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Excitations of the N ‐particle system in the generalized random phase approximation
Author(s) -
Brener N. E.,
Fry J. L.,
Collins T. C.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560180846
Subject(s) - random phase approximation , coulomb , dielectric , function (biology) , dielectric function , term (time) , particle (ecology) , physics , excitation , statistical physics , particle system , quantum mechanics , basis (linear algebra) , mathematics , computer science , oceanography , geometry , evolutionary biology , biology , operating system , geology , electron
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.