1
|
Sammüller F, Hermann S, Schmidt M. Why neural functionals suit statistical mechanics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:243002. [PMID: 38467072 DOI: 10.1088/1361-648x/ad326f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2023] [Accepted: 03/11/2024] [Indexed: 03/13/2024]
Abstract
We describe recent progress in the statistical mechanical description of many-body systems via machine learning combined with concepts from density functional theory and many-body simulations. We argue that the neural functional theory by Sammülleret al(2023Proc. Natl Acad. Sci.120e2312484120) gives a functional representation of direct correlations and of thermodynamics that allows for thorough quality control and consistency checking of the involved methods of artificial intelligence. Addressing a prototypical system we here present a pedagogical application to hard core particle in one spatial dimension, where Percus' exact solution for the free energy functional provides an unambiguous reference. A corresponding standalone numerical tutorial that demonstrates the neural functional concepts together with the underlying fundamentals of Monte Carlo simulations, classical density functional theory, machine learning, and differential programming is available online athttps://github.com/sfalmo/NeuralDFT-Tutorial.
Collapse
Affiliation(s)
- Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| |
Collapse
|
2
|
Mercadier B, Coles SW, Duttine M, Legein C, Body M, Borkiewicz OJ, Lebedev O, Morgan BJ, Masquelier C, Dambournet D. Dynamic Lone Pairs and Fluoride-Ion Disorder in Cubic-BaSnF 4. J Am Chem Soc 2023; 145:23739-23754. [PMID: 37844155 PMCID: PMC10623577 DOI: 10.1021/jacs.3c08232] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2023] [Indexed: 10/18/2023]
Abstract
Introducing compositional or structural disorder within crystalline solid electrolytes is a common strategy for increasing their ionic conductivity. (M,Sn)F2 fluorites have previously been proposed to exhibit two forms of disorder within their cationic host frameworks: occupational disorder from randomly distributed M and Sn cations and orientational disorder from Sn(II) stereoactive lone pairs. Here, we characterize the structure and fluoride-ion dynamics of cubic BaSnF4, using a combination of experimental and computational techniques. Rietveld refinement of the X-ray diffraction (XRD) data confirms an average fluorite structure with {Ba,Sn} cation disorder, and the 119Sn Mössbauer spectrum demonstrates the presence of stereoactive Sn(II) lone pairs. X-ray total-scattering PDF analysis and ab initio molecular dynamics simulations reveal a complex local structure with a high degree of intrinsic fluoride-ion disorder, where 1/3 of fluoride ions occupy octahedral "interstitial" sites: this fluoride-ion disorder is a consequence of repulsion between Sn lone pairs and fluoride ions that destabilizes Sn-coordinated tetrahedral fluoride-ion sites. Variable-temperature 19F NMR experiments and analysis of our molecular dynamics simulations reveal highly inhomogeneous fluoride-ion dynamics, with fluoride ions in Sn-rich local environments significantly more mobile than those in Ba-rich environments. Our simulations also reveal dynamical reorientation of the Sn lone pairs that is biased by the local cation configuration and coupled to the local fluoride-ion dynamics. We end by discussing the effect of host-framework disorder on long-range diffusion pathways in cubic BaSnF4.
