Excitations of the N-particle system in the generalized random phase approximation

In this article we study excitations of the N-particle system by making use of a new formula for the dielectric function, called the generalized RPA (GRPA) formula, that goes beyond the RPA to include both exchange and correlation effects. In this GRPA formula, the first term is the RPA dielectric function, while the second term contains a screened Coulomb interaction. We introduce a method for making the GRPA dielectric function self-consistent with the screening function used to compute it, which leads to an even higher-order expression. We then develop a procedure for obtaining exact excitations of the N-particle system by using the GRPA dielectric function. In this procedure, the N-system excitation energies are given by the frequencies at which the determinant of the dielectric function is equal to zero. This technique, which is not strongly dependent of the size of the basis set used, has the major advantage of being computationally more feasible than other approaches to the problem.