Formal theory of effective π‐electron hamiltonians

Abstract

AbstractWe argue that the goal of developing a satisfactory general formalism for the justification of effective π‐electron Hamiltonians, as well as for ab initio calculation of their parameters (α, β, and γ), has now been achieved. The need for a fully linked many‐body formalism is emphasized; this feature requires a Rayleigh–Schrödinger (RS) type of degenerate perturbation theory. A number of apparently different degenerate RS perturbation formalisms are reviewed. Most of these formalisms are actually identical term‐by‐term, when their RS expansions are worked out explicitly; the formal relations that prove their complete equivalence are presented and discussed. One of these formalisms, a version developed by the author for related open‐shell problems in nuclear physics, is shown to be most convenient for many‐body applications. This is owing to the relatively simple and transparent nature of its general algebraic structure, which facilitates partial summation to infinite order. A simple and concise derivation is presented for the algebraic features of this preferred formalism, and its many‐body (linked cluster) aspects are briefly discussed. The recent development of a nonperturbative (coupled‐cluster) analog of this formalism is also described. Some practical issues are examined, including the choice of orbital basis. Illustrative numerical results are presented, based on the calculations of Iwata and Freed. Several remaining problems are described; these are both qualitative and quantitative in nature, and their resolution will require some detailed calculations.