Similarity-transformed normal-ordered Hamiltonian

The concepts of normal ordering and Wick s theorem provide the mathematical tools needed to derive programmable coupled cluster equations from the more formal expressions given in Eqs. [50] and [51]. If we truncate the cluster operator such that T = Tj + T2 insert it into the similarity-transformed normal-ordered Hamiltonian, H = e lij e, we obtain... 

Alternatively to the hermitean effective Hamiltonian just discussed, we can consider a nonhermitean effective Hamiltonian L obtained by a projecting similarity transformation in intermediate normalization. Actually the first formulation of quasidegenerate DPT by Rutkowski and Schwarz [76] was given in terms of a nonhermitean effective Hamiltonian. This is particularly useful if one wants to extend quasidegenerate DPT to infinite order. 

The transformation to an extended-orbital basis modifies the Hamiltonian matrix of Fig. 3-4. We shall evaluate the new matrix elements here for a perfect crystal to illustrate the technique bear in mind that it is very easy to carry out a similar analysis for imperfect crystals by recalculating the extended orbitals for such systems. We first obtain the diagonal element, / (the denominator is required since B> is not normalized to second order as required for the second-order diagonal terms). We do this by writing out the state... 

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