Wave operators connection with perturbation theory

Connection with perturbation theory the wave and reaction operators in the generd case. 

Connection with perturbation theory the wave and reaction operator in the general case.- Let us now consider the case when the Hamiltonian H consists of two terms H = + V, where the perturbation V does not... 

The coupled cluster (CC) method is actually related to both the perturbation (Section 5.4.2) and the Cl approaches (Section 5.4.3). Like perturbation theory, CC theory is connected to the linked cluster theorem (linked diagram theorem) [101], which proves that MP calculations are size-consistent (see below). Like standard Cl it expresses the correlated wavefunction as a sum of the HF ground state determinant and determinants representing the promotion of electrons from this into virtual MOs. As with the Mpller-Plesset equations, the derivation of the CC equations is complicated. The basic idea is to express the correlated wave-function Tasa sum of determinants by allowing a series of operators 7), 73,... to act on the HF wavefunction ... 

The generalized Bloch equation (12) is the basis of the RS perturbation theory. This equation determines the wave operator and, together with Eq. (11), the energy corrections for all states of interest especially, it leads to perturbation expansions which are independent of the energy of the individual states, just referring the unperturbed basis states. Another form, better suitable for computations, is to cast this equation into a recursive form which connects the wave operators of two consecutive orders in the perturbation V. To obtain this form, let us start from the standard representation of the Bloch equation (16) in intermediate normalization and define... 

In obtaining (14.2.23), we have used the fact that the cluster operator (14.2.22) gives zero when applied to the bra state (HF. The connection with coupled-cluster theory is a close one, which we shall explore in Section 14.3. At this stage, the reader may wish to compare the expression for the Mpller-Plesset anq)litudes (14.2.23) with the expression (13.4.10) used in the perturbation-based optimization of coupled-cluster wave functions. 

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