Operator manifolds truncation

Because of the high research activity level on how to use an MCSCF reference in the GFs (EP and PP), it is not presently clear how to optimally choose truncated sets of 1V operators. It is likely that many workers will carry out test calculations involving many choices of the pertinent operator manifolds before this situation is improved. Moreover, questions concerning when and how to partition the resulting (1V / T/) matrix so as to reduce the dimension of the matrix whose poles are to be found remain unanswered... 

So far everything is exact. A complete manifold of excitation operators, however, means that all excited states are considered, i.e. a full Cl approach. Approximate versions of propagator methods may be generated by restricting the excitation level, i.e. truncating h. A complete specification furthermore requires a selection of the reference, normally taken as either an HF or MCSCF wave function. 

The cluster operator f of the truncated wave function contains only a subset of the full set of excitation operators. For example, in a CCSD calculation, we include in the cluster operator only the single and double excitations out of the Hartree-Fock reference state. The projection manifold Ipi) is initially chosen in the usual manner - that is, such that it spans all the states that may he created when the cluster operator works on the RHF reference state. The total number of amplitudes (and states in the projection manifold) is denoted hy A d-... 

In single-reference CC the excitation operators contain only creation operators (particle or hole) with respect to the Fermi vacuum. In MRCC there is no unique choice of Fermi vacuum, but for any choice annihilation operators will appear in the excitation manifold so that the BCH-expansion of the similarity-transformed Hamiltonian will not truncate to quartic order. 

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