Grand molecular dynamics

A method for open systems

Tahir çaĝin, Bernard Pettitt

Research output: Contribution to journalArticle

83 Citations (Scopus)

Abstract

We present a new molecular dynamics method for studying the dynamics of open systems. The method couples a classical system to a chemical potential reservior. In the formulation, following the extended system dynamics approach, we introduce a variable, v to represent the coupling to the chemical potential reservoir. The new variable governs the dynamics of the variation of number of particles in the system. The number of particles is determined by taking the integer part of v. The fractional part of the new variable is used to scale the potential energy and the kinetic energy of an additional particle; i.e., we introduce a fractional particle. We give the ansatz Lagrangians and equations of motion for both the isothermal and the adiabatic forms of grand molecular dynamics. The averages calculated over the trajectories generated by these equations of motion represent the classical grand canonical ensemble (pVT) and the constant chemical potential adiabatic ensemble (μVL) averages, respectively. The microcanonical phase space densities of the adiabatic and isothermal forms the molecular dynamics method are shown to be equivalent to adiabatic constant chemical potential ensemble, and grand canonical ensemble partition functions. We also discuss the extension to multi-component systems, molecular fluids, ionic solutions and the problems and solutions associated with the implementation of the method. The statistical expressions for thermodynamic functions such as specific heat; adiabatic bulk modulus, Gröneissen parameter and number fluctuations are derived. These expressions are used to analyse trajectories of constant chemical potential systems.

Original languageEnglish (US)
Pages (from-to)5-26
Number of pages22
JournalMolecular Simulation
Volume6
Issue number1-3
DOIs
StatePublished - 1991
Externally publishedYes

Fingerprint

Chemical potential
Open systems
Open Systems
Chemical Potential
Molecular Dynamics
Molecular dynamics
molecular dynamics
Canonical Ensemble
Equations of motion
Equations of Motion
equations of motion
Ensemble
Trajectories
trajectories
Trajectory
Fractional Parts
Multicomponent Systems
Bulk Modulus
space density
Extended Systems

Keywords

  • chemical potential
  • extended system dynamics
  • Molecular dynamics
  • number fluctuations
  • open systems
  • thermodynamic response functions

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Information Systems
  • Materials Science(all)
  • Modeling and Simulation
  • Condensed Matter Physics
  • Chemistry(all)

Cite this

Grand molecular dynamics : A method for open systems. / çaĝin, Tahir; Pettitt, Bernard.

In: Molecular Simulation, Vol. 6, No. 1-3, 1991, p. 5-26.

Research output: Contribution to journalArticle

@article{8b802fd4af73497ab18ac1320864d85e,
title = "Grand molecular dynamics: A method for open systems",
abstract = "We present a new molecular dynamics method for studying the dynamics of open systems. The method couples a classical system to a chemical potential reservior. In the formulation, following the extended system dynamics approach, we introduce a variable, v to represent the coupling to the chemical potential reservoir. The new variable governs the dynamics of the variation of number of particles in the system. The number of particles is determined by taking the integer part of v. The fractional part of the new variable is used to scale the potential energy and the kinetic energy of an additional particle; i.e., we introduce a fractional particle. We give the ansatz Lagrangians and equations of motion for both the isothermal and the adiabatic forms of grand molecular dynamics. The averages calculated over the trajectories generated by these equations of motion represent the classical grand canonical ensemble (pVT) and the constant chemical potential adiabatic ensemble (μVL) averages, respectively. The microcanonical phase space densities of the adiabatic and isothermal forms the molecular dynamics method are shown to be equivalent to adiabatic constant chemical potential ensemble, and grand canonical ensemble partition functions. We also discuss the extension to multi-component systems, molecular fluids, ionic solutions and the problems and solutions associated with the implementation of the method. The statistical expressions for thermodynamic functions such as specific heat; adiabatic bulk modulus, Gr{\"o}neissen parameter and number fluctuations are derived. These expressions are used to analyse trajectories of constant chemical potential systems.",
keywords = "chemical potential, extended system dynamics, Molecular dynamics, number fluctuations, open systems, thermodynamic response functions",
author = "Tahir {\cc}aĝin and Bernard Pettitt",
year = "1991",
doi = "10.1080/08927029108022137",
language = "English (US)",
volume = "6",
pages = "5--26",
journal = "Molecular Simulation",
issn = "0892-7022",
publisher = "Taylor and Francis Ltd.",
number = "1-3",

}

TY - JOUR

T1 - Grand molecular dynamics

T2 - A method for open systems

AU - çaĝin, Tahir

AU - Pettitt, Bernard

PY - 1991

Y1 - 1991

N2 - We present a new molecular dynamics method for studying the dynamics of open systems. The method couples a classical system to a chemical potential reservior. In the formulation, following the extended system dynamics approach, we introduce a variable, v to represent the coupling to the chemical potential reservoir. The new variable governs the dynamics of the variation of number of particles in the system. The number of particles is determined by taking the integer part of v. The fractional part of the new variable is used to scale the potential energy and the kinetic energy of an additional particle; i.e., we introduce a fractional particle. We give the ansatz Lagrangians and equations of motion for both the isothermal and the adiabatic forms of grand molecular dynamics. The averages calculated over the trajectories generated by these equations of motion represent the classical grand canonical ensemble (pVT) and the constant chemical potential adiabatic ensemble (μVL) averages, respectively. The microcanonical phase space densities of the adiabatic and isothermal forms the molecular dynamics method are shown to be equivalent to adiabatic constant chemical potential ensemble, and grand canonical ensemble partition functions. We also discuss the extension to multi-component systems, molecular fluids, ionic solutions and the problems and solutions associated with the implementation of the method. The statistical expressions for thermodynamic functions such as specific heat; adiabatic bulk modulus, Gröneissen parameter and number fluctuations are derived. These expressions are used to analyse trajectories of constant chemical potential systems.

AB - We present a new molecular dynamics method for studying the dynamics of open systems. The method couples a classical system to a chemical potential reservior. In the formulation, following the extended system dynamics approach, we introduce a variable, v to represent the coupling to the chemical potential reservoir. The new variable governs the dynamics of the variation of number of particles in the system. The number of particles is determined by taking the integer part of v. The fractional part of the new variable is used to scale the potential energy and the kinetic energy of an additional particle; i.e., we introduce a fractional particle. We give the ansatz Lagrangians and equations of motion for both the isothermal and the adiabatic forms of grand molecular dynamics. The averages calculated over the trajectories generated by these equations of motion represent the classical grand canonical ensemble (pVT) and the constant chemical potential adiabatic ensemble (μVL) averages, respectively. The microcanonical phase space densities of the adiabatic and isothermal forms the molecular dynamics method are shown to be equivalent to adiabatic constant chemical potential ensemble, and grand canonical ensemble partition functions. We also discuss the extension to multi-component systems, molecular fluids, ionic solutions and the problems and solutions associated with the implementation of the method. The statistical expressions for thermodynamic functions such as specific heat; adiabatic bulk modulus, Gröneissen parameter and number fluctuations are derived. These expressions are used to analyse trajectories of constant chemical potential systems.

KW - chemical potential

KW - extended system dynamics

KW - Molecular dynamics

KW - number fluctuations

KW - open systems

KW - thermodynamic response functions

UR - http://www.scopus.com/inward/record.url?scp=0002899271&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002899271&partnerID=8YFLogxK

U2 - 10.1080/08927029108022137

DO - 10.1080/08927029108022137

M3 - Article

VL - 6

SP - 5

EP - 26

JO - Molecular Simulation

JF - Molecular Simulation

SN - 0892-7022

IS - 1-3

ER -