Polarization energies in the fragment molecular orbital method.

Using isolated and polarized states of fragments, a method for computing the polarization energies in density functional theory (DFT) and density-functional tight-binding (DFTB) is developed in the framework of the fragment molecular orbital method. For DFTB, the method is extended into the use of periodic boundary conditions (PBC), for which a new component, a periodic self-polarization energy, is derived. The couplings of the polarization to other components in the pair interaction energy analysis (PIEDA) are derived for DFT and DFTB, and compared to Hartree-Fock and second-order Møller-Plesset perturbation theory (MP2). The effect of the self-consistent (DFT) and perturbative (MP2) treatment of the electron correlation on the polarization is discussed. The difference in the polarization in the bulk (PBC) and micro (cluster) solvation is elucidated.