Calculation of entropy from Molecular Dynamics:
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The estimation of free energies for gases and solids has long since a solved theoretical problem, but serious problems remain for the estimation of free energies, particularly entropy, in the liquid state. Free Energy Perturbation (FEP) and Thermodynamic Integration (TI) have long been established as reliable and, depending on the choice of force field, accurate methods for the estimation of solvation free energies. These methods have been able to achieve a high degree of statistical precision obtaining uncertainties for the free energy of hydration of 0.02– 0.06 kcal/mol for all aminoacids side chains, equivalent to that obtained in experimental hydration free energy measurements of the same molecules. The caveats of these methods are the long simulation runs required. State of the art calculations require over 100 simulations, each 5 nanoseconds in length are required, taking over 8 CPU years in a 2.8 GHz processor to complete [1]. We report on results of the application of the Two Phase Thermodynamic model (2PT) [2] to the estimation of free energies of liquids, using first principles models (QM charges and FF parameters) over 25 ps of MD obtain in less than 1 cpu hour. Our first focus, the estimation of entropies in the liquid state, appears very encouraging, with errors on the order of 0.1 kcal/mol*K for liquid water at room temperature. Other examples will include common protic and aprotic solvents for which reliable experimental entropies exist.
Fig 1. Power spectrum for water at 300 K. The power spectrum is decomposed into a gas (diffusive) and a solid (fixed) spectra and their contributions added to yield the free energy of the liquid state.
[1] Michael R. Shirts and Vijay S. Pande, Solvation free energies of amino acid side chain analogs for common molecular mechanics water models, The Journal Of Chemical Physics, 122, 134508, 2005
[2] Shiang-Tai Lin, Mario Blanco, and William A. Goddard III, The two-phase model for calculating thermodynamic properties of liquids from molecular dynamics: Validation for the phase diagram of Lennard-Jones fluids , J. Phys. Chem., 119, 11792, 2003