Analytical derivatives for molecular solutes. I. Hartree–Fock energy first derivatives with respect to external parameters in the polarizable continuum model

Analytical expressions for the derivatives of the free energy of solution of molecular solutes with respect to the dielectric constant and to a parameter defining the size of the cavity are here presented. These derivatives refer to a version of the model that describes solutes at ab initio Hartree–Fock level (as well as at the classical level) placed within a cavity reproducing the molecular shape. Attention is paid to the appropriate description of the boundary conditions which determine the integral value of the apparent charge spread on the cavity surface.