A consistent third-order propagator method for electronic excitation

A propagator method referred to as third-order algebraic-diagrammatic const ruction [ADC(3)] for the direct computation of electronic excitation energi es and transition moments is presented. This approach is based on a specifi c reformulation of the diagrammatic perturbation expansion for the polariza tion propagator, and extends the existing second-order [ADC(2)] scheme to t he next level of perturbation theory. The computational scheme combines dia gonalization of a Hermitian secular matrix and perturbation theory for the matrix elements. The characteristic properties of the method are compact co nfiguration spaces, regular perturbation expansions, and size-consistent re sults. The configuration space is spanned by singly and doubly excited stat es, while the perturbation expansions in the secular matrix extend through third order in the p-h block, second order in the p-h/2p-2h coupling block, and first order in the 2p-2h block. While the simpler ADC(2) method, repre senting a counterpart to the MP2 (second-order Moller-Plesset) ground-state method, recommends itself for application to larger molecules, the ADC(3) scheme is aimed at a more accurate description of molecular excitation spec tra. The relationship of the ADC(3) scheme with coupled cluster methods is discussed, focusing here in particular on the treatment of transition momen ts. (C) 1999 American Institute of Physics. [S0021-9606(99)30345-7].