Lower and upper bounds for the absolute free energy by the hypothetical scanning Monte Carlo method: Application to liquid argon and water
- 8 December 2004
- journal article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 121 (22), 10889-10904
- https://doi.org/10.1063/1.1814355
Abstract
The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy S and free energy F by analyzing Boltzmann samples obtained by Monte Carlo or molecular dynamics techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by gradually placing the molecules in their positions at i using transition probabilities (TPs). At each step of the process the system is divided into two parts, the already treated molecules (the "past"), which are fixed, and the as yet unspecified (mobile) "future" molecules. Obtaining the TP exactly requires calculating partition functions over all positions of the future molecules in the presence of the frozen past, thus it is customary to invoke various approximations to best represent these quantities. In a recent publication [Proc. Natl. Acad. Sci. USA 101, 9235 (2004)] we developed a version of HS called complete HSMC, where each TP is calculated from an MC simulation involving all of the future molecules (the complete future); the method was applied very successfully to Lennard-Jones systems (liquid argon) and a box of TIP3P water molecules. In its basic implementation the method provides lower and upper bounds for F, where the latter can be evaluated only for relatively small systems. Here we introduce a new expression for an upper bound, which can be evaluated for larger systems. We also propose a new exact expression for F and verify its effectiveness. These free energy functionals lead to significantly improved accuracy (as applied to the liquid systems above) which is comparable to our thermodynamic integration results. We formalize and discuss theoretical aspects of HSMC that have not been addressed in previous studies. Additionally, several functionals are developed and shown to provide the free energy through the analysis of a single configuration.Keywords
This publication has 41 references indexed in Scilit:
- Partition functions and equilibrium measures in two-dimensional and quasi-three-dimensional turbulencePhysics of Fluids, 1996
- Computer simulation of the free energy of peptides with the local states method: Analogues of gonadotropin releasing hormone in the random coil and stable statesBiopolymers, 1994
- Separation-shifted scaling, a new scaling method for Lennard-Jones interactions in thermodynamic integrationThe Journal of Chemical Physics, 1994
- Free energy calculations: Applications to chemical and biochemical phenomenaChemical Reviews, 1993
- Direct Calculation of the Excess Free Energy of the Dense Lennard-Jones FluidMolecular Simulation, 1989
- Grand-canonical ensemble Monte Carlo study of dense liquidMolecular Physics, 1987
- Computer simulation of the free energy of polymer chains with excluded volume and with finite interactionsPhysical Review A, 1985
- Comparison of simple potential functions for simulating liquid waterThe Journal of Chemical Physics, 1983
- Monte Carlo free energy estimates using non-Boltzmann sampling: Application to the sub-critical Lennard-Jones fluidChemical Physics Letters, 1974
- Monte Carlo Evaluation of the Partition Function for a Hard-Disk SystemPhysical Review A, 1973