Missing-state analysis: A method for determining the origin of molecular nonlinear optical properties

A ‘‘missing-state’’ analysis is introduced and used to identify excited states and dynamics important for ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ and ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$. This method is applied to the Pariser-Pople-Parr self-consistent-field configuration-interaction transition moments and energies that are used to calculate the second-harmonic susceptibility ${\chi }_{2\omega }^{\mathrm{}\left(2\right)\mathrm{}}$ and the third-harmonic susceptibility ${\chi }_{3\omega }^{\mathrm{}\left(3\right)\mathrm{}}$ for a group of organic molecules. Examination of charge and bond-order distributions for the relevant states reveals the nature of the states that contribute to the nonlinear optical processes. Results are presented for benzene, nitrobenzene, p-dinitrobenzene, and p-nitroaniline.