Collapse
Affiliation(s)
- Briséïs Mercadier
- Réseau
sur le Stockage Electrochimique de l’Energie, RS2E, FR CNRS
3459, 80039 Amiens Cedex, France
- Sorbonne
Université, CNRS, Physicochimie des Electrolytes et Nanosystèmes
Interfaciaux, UMR CNRS 8234, 75005 Paris, France
- Laboratoire
de Réactivité et de Chimie du Solides, UMR CNRS 7314, 80039 Amiens Cedex, France
| | - Samuel W. Coles
- Department
of Chemistry, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
- Quad
One, Harwell Science and Innovation Campus, The Faraday Institution, Didcot OX11 0RA, United Kingdom
| | - Mathieu Duttine
- Institut
de Chimie de la Matière Condensée de Bordeaux, UMR CNRS
5026, 33608 Pessac, France
| | - Christophe Legein
- Institut
des Molécules et Matériaux du Mans, UMR CNRS 6283, Le
Mans Université, 72085 Le Mans Cedex 9, France
| | - Monique Body
- Institut
des Molécules et Matériaux du Mans, UMR CNRS 6283, Le
Mans Université, 72085 Le Mans Cedex 9, France
| | - Olaf J. Borkiewicz
- X-ray
Science Division, Advanced Photon Source, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Oleg Lebedev
- Laboratoire
de Cristallographie et Sciences des Matériaux, CRISMAT, 14000 Caen, France
| | - Benjamin J. Morgan
- Department
of Chemistry, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
- Quad
One, Harwell Science and Innovation Campus, The Faraday Institution, Didcot OX11 0RA, United Kingdom
| | - Christian Masquelier
- Réseau
sur le Stockage Electrochimique de l’Energie, RS2E, FR CNRS
3459, 80039 Amiens Cedex, France
- Laboratoire
de Réactivité et de Chimie du Solides, UMR CNRS 7314, 80039 Amiens Cedex, France
| | - Damien Dambournet
- Réseau
sur le Stockage Electrochimique de l’Energie, RS2E, FR CNRS
3459, 80039 Amiens Cedex, France
- Sorbonne
Université, CNRS, Physicochimie des Electrolytes et Nanosystèmes
Interfaciaux, UMR CNRS 8234, 75005 Paris, France
| |
Collapse
|
3
|
Eckert T, Stuhlmüller NCX, Sammüller F, Schmidt M. Local measures of fluctuations in inhomogeneous liquids: statistical mechanics and illustrative applications. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:425102. [PMID: 37414000 DOI: 10.1088/1361-648x/ace50c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2023] [Accepted: 07/06/2023] [Indexed: 07/08/2023]
Abstract
We show in detail how three one-body fluctuation profiles, namely the local compressibility, the local thermal susceptibility, and the reduced density, can be obtained from a statistical mechanical many-body description of classical particle-based systems. We present several different and equivalent routes to the definition of each fluctuation profile, facilitating their explicit numerical calculation in inhomogeneous equilibrium systems. This underlying framework is used for the derivation of further properties such as hard wall contact theorems and novel types of inhomogeneous one-body Ornstein-Zernike equations. The practical accessibility of all three fluctuation profiles is exemplified by grand canonical Monte Carlo simulations that we present for hard sphere, Gaussian core and Lennard-Jones fluids in confinement.
Collapse
Affiliation(s)
- Tobias Eckert
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Nico C X Stuhlmüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| |
Collapse
|
4
|
Sammüller F, Hermann S, de Las Heras D, Schmidt M. Noether-Constrained Correlations in Equilibrium Liquids. PHYSICAL REVIEW LETTERS 2023; 130:268203. [PMID: 37450808 DOI: 10.1103/physrevlett.130.268203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Accepted: 06/12/2023] [Indexed: 07/18/2023]
Abstract
Liquid structure carries deep imprints of an inherent thermal invariance against a spatial transformation of the underlying classical many-body Hamiltonian. At first order in the transformation field Noether's theorem yields the local force balance. Three distinct two-body correlation functions emerge at second order, namely the standard two-body density, the localized force-force correlation function, and the localized force gradient. An exact Noether sum rule interrelates these correlators. Simulations of Lennard-Jones, Yukawa, soft-sphere dipolar, Stockmayer, Gay-Berne and Weeks-Chandler-Andersen liquids, of monatomic water and of a colloidal gel former demonstrate the fundamental role in the characterization of spatial structure.
Collapse
Affiliation(s)
- Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| |
Collapse
|
5
|
de Las Heras D, Zimmermann T, Sammüller F, Hermann S, Schmidt M. Perspective: How to overcome dynamical density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:271501. [PMID: 37023762 DOI: 10.1088/1361-648x/accb33] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2023] [Accepted: 04/06/2023] [Indexed: 06/19/2023]
Abstract
We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, and machine learning nonequilibrium phenomena that occur in soft matter. To give guidance for navigating the theoretical and practical challenges that lie ahead, we discuss and exemplify the limitations of dynamical density functional theory (DDFT). Instead of the implied adiabatic sequence of equilibrium states that this approach provides as a makeshift for the true time evolution, we posit that the pending theoretical tasks lie in developing a systematic understanding of the dynamical functional relationships that govern the genuine nonequilibrium physics. While static density functional theory gives a comprehensive account of the equilibrium properties of many-body systems, we argue that power functional theory is the only present contender to shed similar insights into nonequilibrium dynamics, including the recognition and implementation of exact sum rules that result from the Noether theorem. As a demonstration of the power functional point of view, we consider an idealized steady sedimentation flow of the three-dimensional Lennard-Jones fluid and machine-learn the kinematic map from the mean motion to the internal force field. The trained model is capable of both predicting and designing the steady state dynamics universally for various target density modulations. This demonstrates the significant potential of using such techniques in nonequilibrium many-body physics and overcomes both the conceptual constraints of DDFT as well as the limited availability of its analytical functional approximations.
