Theory of Linear Response in Molecules

Abstract

Consider a molecule weakly interacting with the external field, The change of any physical quantity of this molecule, in terms of the linear approximation to this interaction, is expressed as a commutator of two operators representing this physical quantity and interaction, respectively. lf we estimate the average value of this commutator, or the correlation function in space-time, in the lowest order (Hartree-Fock approximation), we obtain the result usually derived from the second order perturbation theery. ln the higher order approximation, say, taking into acount the electronic correlation, a technique of the many-body theory is effectively applicable. The above mentioned commutater is itself a retarded Green s function. To estimate this in terms of the systematic perturbation expansions, or diagramatically, we have to use the following procedures; first, the corresponding temperature Green s function is calculated, second, from it the desired retarded Green s function is obtained through analytical continuation. Actual calculation is performed up to the first order with respect to the electronic correlation.