Electronic hyperpolarizability calculation without the periodic images error for a large nonlinear molecule

A Green's-function technique, i.e., the effective screening medium method of Otani and Sugino [Phys. Rev. B 73, 115407 (2006)] for solving the Poisson's equation for a large organic nonlinear optical (NLO) molecule is investigated. This approach is essentially as efficient as the periodic treatment of the reciprocal-space method using fast Fourier transform while the direction along the dipole moment solved analytically under a given boundary condition. Unlike other correction methods such as the cutoff or multipole method, this scheme only requires the minimum size of the supercell. Here we study an application to the linear and second-order nonlinear optical properties of the NLO molecules in gas phase within the time-dependent density-functional theory and address a large periodic image error associated with the reciprocal-space method. We conclude that the Green's-function method is especially important and useful for a large-scale nonlinear molecule including future possibility of incorporating solvent effects.