Generalized Susceptibility Theory I. Theories of Hypochromism

A general theory is developed for the linear response of an interacting molecular system to an external field. The exact ground state of the system is expressed in terms of the uncoupled molecule (zeroth-order) state by means of adiabatic time-dependent perturbation theory. Including the external field to first order in the time-development operator leads to an infinite-order expansion of the linear response function for physical quantities such as current-charge density and electric-dipole polarization. Two basic approximations involving partial decorrelation of charge motion and spatial separability of the molecules allow the response function to be determined by a simplified Dyson-type equation, which can be put into closed form by further approximations. The approximate linear response function (susceptibility) so obtained is given in terms of the isolated molecule susceptibility and corresponds exactly to the results of classical, local field theory. Emphasis throughout is placed on the effect of molecular interaction on absorption spectra. Comparisons among theories of hypochromism show clearly that all previously reported theories are mutually compatible and are either equivalent to, or are contained in, the theory developed here. The relation of the present theory to a coupled equivalent oscillator model is discussed and the results are applied to a simple physical model.