Part V
A Look at Related Methods
We set out from diagrammatic perturbation theory for propagators, developed a
practical approach for deriving systematic higher-order approximation schemes, and
finally established a relationship to a wave-function description by identifying the
direct ADC schemes as intermediate state representations (ISR) based on correlated
excited (CE) states. In the final two chapters we will make contact with two important
concepts, both of which can be understood as particular ISR variants: The equationof-motion (EOM) method establishing an algebraic approach to the electron and
other propagators (Chap. 16) and the coupled-cluster (CC) theory for generalized
electronic excitations (Chap.17). The intuitive idea underlying the use of CE states
is that the excitation, removal or attachment of an electron will affect the initial
N -electron ground state to a certain extent, but not totally alter it. Therefore the use of
CE basis states conveying the ground-state information should afford some advantage
over the simple CI treatment in which every excited state must be constructed from
the scratch as an expansion in terms of the uncorrelated HF excitations. However,
as we have seen, a proper orthonormalization of the CE states is crucial for these
advantages to materialize. So it will be interesting to see how the orthonormalization
of the CE states is handled in the context of the EOM and CC methods.
A Look at Related Methods
We set out from diagrammatic perturbation theory for propagators, developed a
practical approach for deriving systematic higher-order approximation schemes, and
finally established a relationship to a wave-function description by identifying the
direct ADC schemes as intermediate state representations (ISR) based on correlated
excited (CE) states. In the final two chapters we will make contact with two important
concepts, both of which can be understood as particular ISR variants: The equationof-motion (EOM) method establishing an algebraic approach to the electron and
other propagators (Chap. 16) and the coupled-cluster (CC) theory for generalized
electronic excitations (Chap.17). The intuitive idea underlying the use of CE states
is that the excitation, removal or attachment of an electron will affect the initial
N -electron ground state to a certain extent, but not totally alter it. Therefore the use of
CE basis states conveying the ground-state information should afford some advantage
over the simple CI treatment in which every excited state must be constructed from
the scratch as an expansion in terms of the uncorrelated HF excitations. However,
as we have seen, a proper orthonormalization of the CE states is crucial for these
advantages to materialize. So it will be interesting to see how the orthonormalization
of the CE states is handled in the context of the EOM and CC methods.