Continual Model of Medium IV: Calculation of analytical gradients for solvation energy over atomic coordinates

In the given paper we describe methods finding analytical gradients (derivatives) of solvation energy over atomic coordinates. It is made both for not polar energy and for the polar energy found by methods PCM, COSMO and SGB. These gradients are searched with use of analytical gradients of parameters (coordinates, normal vectors and squares) the surface meshes. The surface meshes are located on both the optimal smooth molecular surfaces: solvent excluded surface (SES) and surface solvent accessible surface (SAS) received from SES. These surfaces are found by methods of primary and secondary rolling according to the algorithm described in the previous papers of the series.