Collapse
Affiliation(s)
- Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Toni Zimmermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| |
Collapse
|
6
|
Heyes DM, Dini D, Pieprzyk S, Brańka AC. Departures from perfect isomorph behavior in Lennard-Jones fluids and solids. J Chem Phys 2023; 158:134502. [PMID: 37031156 DOI: 10.1063/5.0143651] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/05/2023] Open
Abstract
Isomorphs are lines on a fluid or solid phase diagram along which the microstructure is invariant on affine density scaling of the molecular coordinates. Only inverse power (IP) and hard sphere potential systems are perfectly isomorphic. This work provides new theoretical tools and criteria to determine the extent of deviation from perfect isomorphicity for other pair potentials using the Lennard-Jones (LJ) system as a test case. A simple prescription for predicting isomorphs in the fluid range using the freezing line as a reference is shown to be quite accurate for the LJ system. The shear viscosity and self-diffusion coefficient scale well are calculated using this method, which enables comments on the physical significance of the correlations found previously in the literature to be made. The virial–potential energy fluctuation and the concept of an effective IPL system and exponent, n′, are investigated, particularly with reference to the LJ freezing and melting lines. It is shown that the exponent, n′, converges to the value 12 at a high temperature as ∼ T−1/2, where T is the temperature. Analytic expressions are derived for the density, temperature, and radius derivatives of the radial distribution function along an isomorph that can be used in molecular simulation. The variance of the radial distribution function and radial fluctuation function are shown to be isomorph invariant.
Collapse
Affiliation(s)
- D. M. Heyes
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - D. Dini
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - S. Pieprzyk
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| | - A. C. Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| |
Collapse
|
7
|
Renner J, Schmidt M, de Las Heras D. Reduced-variance orientational distribution functions from torque sampling. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:235901. [PMID: 36974000 DOI: 10.1088/1361-648x/acc522] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Accepted: 03/08/2023] [Indexed: 06/18/2023]
Abstract
We introduce a method to sample the orientational distribution function in computer simulations. The method is based on the exact torque balance equation for classical many-body systems of interacting anisotropic particles in equilibrium. Instead of the traditional counting of events, we reconstruct the orientational distribution function via an orientational integral of the torque acting on the particles. We test the torque sampling method in two- and three-dimensions, using both Langevin dynamics and overdamped Brownian dynamics, and with two interparticle interaction potentials. In all cases the torque sampling method produces profiles of the orientational distribution function with better accuracy than those obtained with the traditional counting method. The accuracy of the torque sampling method is independent of the bin size, and hence it is possible to resolve the orientational distribution function with arbitrarily small angular resolutions.
Collapse
Affiliation(s)
- Johannes Renner
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| |
Collapse
|
8
|
Sammüller F, Hermann S, Schmidt M. Comparative study of force-based classical density functional theory. Phys Rev E 2023; 107:034109. [PMID: 37072997 DOI: 10.1103/physreve.107.034109] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2022] [Accepted: 02/17/2023] [Indexed: 04/20/2023]
Abstract
We reexamine results obtained with the recently proposed density functional theory framework based on forces (force-DFT) [S. M. Tschopp et al., Phys. Rev. E 106, 014115 (2022)2470-004510.1103/PhysRevE.106.014115]. We compare inhomogeneous density profiles for hard sphere fluids to results from both standard density functional theory and from computer simulations. Test situations include the equilibrium hard sphere fluid adsorbed against a planar hard wall and the dynamical relaxation of hard spheres in a switched harmonic potential. The comparison to grand canonical Monte Carlo simulation profiles shows that equilibrium force-DFT alone does not improve upon results obtained with the standard Rosenfeld functional. Similar behavior holds for the relaxation dynamics, where we use our event-driven Brownian dynamics data as benchmark. Based on an appropriate linear combination of standard and force-DFT results, we investigate a simple hybrid scheme which rectifies these deficiencies in both the equilibrium and the dynamical case. We explicitly demonstrate that although the hybrid method is based on the original Rosenfeld fundamental measure functional, its performance is comparable to that of the more advanced White Bear theory.
