relationship between local molecular field theory and density functional theory for non-uniform liquids. J Chem Phys 2013; 138:014502. [PMID: 23298050 DOI: 10.1063/1.4771976] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The local molecular field theory (LMF) developed by Weeks and co-workers has proved successful for treating the structure and thermodynamics of a variety of non-uniform liquids. By reformulating LMF in terms of one-body direct correlation functions we recast the theory in the framework of classical density functional theory (DFT). We show that the general LMF equation for the effective reference potential φ(R)(r) follows directly from the standard mean-field DFT treatment of attractive interatomic forces. Using an accurate (fundamental measures) DFT for the non-uniform hard-sphere reference fluid we determine φ(R)(r) for a hard-core Yukawa liquid adsorbed at a planar hard wall. In the approach to bulk liquid-gas coexistence we find the effective potentials exhibit rich structure that can include damped oscillations at large distances from the wall as well as the repulsive hump near the wall required to generate the low density "gas" layer characteristic of complete drying. We argue that it would be difficult to obtain the same level of detail from other (non-DFT based) implementations of LMF. LMF emphasizes the importance of making an intelligent division of the interatomic pair potential of the full system into a reference part and a remainder that can be treated in mean-field approximation. We investigate different divisions for an exactly solvable one-dimensional model where the pair potential has a hard-core plus a linear attractive tail. Results for the structure factor and the equation of state of the uniform fluid show that including a significant portion of the attraction in the reference system can be much more accurate than treating the full attractive tail in mean-field approximation. We discuss further aspects of the relationship between LMF and DFT.
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Affiliation(s)
- A J Archer
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.
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20
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Abstract
Monovalent ion hydration entropies are analyzed via energetic partitioning of the potential distribution theorem free energy. Extensive molecular dynamics simulations and free energy calculations are performed over a range of temperatures to determine the electrostatic and van der Waals components of the entropy. The far-field electrostatic contribution is negative and small in magnitude, and it does not vary significantly as a function of ion size, consistent with dielectric models. The local electrostatic contribution, however, varies widely as a function of ion size; the sign yields a direct indication of the kosmotropic (strongly hydrated) or chaotropic (weakly hydrated) nature of the ion hydration. The results provide a thermodynamic signature for specific ion effects in hydration and are consistent with experiments that suggest minimal perturbations of water structure outside the first hydration shell. The hydration entropies are also examined in relation to the corresponding entropies for the isoelectronic rare gas pairs; an inverse correlation is observed, as expected from thermodynamic hydration data.
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Affiliation(s)
- Thomas L Beck
- Department of Chemistry, University of Cincinnati, Cincinnati, Ohio 45221-0172, United States.
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21
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Rodgers JM, Hu Z, Weeks JD. On the efficient and accurate short-ranged simulations of uniform polar molecular liquids. Mol Phys 2011. [DOI: 10.1080/00268976.2011.554332] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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