The extension of the fragment molecular orbital method with the many-particle Green's function

By using the many-particle Green's function (GF) the extension of the fragment molecular orbital (FMO) method by Kitaura et al. [Chem. Phys. Lett. 313, 701 (1999)] is proposed. It is shown that the partial summation of the cluster expansion of GF reproduces the same extrapolation formula as that of FMO. Therefore we can determine the excitation energy, the transition moment, and the linear response of a molecule from GF approximated with the FMO procedure. It is also shown that no wave function exists which is consistent to the FMO results. The perturbation expansion in which the self-consistent charge approximation defines the unperturbed state is reported. By using it the three-body effects missing in the pair approximation of FMO are analyzed and the corrections to the energy and the reduced density matrices are proposed. In contrast to the previous works these new corrections are not expressed as the addition or the subtraction of the energies of fragments. They are size extensive and require only the quantities available by the FMO calculation. The accuracy of these corrections is validated with the extended Hubbard model and the several test molecules.