Collapse
Affiliation(s)
- Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| |
Collapse
|
9
|
Sammüller F, de Las Heras D, Schmidt M. Inhomogeneous steady shear dynamics of a three-body colloidal gel former. J Chem Phys 2023; 158:054908. [PMID: 36754804 DOI: 10.1063/5.0130655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
We investigate the stationary flow of a colloidal gel under an inhomogeneous external shear force using adaptive Brownian dynamics simulations. The interparticle forces are derived from the Stillinger-Weber potential, where the three-body term is tuned to enable network formation and gelation in equilibrium. When subjected to the shear force field, the system develops remarkable modulations in the one-body density profile. Depending on the shear magnitude, particles accumulate either in quiescent regions or in the vicinity of maximum net flow, and we deduce this strong non-equilibrium response to be characteristic of the gel state. Studying the components of the internal force parallel and perpendicular to the flow direction reveals that the emerging flow and structure of the stationary state are driven by significant viscous and structural superadiabatic forces. Thereby, the magnitude and nature of the observed non-equilibrium phenomena differ from the corresponding behavior of simple fluids. We demonstrate that a simple power functional theory reproduces accurately the viscous force profile, giving a rationale of the complex dynamical behavior of the system.
Collapse
Affiliation(s)
- Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| |
Collapse
|
10
|
Simon JM, Krüger P, Schnell SK, Vlugt TJH, Kjelstrup S, Bedeaux D. Kirkwood-Buff integrals: From fluctuations in finite volumes to the thermodynamic limit. J Chem Phys 2022; 157:130901. [PMID: 36209013 DOI: 10.1063/5.0106162] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The Kirkwood-Buff theory is a cornerstone of the statistical mechanics of liquids and solutions. It relates volume integrals over the radial distribution function, so-called Kirkwood-Buff integrals (KBIs), to particle number fluctuations and thereby to various macroscopic thermodynamic quantities such as the isothermal compressibility and partial molar volumes. Recently, the field has seen a strong revival with breakthroughs in the numerical computation of KBIs and applications to complex systems such as bio-molecules. One of the main emergent results is the possibility to use the finite volume KBIs as a tool to access finite volume thermodynamic quantities. The purpose of this Perspective is to shed new light on the latest developments and discuss future avenues.
Collapse
Affiliation(s)
- J-M Simon
- Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR-6303 CNRS - Université de Bourgogne Franche-Comté, F-21078 Dijon, France
| | - P Krüger
- Graduate School of Science and Engineering, Molecular Chirality Research Center, Chiba University, Chiba 263-8522, Japan
| | - S K Schnell
- Department of Materials Science and Engineering, NTNU - Norwegian University of Science and Technology, N-7491 Trondheim, Norway
| | - T J H Vlugt
- Process & Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628CB Delft, The Netherlands
| | - S Kjelstrup
- Center of Excellence PoreLab, Department of Chemistry, Faculty of Natural Sciences, NTNU - Norwegian University of Science and Technology, Trondheim, Norway
| | - D Bedeaux
- Center of Excellence PoreLab, Department of Chemistry, Faculty of Natural Sciences, NTNU - Norwegian University of Science and Technology, Trondheim, Norway
| |
Collapse
|
11
|
Bienvenu A, Feldt J, Toulouse J, Assaraf R. Systematic lowering of the scaling of Monte Carlo calculations by partitioning and subsampling. Phys Rev E 2022; 106:025301. [PMID: 36109951 DOI: 10.1103/physreve.106.025301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2022] [Accepted: 07/05/2022] [Indexed: 06/15/2023]
Abstract
We propose to compute physical properties by Monte Carlo calculations using conditional expectation values. The latter are obtained on top of the usual Monte Carlo sampling by partitioning the physical space in several subspaces or fragments, and subsampling each fragment (i.e., performing side walks) while freezing the environment. No bias is introduced and a zero-variance principle holds in the limit of separability, i.e., when the fragments are independent. In practice, the usual bottleneck of Monte Carlo calculations-the scaling of the statistical fluctuations as a function of the number of particles N-is relieved for extensive observables. We illustrate the method in variational Monte Carlo on the two-dimensional Hubbard model and on metallic hydrogen chains using Jastrow-Slater wave functions. A factor O(N) is gained in numerical efficiency.
