Simulation techniques thermodynamic integration

Straatsma, T.P, Berendsen, H.J.C. Free energy of ionic hydration Analysis of a thermodynamic integration technique to evaluate free energy differences by molecular dynamics simulations. J. Chem. Phys. 89 (1988) 5876-5886. 

Various methodologies have been developed to determine the free energy barriers from MD simulations. One of the common approaches applied in ab initio MD, known as the potential of mean force method has been derived from the thermodynamic integration technique. 34,35 In a canonical (NVT) ensemble the free energy difference, AA, between the two states, 0 and 1, can be calculated as the integral... 

Straatsma, T. P. (1987). Free energy evaluation by molecular dynamics simulations. Analysis of the perturbation method and a thermodynamic integration technique. In Department of Biophysical ChemistryUniversity of... 

Recent years have seen the extensive application of computer simulation techniques to the study of condensed phases of matter. The two techniques of major importance are the Monte Carlo method and the method of molecular dynamics. Monte Carlo methods are ways of evaluating the partition function of a many-particle system through sampling the multidimensional integral that defines it, and can be used only for the study of equilibrium quantities such as thermodynamic properties and average local structure. Molecular dynamics methods solve Newton s classical equations of motion for a system of particles placed in a box with periodic boundary conditions, and can be used to study both equilibrium and nonequilibrium properties such as time correlation functions. 

This chapter has reviewed theoretical and practical aspects of thermodynamic perturbation and thermodynamic integration, two popular methods of extracting free energies from molecular simulations. These methods find broad application in molecular simulation studies of chemical and biochemical systems. The fundamental importance of free energy in physical and chemical processes will inspire further development and refinement of these techniques. With the increasing performance of new computer architectures,these free energy techniques will become even more powerful and versatile tools. 

Figure 26 Phase diagram for the /j4t4-solute-solvent system in three dimensions. The open circles are the data obtained from Monte Carlo simulations (a thin dashed line is drawn through these points to guide the eyes). The quasichemical results are shown by the solid lines. The filled squares are based on the thermodynamic integration technique, while the filled circles are plait point estimates. (From Ref 25.)...

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