Analytical second derivatives of the free energy in solution by polarizable continuum models

We present an algorithm for the analytical evaluation of flee energy second derivatives with respect to nuclear displacements in the framework of the polarizable continuum model (PCM). The algorithm has been obtained for two recently proposed PCM versions, namely the conductor-like and the isotropic integral equation formalism models, and it can be applied to Hartree-Fock and to density functional SCF calculations on closed- and open-shell systems. The formal derivation is shown in detail and a number of numerical tests are presented: the applications show that analytical results are in excellent agreement with those obtained numerically and, as in vacuo, the analytical procedure is far more efficient. The presented algorithm can be routinely used with an upcoming release of the Gaussian program. (C) 1998 American Institute of Physics. [S0021-9606(98)30838-7].