Ab initio calculation of the free energy of liquid water

Mezei, Mihaly; Swaminathan, S.; Beveridge, David L.

doi:10.1021/ja00478a070

Cited by 108 publications

(69 citation statements)

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“…Several studies of the free energy of argon (21, 26 -31) and water (32)(33)(34)(35)(36)(37)(38) have been published, most of them for systems that differ in size (as well as other modeling details) from the present ones. Therefore, for an objective evaluation of our results, we also calculated the free energies for our particular systems of argon and water by using TI.…”

Section: Resultsmentioning

confidence: 99%

A simulation method for calculating the absolute entropy and free energy of fluids: Application to liquid argon and water

White

Meirovitch

2004

Proc. Natl. Acad. Sci. U.S.A.

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The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy and free energy by analyzing Boltzmann samples obtained by Monte Carlo (MC) or molecular dynamics techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by adding its atoms gradually to the initially empty volume, i.e., by placing them in their positions at i using transition probabilities (TPs). At each step of the process, the volume is divided into two parts, the already visited part (the ''past'') and the ''future'' part, where obtaining the TP requires calculating partition functions over the future part in the presence of the frozen past. In recent publications, the TPs were calculated approximately by taking into account only partial future. Here we present a ''complete HSMC'' procedure, where the TPs are calculated from MC simulations carried out over the complete future. The complete HSMC method is applied to systems of liquid argon and the TIP3P model of water, and very good results for the free energy are obtained, as compared with results obtained by thermodynamic integration.T he absolute entropy, S, is a measure of order and is also a fundamental component of the absolute Helmholtz free energy, F, F ϭ E Ϫ TS, where E is the energy and T is the absolute temperature. The free energy is a key quantity as it constitutes the correct criterion of stability, which is mandatory for determining the relative populations of protein structures, for example. However, calculation of S and therefore F of a complex system, such as a peptide or a protein in water by computer simulation, is an extremely difficult problem (1-4). Using any simulation technique, it is relatively easy to calculate the energy, E i , which is ''written'' on system configuration i in terms of microscopic interactions (e.g., Lennard-Jones interactions of argon). On the other hand, calculating S Ϸ Ϫln P i B requires knowledge of the value of the Boltzmann probability, which is the sampling probability. However, P i B is not provided directly by the commonly used dynamical techniques, Metropolis Monte Carlo (MC) (5) and molecular dynamics (MD) (6 -7), therefore, F is unknown as well. In most cases, calculation of F is based on reversible thermodynamic integration (TI) techniques that provide the difference in the free energy, ⌬F m,n , between two states m and n, (e.g., helical and hairpin states of a peptide) and only when the absolute entropy of one state is known can that of the other be obtained. Although TI is a robust approach (refs. 1-4, 8, and 9 and references therein), for proteins, such integration is feasible only if the structural variance between the two states is very small; otherwise, the integration path can become prohibitively lengthy and complex. Therefore, it is important to develop methods that provide ln P i B at least approximately, enabling one to calculate the absolute F m and F n from two samples of the states m and n; in this case ⌬F m,n ϭ F m Ϫ F n can be calculated even for significa...

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Section: Resultsmentioning

confidence: 99%

A simulation method for calculating the absolute entropy and free energy of fluids: Application to liquid argon and water

White

Meirovitch

2004

Proc. Natl. Acad. Sci. U.S.A.

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“…Many early applications focused on solvation free energies. [26][27][28][29][30][31][32][33][34][35][36][37][38] Soon after the basic idea for relative binding free energy calculations was laid out, 39 the first applications to binding followed, in host-guest systems 30,40,41 and proteins. 35,[42][43][44][45][46][47] Several early reviews provide useful perspective.…”

Section: B Free Energy Calculations Could Guide Structure-based Designmentioning

confidence: 99%

Perspective: Alchemical free energy calculations for drug discovery

Mobley

Klimovich²

2012

The Journal of Chemical Physics

228

295

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“…Free-energy calculation involves either a direct calculation of entropy or special thermodynamic integration methods. [56][57][58] At present, methods to calculate free energy are still under development and computationally very expensive.59 To date, we have not performed any free-energy calculations with our protein-PEG-water systems, but once the methodology is validated, such calculations will enable direct comparisons between experiments and simulations.…”

Section: The Excluded Volume and Effect Of Solventsmentioning

confidence: 99%