Collapse
Affiliation(s)
- Antoine Bienvenu
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
| | - Jonas Feldt
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
- Institut Universitaire de France, F-75005 Paris, France
| | - Roland Assaraf
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
| |
Collapse
|
12
|
Tschopp SM, Sammüller F, Hermann S, Schmidt M, Brader JM. Force density functional theory in- and out-of-equilibrium. Phys Rev E 2022; 106:014115. [PMID: 35974621 DOI: 10.1103/physreve.106.014115] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 06/06/2022] [Indexed: 06/15/2023]
Abstract
When a fluid is subject to an external field, as is the case near an interface or under spatial confinement, then the density becomes spatially inhomogeneous. Although the one-body density provides much useful information, a higher level of resolution is provided by the two-body correlations. These give a statistical description of the internal microstructure of the fluid and enable calculation of the average interparticle force, which plays an essential role in determining both the equilibrium and dynamic properties of interacting fluids. We present a theoretical framework for the description of inhomogeneous (classical) many-body systems, based explicitly on the two-body correlation functions. By consideration of local Noether-invariance against spatial distortion of the system we demonstrate the fundamental status of the Yvon-Born-Green (YBG) equation as a local force-balance within the fluid. Using the inhomogeneous Ornstein-Zernike equation we show that the two-body correlations are density functionals and, thus, that the average interparticle force entering the YBG equation is also a functional of the one-body density. The force-based theory we develop provides an alternative to standard density functional theory for the study of inhomogeneous systems both in- and out-of-equilibrium. We compare force-based density profiles to the results of the standard potential-based (dynamical) density functional theory. In-equilibrium, we confirm both analytically and numerically that the standard approach yields profiles that are consistent with the compressibility pressure, whereas the force-density functional gives profiles consistent with the virial pressure. For both approaches we explicitly prove the hard-wall contact theorem that connects the value of the density profile at the hard-wall with the bulk pressure. The structure of the theory offers deep insights into the nature of correlation in dense and inhomogeneous systems.
Collapse
Affiliation(s)
- Salomée M Tschopp
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
| | - Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Joseph M Brader
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
| |
Collapse
|
13
|
Coles SW, Mangaud E, Frenkel D, Rotenberg B. Reduced variance analysis of molecular dynamics simulations by linear combination of estimators. J Chem Phys 2021; 154:191101. [PMID: 34240909 DOI: 10.1063/5.0053737] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Building upon recent developments of force-based estimators with a reduced variance for the computation of densities, radial distribution functions, or local transport properties from molecular simulations, we show that the variance can be further reduced by considering optimal linear combinations of such estimators. This control variates approach, well known in statistics and already used in other branches of computational physics, has been comparatively much less exploited in molecular simulations. We illustrate this idea on the radial distribution function and the one-dimensional density of a bulk and confined Lennard-Jones fluid, where the optimal combination of estimators is determined for each distance or position, respectively. In addition to reducing the variance everywhere at virtually no additional cost, this approach cures an artifact of the initial force-based estimators, namely, small but non-zero values of the quantities in regions where they should vanish. Beyond the examples considered here, the present work highlights, more generally, the underexplored potential of control variates to estimate observables from molecular simulations.
Collapse
Affiliation(s)
- S W Coles
- Department of Chemistry, University of Bath, Claverton Down BA2 7AY, United Kingdom
| | - E Mangaud
- MSME, Université Gustave Eiffel, UPEC, CNRS, F-77454 Marne-la-Vallée, France
| | - D Frenkel
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - B Rotenberg
- Physicochimie des électrolytes et Nanosystèmes Interfaciaux, Sorbonne Université, CNRS, F-75005 Paris, France
| |
Collapse
|
14
|
Sutherland BJ, Moore WHD, Manolopoulos DE. Nuclear quantum effects in thermal conductivity from centroid molecular dynamics. J Chem Phys 2021; 154:174104. [PMID: 34241048 DOI: 10.1063/5.0051663] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We show that the centroid molecular dynamics (CMD) method provides a realistic way to calculate the thermal diffusivity a = λ/ρcV of a quantum mechanical liquid such as para-hydrogen. Once a has been calculated, the thermal conductivity can be obtained from λ = ρcVa, where ρ is the density of the liquid and cV is the constant-volume heat capacity. The use of this formula requires an accurate quantum mechanical heat capacity cV, which can be obtained from a path integral molecular dynamics simulation. The thermal diffusivity can be calculated either from the decay of the equilibrium density fluctuations in the liquid or by using the Green-Kubo relation to calculate the CMD approximation to λ and then dividing this by the corresponding approximation to ρcV. We show that both approaches give the same results for liquid para-hydrogen and that these results are in good agreement with the experimental measurements of the thermal conductivity over a wide temperature range. In particular, they correctly predict a decrease in the thermal conductivity at low temperatures-an effect that stems from the decrease in the quantum mechanical heat capacity and has eluded previous para-hydrogen simulations. We also show that the method gives equally good agreement with the experimental measurements for the thermal conductivity of normal liquid helium.
