On the Construction of Size Extensive Effective Hamiltonians in General Model Spaces Using Quasi-Hilbert and Quasi-Fock Strategies

Abstract

There has been an ever-growing interest over the last two decades towards developing and implementing the formalism of effective hamiltonians [1] in the framework of many-body perturbation theory (MBPT) and coupled cluster (CC) theory [2, 3]. One major thrust in all these developments has been the desire to obtain size-extensive effective hamiltonians Heff which give size-extensive energies upon diagonalization within the model space. The traditional formulations of both MBPT [4] and CC theory [5–9] for the open-shells were built upon complete model spaces (CMS), and a connected Heff could be obtained in all these formalisms. The energies obtained on diagonalization were automatically size-extensive owing to the completeness of the model space.