Origin of the second-order optical susceptibilities of crystalline substituted benzene

An analysis of the second-order optical nonlinearities of crystalline substituted benzene is presented. A new irreducible tensor formalism for the decomposition of a crystal tensor as the sum of the contributions of microscopic units is developed and applied to the study of the second-order susceptibility in four benzene derivatives with related structures and substituent radicals ($m$-dinitrobenzene, $m$-nitroaniline, $m$-aminophenol, and resorcinol). It is shown that an additivity approach can precisely account for the crystal nonlinearities and enables one to calculate the contributions of each radical to the nonlinearity of the molecule. these contributions are found to be strongly related to the donor or acceptor character of the radical. A very simple model is proposed to explain this relation.