Collapse
Affiliation(s)
- Benjamin J Sutherland
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - William H D Moore
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - David E Manolopoulos
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| |
Collapse
|
15
|
Kalayan J, Henchman RH. Convergence behaviour of solvation shells in simulated liquids. Phys Chem Chem Phys 2021; 23:4892-4900. [PMID: 33616583 DOI: 10.1039/d0cp05903j] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
A convenient way to analyse solvent structure around a solute is to use solvation shells, whereby solvent position around the solute is discretised by the size of a solvent molecule, leading to multiple shells around the solute. The two main ways to define multiple shells around a solute are either directly with respect to the solute, called solute-centric, or locally for both solute and solvent molecules alike. It might be assumed that both methods lead to solvation shells with similar properties. However, our analysis suggests otherwise. Solvation shells are analysed in a series of simulations of five pure liquids of differing polarity. Shells are defined locally working outwards from each molecule treated as a reference molecule using two methods: the cutoff at the first minimum in the radial distribution function and the parameter-free Relative Angular Distance method (RAD). The molecular properties studied are potential energy, coordination number and coordination radius. Rather than converging to bulk values, as might be expected for pure solvents, properties are found to deviate as a function of shell index. This behaviour occurs because molecules with larger coordination numbers and radius have more neighbours, which make them more likely to be connected to the reference molecule via fewer shells. The effect is amplified for RAD because of its more variable coordination radii and for water with its more open structure and stronger interactions. These findings indicate that locally defined shells should not be thought of as directly comparable to solute-centric shells or to distance. As well as showing how box size and cutoff affect the non-convergence, to restore convergence we propose a hybrid method by defining a new set of shells with boundaries at the uppermost distance of each locally derived shell.
Collapse
Affiliation(s)
- Jas Kalayan
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester M1 7DN, UK. and Department of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Richard H Henchman
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester M1 7DN, UK. and Department of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| |
Collapse
|
16
|
Rotenberg B. Use the force! Reduced variance estimators for densities, radial distribution functions, and local mobilities in molecular simulations. J Chem Phys 2020; 153:150902. [DOI: 10.1063/5.0029113] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- Benjamin Rotenberg
- Sorbonne Université, CNRS, Physico-Chimie des électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| |
Collapse
|
17
|
Mangaud E, Rotenberg B. Sampling mobility profiles of confined fluids with equilibrium molecular dynamics simulations. J Chem Phys 2020; 153:044125. [DOI: 10.1063/5.0013952] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Affiliation(s)
- Etienne Mangaud
- Sorbonne Université, CNRS, Physicochimie des électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Physicochimie des électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| |
Collapse
|
18
|
Dawass N, Krüger P, Schnell SK, Moultos OA, Economou IG, Vlugt TJH, Simon JM. Kirkwood-Buff Integrals Using Molecular Simulation: Estimation of Surface Effects. NANOMATERIALS 2020; 10:nano10040771. [PMID: 32316368 PMCID: PMC7221661 DOI: 10.3390/nano10040771] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/13/2020] [Revised: 04/06/2020] [Accepted: 04/13/2020] [Indexed: 11/24/2022]
Abstract
Kirkwood-Buff (KB) integrals provide a connection between microscopic properties and thermodynamic properties of multicomponent fluids. The estimation of KB integrals using molecular simulations of finite systems requires accounting for finite size effects. In the small system method, properties of finite subvolumes with different sizes embedded in a larger volume can be used to extrapolate to macroscopic thermodynamic properties. KB integrals computed from small subvolumes scale with the inverse size of the system. This scaling was used to find KB integrals in the thermodynamic limit. To reduce numerical inaccuracies that arise from this extrapolation, alternative approaches were considered in this work. Three methods for computing KB integrals in the thermodynamic limit from information of radial distribution functions (RDFs) of finite systems were compared. These methods allowed for the computation of surface effects. KB integrals and surface terms in the thermodynamic limit were computed for Lennard–Jones (LJ) and Weeks–Chandler–Andersen (WCA) fluids. It was found that all three methods converge to the same value. The main differentiating factor was the speed of convergence with system size L. The method that required the smallest size was the one which exploited the scaling of the finite volume KB integral multiplied by L. The relationship between KB integrals and surface effects was studied for a range of densities.
