Direct determination of effective Hamiltonians by wave-operator methods. I. General formalism

The determination of the most standard effective Hamiltonians is obtained by means of a simple general similarity transformation. The wave operator is shown to be a solution of an operator equation which is the analog of the M{}ller equations of scattering theory and which generalizes those previously established by Bloch, L\"owdin, J{}rgensen, and Lindgren. The wave-operator equation is solved by efficient iteration or perturbation-iteration methods which exhibit good convergence properties for degenerate systems and/or in presence of intruder states. In the following paper the method is applied to the theoretical determination of transferable effective-spin interactions.