Intermediate Hamiltonians as a new class of effective Hamiltonians

Abstract

The theory of effective Hamiltonians is well established. However, limitations appear in its applicability for many problems in molecular physics and quantum chemistry. The standard effective Hamiltonians may become strongly non-Hermitian when there is a large coupling between the model space, in which they are defined, and the outer space Moreover, in the presence of intruder states, discontinuities appear in the matrix elements of these effective Hamiltonians as a function of the internuclear distances. To solve these difficulties, a new class of effective Hamiltonians (called intermediate Hamiltonians) is presented; only one part of their roots are exact eigen-energies of the full Hamiltonian. The theory of these intermediate Hamiltonians is presented by means of a new wave-operator R which is the analogue of the wave-operator Omega in the theory of effective Hamiltonians. Solutions are obtained by a generalised degenerate perturbation theory (GDPT) and by iterative procedures. Two model systems are numerically solved which demonstrate the good convergence properties of GDPT with respect to standard degenerate perturbation theory (DPT). Continuity of the solutions is also checked in the presence of an intruder state.