Collapse
Affiliation(s)
- Noura Dawass
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628CB Delft, The Netherlands
| | - Peter Krüger
- Graduate School of Engineering and Molecular Chirality Research Center, Chiba University, Chiba 263-8522, Japan
| | - Sondre K Schnell
- Department of Materials Science and Engineering, NTNU, N-7491 Trondheim, Norway
| | - Othonas A Moultos
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628CB Delft, The Netherlands
| | - Ioannis G Economou
- National Center for Scientific Research Demokritos, Institute of Nanoscience and Nanotechnology, Molecular Thermodynamics and Modelling of Materials Laboratory, GR 153 10 Aghia Paraskevi Attikis, Greece
- Chemical Engineering Program, Texas A&M University at Qatar, Education City, PO Box 23874 Doha, Qatar
| | - Thijs J H Vlugt
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628CB Delft, The Netherlands
| | - Jean-Marc Simon
- ICB, UMR 6303 CNRS - Université de Bourgogne, F-21078 Dijon, France
| |
Collapse
|
19
|
Coles SW, Park C, Nikam R, Kanduč M, Dzubiella J, Rotenberg B. Correlation Length in Concentrated Electrolytes: Insights from All-Atom Molecular Dynamics Simulations. J Phys Chem B 2020; 124:1778-1786. [PMID: 32031810 DOI: 10.1021/acs.jpcb.9b10542] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We study the correlation length of the charge-charge pair correlations in concentrated electrolyte solutions by means of all-atom, explicit-solvent molecular dynamics simulations. We investigate LiCl and NaI in water, which constitute highly soluble, prototypical salts for experiments, as well as two more complex, molecular electrolyte systems of lithium bis(trifluoromethane)sulfonimide (LiTFSI), a salt commonly employed in electrochemical storage systems, in water, and in an organic solvent mixture of dimethoxyethane and dioxolane. Our simulations support the recent experimental observations as well as theoretical predictions of a nonmonotonic behavior of the correlation length with increasing salt concentration. We observe a Debye-Hückel like regime at low concentration, followed by a minimum reached when d/λD ≃ 1, where λD is the Debye correlation length and d is the effective ionic diameter, and an increasing correlation length with salt concentration in very concentrated electrolytes. As in the experiments, we find that the screening length in the concentrated regime follows a universal scaling law as a function d/λD for all studied salts. However, the scaling exponent is significantly lower than the experimentally measured one and lies in the range of the theoretical predictions based on much simpler electrolyte models.
Collapse
Affiliation(s)
- Samuel W Coles
- Sorbonne Université, CNRS, Physicochimie des électrolytes et Nanosystèmes Interfaciaux, UMR PHENIX, 4 pl. Jussieu, F-75005 Paris, France
| | - Chanbum Park
- Research Group for Simulations of Energy Materials, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany.,Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany
| | - Rohit Nikam
- Research Group for Simulations of Energy Materials, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany.,Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany
| | - Matej Kanduč
- Research Group for Simulations of Energy Materials, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany.,Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
| | - Joachim Dzubiella
- Research Group for Simulations of Energy Materials, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany.,Applied Theoretical Physics-Computational Physics, Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Physicochimie des électrolytes et Nanosystèmes Interfaciaux, UMR PHENIX, F-75005 Paris, France
| |
Collapse
|
20
|
Luukkonen S, Levesque M, Belloni L, Borgis D. Hydration free energies and solvation structures with molecular density functional theory in the hypernetted chain approximation. J Chem Phys 2020; 152:064110. [DOI: 10.1063/1.5142651] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- Sohvi Luukkonen
- Maison de la Simulation, USR 3441 CNRS-CEA-Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - Maximilien Levesque
- PASTEUR, Département de Chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS, 75005 Paris, France
| | - Luc Belloni
- LIONS, NIMBE, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - Daniel Borgis
- Maison de la Simulation, USR 3441 CNRS-CEA-Université Paris-Saclay, 91191 Gif-sur-Yvette, France
- PASTEUR, Département de Chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS, 75005 Paris, France
| |
Collapse
|
21
|
Trokhymchuk A, Schultz AJ, Kofke DA. Alternative ensemble averages in molecular dynamics simulation of hard spheres. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1664779] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Andrij Trokhymchuk
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Lviv, Ukraine
| | - Andrew J. Schultz
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, NY, USA
| | - David A. Kofke
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, NY, USA
| |
Collapse
|
22
|
Coles SW, Borgis D, Vuilleumier R, Rotenberg B. Computing three-dimensional densities from force densities improves statistical efficiency. J Chem Phys 2019. [DOI: 10.1063/1.5111697] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- Samuel W. Coles
