Electronic energy coupled-cluster waves functions

The coupled-cluster electronic state is uniquely defined by the set of the cluster amplitudes and these amplitudes are used to obtain the coupled-cluster energy from Eq. (33). Due to the fact that the Ansatz of the coupled-cluster wave function has the exponential parametrization [Eq. (28)] the energy is size-extensive. This is an obvious advantage of the coupled-cluster formalism compared to some other techniques (e.g. configuration interaction). For a general discussion of coupled-cluster theory and the coupled-cluster equations see Refs. [5, 36]. 

Table 5.11 The difference between the cc-pVDZ electronic energies of restricted coupled-cluster wave functions and the FCT wave function E — Epa) of the C2, water molecule for the OH distances Rref and 2Rta (in E, ). The HOH bond angle is fixed at 110.565° and Rret = l.84345oo...

Frequency-dependent response functions can only be computed within approximate electronic structure models that allow definition of the time-dependent expectation value. Hence, frequency-dependent response functions are not defined for approximate methods that provide an energy but no wave function. Such methods include MoUer-Plesset (MP) perturbation theory, multiconfigurational second-order perturbation theory (CASPT2), and coupled cluster singles and doubles with non-iterative perturbative triples [CCSD(T)]. As we shall see later, it is possible to derive static response functions for such methods. 

Of course, with HF wave functions in hand, it is possible to carry out post-HF calculations to partially correct for electron correlation effects. The poor quality of the HF wave functions, however, militate against any treatment much less sophisticated than coupled-cluster. At the CCSD(T)/cc-pVDZ level, the predicted energy of the lowest closed-shell singlet is in fair agreement with experiment (other data in the table suggest that use of a triple- basis set would improve the CCSD(T) estimate). The energy of the second closed-shell singlet state... 

T. Korona, B. Jeziorski, One-electron properties and electrostatic interaction energies from the expectation value expression and wave function of singles and doubles coupled cluster theory. 

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