Elementary presentation of self-consistent intermediate Hamiltonians and proposal of two totally dressed singles and doubles configuration interaction methods

Intermediate Hamiltonians are effective Hamiltonians which are defined on an N-dimensional model space but which only provide n<N exact eigenvalues and the projections of the corresponding eigenvectors onto the model space. For a single root research, the intermediate Hamiltonian may be obtained from the restriction of the Hamiltonian to the model space by an appropriate, uniquely defined dressing of the diagonal energies or of the first column. Approximate self-consistent dressings may be proposed. The simplest perturbative form gives the same result as the original 2nd order intermediate Hamiltonian or the ‘‘shifted Bk’’ technique but it is of easier implementation. Self-consistent inclusion of higher order exclusion principle violating corrections greatly improves the results, especially for nearly degenerate problems, as shown on several illustrative applications. Possible generalizations to enlarged or reduced model spaces are discussed.