Free energy thermodynamic integration methods

Simulations, Time-dependent Methods and Solvation Models 16.1 Simulation Methods 16.1.1 Free Energy Methods 16.1.2 Thermodynamic Perturbation Methods 16.1.3 Thermodynamic Integration Methods 16.2 Time-dependent Methods ill 373 380 380 381 383 ... 

This is the master equation for the free energy method termed thermodynamic integration (TI). In practice, the integrand in equation (32) is evaluated at a series of discrete points, and the integral is approximated from these points using... 

Thermodynamic integration (TI) provides another related method for determining free energy differences in simulations. " The approach involves calculation of a free energy difference through integration,... 

What has been developed within the last 20 years is the computation of thermodynamic properties including free energy and entropy [12, 13, 14]. But the ground work for free energy perturbation was done by Valleau and Torrie in 1977 [15], for particle insertion by Widom in 1963 and 1982 [16, 17] and for umbrella sampling by Torrie and Valleau in 1974 and 1977 [18, 19]. These methods were primarily developed for use with Monte Carlo simulations continuous thermodynamic integration in MD was first described in 1986 [20]. 

The overall free energy can be partitioned into individual contributions if the thermo-lynamic integration method is used [Boresch et al. 1994 Boresch and Karplus 1995]. The itarting point is the thermodynamic integration formula for the free energy ... 

As noted above, it is very difficult to calculate entropic quantities with any reasonable accmacy within a finite simulation time. It is, however, possible to calculate differences in such quantities. Of special importance is the Gibbs free energy, as it is the natoal thermodynamical quantity under normal experimental conditions (constant temperature and pressme. Table 16.1), but we will illustrate the principle with the Helmholtz free energy instead. As indicated in eq. (16.1) the fundamental problem is the same. There are two commonly used methods for calculating differences in free energy Thermodynamic Perturbation and Thermodynamic Integration. 

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