- Sorbonne Université, CNRS, Physicochimie des électrolytes et nanosystèmes interfaciaux, UMR PHENIX, F-75005 Paris, France
| | - Daniel Borgis
- PASTEUR, Département de chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS, F-75005 Paris, France
- Maison de la Simulation, CEA, CNRS, Université Paris-Sud, UVSQ, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
| | - Rodolphe Vuilleumier
- PASTEUR, Département de chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS, F-75005 Paris, France
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Physicochimie des électrolytes et nanosystèmes interfaciaux, UMR PHENIX, F-75005 Paris, France
| |
Collapse
|
23
|
de Las Heras D, Renner J, Schmidt M. Custom flow in overdamped Brownian dynamics. Phys Rev E 2019; 99:023306. [PMID: 30934221 DOI: 10.1103/physreve.99.023306] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2018] [Indexed: 11/07/2022]
Abstract
When an external field drives a colloidal system out of equilibrium, the ensuing colloidal response can be very complex, and obtaining a detailed physical understanding often requires case-by-case considerations. To facilitate systematic analysis, here we present a general iterative scheme for the determination of the unique external force field that yields prescribed inhomogeneous stationary or time-dependent flow in an overdamped Brownian many-body system. The computer simulation method is based on the exact one-body force balance equation and allows to specifically tailor both gradient and rotational velocity contributions, as well as to freely control the one-body density distribution. Hence, compressibility of the flow field can be fully adjusted. The practical convergence to a unique external force field demonstrates the existence of a functional map from both velocity and density to external force field, as predicted by the power functional variational framework. In equilibrium, the method allows to find the conservative force field that generates a prescribed target density profile, and hence implements the Mermin-Evans classical density functional map from density distribution to external potential. The conceptual tools developed here enable one to gain detailed physical insight into complex flow behaviour, as we demonstrate in prototypical situations.
Collapse
Affiliation(s)
- Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Johannes Renner
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| |
Collapse
|
24
|
|
25
|
Krinninger P, Schmidt M. Power functional theory for active Brownian particles: General formulation and power sum rules. J Chem Phys 2019; 150:074112. [DOI: 10.1063/1.5061764] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Philip Krinninger
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| |
Collapse
|
26
|
Purohit A, Schultz AJ, Kofke DA. Force-sampling methods for density distributions as instances of mapped averaging. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1572243] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Apoorva Purohit
- Department of Chemical and Biological Engineering, The State University of New York, Buffalo, NY, USA
| | - Andrew J. Schultz
- Department of Chemical and Biological Engineering, The State University of New York, Buffalo, NY, USA
| | - David A. Kofke
- Department of Chemical and Biological Engineering, The State University of New York, Buffalo, NY, USA
| |
Collapse
|
27
|
de Las Heras D, Schmidt M. Better Than Counting: Density Profiles from Force Sampling. PHYSICAL REVIEW LETTERS 2018; 120:218001. [PMID: 29883170 DOI: 10.1103/physrevlett.120.218001] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2017] [Revised: 01/30/2018] [Indexed: 06/08/2023]
Abstract
Calculating one-body density profiles in equilibrium via particle-based simulation methods involves counting of events of particle occurrences at (histogram-resolved) space points. Here, we investigate an alternative method based on a histogram of the local force density. Via an exact sum rule, the density profile is obtained with a simple spatial integration. The method circumvents the inherent ideal gas fluctuations. We have tested the method in Monte Carlo, Brownian dynamics, and molecular dynamics simulations. The results carry a statistical uncertainty smaller than that of the standard counting method, reducing therefore the computation time.
Collapse
Affiliation(s)
- Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| |
Collapse
|
28
|
de Las Heras D, Schmidt M. Velocity Gradient Power Functional for Brownian Dynamics. PHYSICAL REVIEW LETTERS 2018; 120:028001. [PMID: 29376691 DOI: 10.1103/physrevlett.120.028001] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2017] [Indexed: 06/07/2023]
Abstract
We present an explicit and simple approximation for the superadiabatic excess (over ideal gas) free power functional, admitting the study of the nonequilibrium dynamics of overdamped Brownian many-body systems. The functional depends on the local velocity gradient and is systematically obtained from treating the microscopic stress distribution as a conjugate field. The resulting superadiabatic forces are beyond dynamical density functional theory and are of a viscous nature. Their high accuracy is demonstrated by comparison to simulation results.
Collapse
Affiliation(s)
- Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| |
Collapse
|