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Optimal sampling efficiency in Monte Carlo sampling with an approximate potential

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.3116788· OSTI ID:956349
 [1];  [1];  [2]
  1. Los Alamos National Laboratory
  2. U MISSOURI
+ Show Author Affiliations
Building on the work of Iftimie et al., Boltzmann sampling of an approximate potential (the 'reference' system) is used to build a Markov chain in the isothermal-isobaric ensemble. At the endpoints of the chain, the energy is evaluated at a higher level of approximation (the 'full' system) and a composite move encompassing all of the intervening steps is accepted on the basis of a modified Metropolis criterion. For reference system chains of sufficient length, consecutive full energies are statistically decorrelated and thus far fewer are required to build ensemble averages with a given variance. Without modifying the original algorithm, however, the maximum reference chain length is too short to decorrelate full configurations without dramatically lowering the acceptance probability of the composite move. This difficulty stems from the fact that the reference and full potentials sample different statistical distributions. By manipulating the thermodynamic variables characterizing the reference system (pressure and temperature, in this case), we maximize the average acceptance probability of composite moves, lengthening significantly the random walk between consecutive full energy evaluations. In this manner, the number of full energy evaluations needed to precisely characterize equilibrium properties is dramatically reduced. The method is applied to a model fluid, but implications for sampling high-dimensional systems with ab initio or density functional theory (DFT) potentials are discussed.
Research Organization:
Los Alamos National Laboratory (LANL)
Sponsoring Organization:
DOE
DOE Contract Number:
AC52-06NA25396
OSTI ID:
956349
Report Number(s):
LA-UR-09-00498; LA-UR-09-498
Journal Information:
Journal of Chemical Physics, Journal Name: Journal of Chemical Physics; ISSN JCPSA6; ISSN 0021-9606
Country of Publication:
United States
Language:
English

References (48)

Temperature Scaling Method for Markov Chains journal December 2008
Reactive Canonical Monte Carlo book January 1999
Unified Approach for Molecular Dynamics and Density-Functional Theory journal November 1985
Vapor–liquid equilibria of water from first principles: comparison of density functionals and basis sets journal November 2006
Strict detailed balance is unnecessary in Monte Carlo simulation journal February 1999
Monte Carlo simulation of equilibrium chemical composition of molecular fluid mixtures in the N atoms PT ensemble journal June 1991
On a novel Monte Carlo scheme for simulating water and aqueous solutions journal May 1978
CHEMISTRY: Shaped Laser Pulses as Reagents journal January 2003
Efficient estimation of free energy differences from Monte Carlo data journal October 1976
Multilevel summation and Monte Carlo simulations journal August 2006
Monte Carlo sampling methods using Markov chains and their applications journal April 1970
Equation of State Calculations by Fast Computing Machines journal June 1953
Efficient sampling for ab initio Monte Carlo simulation of molecular clusters using an interpolated potential energy surface journal January 2009
Simulation of chemical reaction equilibria by the reaction ensemble Monte Carlo method: a review† journal February 2008
Multiple “time step” Monte Carlo simulations: Application to charged systems with Ewald summation journal January 2004
Studies in Molecular Dynamics. I. General Method journal August 1959
Stochastic potential switching algorithm for Monte Carlo simulations of complex systems journal June 2005
Two-surface Monte Carlo with basin hopping: Quantum mechanical trajectory and multiple stationary points of water cluster journal April 2008
An efficient Monte Carlo method for calculating ab initio transition state theory reaction rates in solution journal December 2003
Tests of the empirical potential structure refinement method and a new method of application to neutron diffraction data on water journal September 2001
Multiphoton Control of the 1,3-Cyclohexadiene Ring-Opening Reaction in the Presence of Competing Solvent Reactions journal July 2008
Separation of quantum and classical behavior in proton transfer reactions: Implications from studies of secondary kinetic isotope effects journal October 2002
Resolution Exchange Simulation journal January 2006
Monte Carlo simulations using sampling from an approximate potential journal May 2003
Monte Carlo free energy calculations using electronic structure methods journal April 2008
Sampling enhancement for the quantum mechanical potential based molecular dynamics simulations: A general algorithm and its extension for free energy calculation on rugged energy surface journal March 2007
Reactive canonical Monte Carlo: A new simulation technique for reacting or associating fluids journal February 1994
Accelerating quantum mechanical/molecular mechanical sampling using pure molecular mechanical potential as an importance function: The case of effective fragment potential journal February 2005
On the force bias Monte Carlo simulation of water: methodology, optimization and comparison with molecular dynamics journal June 1979
Isothermal–isobaric Monte Carlo simulations of liquid lithium using density functional theory journal January 2006
Linear scaling electronic structure methods journal July 1999
Isobaric-Isothermal Monte Carlo Simulations from First Principles: Application to Liquid Water at Ambient Conditions journal September 2005
The thermodynamics of dense fluid nitrogen by molecular dynamics journal February 1984
Empirical potential Monte Carlo simulation of fluid structure journal January 1996
Ab initio molecular dynamics: basic concepts, current trends and novel applications journal December 2002
Using a classical potential as an efficient importance function for sampling from an ab initio potential journal January 2000
Protein-Ligand Binding Affinity Predictions by Implicit Solvent Simulations:  A Tool for Lead Optimization? journal November 2006
Efficient ab initio sampling methods in rate constant calculations for proton-transfer reactions journal April 2001
Liquid Water from First Principles:  Investigation of Different Sampling Approaches journal August 2004
Efficient Generalized Born Models for Monte Carlo Simulations journal April 2006
Resolution Exchange Simulation with Incremental Coarsening journal May 2006
Machine Calculation of Thermodynamic Properties of a Simple Fluid at Supercritical Temperatures journal December 1967
Assessment of Two Surface Monte Carlo (TSMC) method to find stationary points of (H2O)15 and (H2O)20 clusters journal May 2007
Multiple “time step” Monte Carlo journal November 2002
Toward a Monte Carlo program for simulating vapor–liquid phase equilibria from first principles journal July 2005
Electron correlation effects on the N2–N2 interaction journal August 1984
NpT ‐Ensemble Monte Carlo Calculations for the Hard‐Disk Fluid journal January 1970
Brownian dynamics as smart Monte Carlo simulation journal November 1978

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Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
APPROXIMATIONS
EFFICIENCY
FLUID MECHANICS
MONTE CARLO METHOD
PROBABILITY
SAMPLING
THERMODYNAMICS