Free energy gradient

Also, because such derivatives are to be evaluated at the equilibrium geometry, a key point is the determination of that geometry on the solvated PES, which leads to the so-called indirect solvent effects , which still requires a viable method to calculate free energy gradients (and possibly hessians). The problem of the formulation of free energy derivatives within continuum solvation models is treated elsewhere in this book and for this reason it will not considered here. Instead, it is worth remarking in this context another implication of such a formulation, i.e. that a choice between a complete equilibrium scheme or the account for vibrational and/or electronic nonequilibrium solvent effects [42, 43] should be done (see below). 

A completely different approach has also been proposed to compute dQJdx [14,15] instead of finding the derivatives of Equation (3.7), one can differentiate the basic PCM electrostatic equations and then find the solutions to the new equations. By the repeated application of the divergence theorem, this procedure leads to the following expression for the free energy gradients ... 

Because of its use of average quantities, the free-energy gradient method is especially suited for use together with the MFA. Their joint application permits a considerable saving of computation time. The force experienced by the solute nuclei when the geometry is defined by the point r of the FES is [21-23]... 

Equation (7-22) can be finally summed to the standard DFT contribution to give the expression for the total free energy gradient of each state in the presence of the solvent ... 

Analytical RISM-MP2 free energy gradient method Application to the Schlenk equilibrium of Grignard reagent ... 

Equations (49), (50) and (51) can be differentiated with respect to external perturbations (e. g. electric or magnetic fields) and with respect to nuclear coordinates, allowing for the analytical computation of free energy gradients [103,104] and second derivatives [106,110] they are used for geometry optimisations in solution, and for the calculation of force constants, polarizabilities etc. 

---