Gabriel Hose

Diagrammatic many-body perturbation theory for general model spaces

Previous formulations, due to Brandow (1977) and subsequent authors, are limited to complete model spaces, including all possible occupations of open-shell orbitals. This definition of the model space may be troublesome for systems with several open shells, such as most molecular excited states, leading to intruder states and slowing or even destroying the convergence of the perturbation series. The formalism presented here applies to any model space, whether complete or incomplete, degenerate, quasi-degenerate or non-degenerate. Certain types of unlinked diagrams may appear for incomplete, quasi-degenerate model spaces. The orbitals are partitioned into two classes (holes and particles) for the purpose of diagram summation instead of Brandows three (core, valence and particles), with the partitioning for a particular element of the effective interaction matrix determined by the ket state of that element.

A General-Model-Space Diagrammatic Perturbation Theory

A diagrammatic many-body perturbation theory applicable to arbitrary model spaces is presented. The necessity of having a complete model space (all possible occupancies of the partially-filled shells) is avoided. This requirement may be troublesome for systems with several well-spaced open shells, such as most atomic and molecular excited states, as a complete model space spans a very broad energy range and leaves out states within that range, leading to poor or no convergence of the perturbation series. The method presented here would be particularly useful for such states. The solution of a model problem (He2 excited Σg+ states) is demonstrated.

Mode localization in highly excited vibrational states: Fundamentals of structure in overtone and multiphoton spectra

Abstract Fundamental classical and quantum arguments are presented that strongly indicate that the usual arguments leading to the expectation that the high vibrational states of polyatomic molecules form exclusively a uniform mode-mixed quasicontinuum are flawed. The basic dynamics shows that a uniform mode-mixed quasicontinuum exists but embedded in it can be mode-localized states characterized by extreme motion. Experimental evidence for these ideas is reviewed.

The shifted scheme in the general-model-space diagrammatic perturbation theory

Abstract The shifted scheme of many-body perturbation theory is applied to open-shell states within the framework of the general-model-space theory. Rules for shifting the denominators of folded diagrams. which appear in open-shell perturbation expansions, are given. The finite-order energies in the shifted scheme obtained in two equivalent representations may differ. This happens, for instance, in the case of triplet states. For 3 Σ u + states of the He 2 , differences up to 0.07 mhartree have been found in third order. A similar phenomenon is the size inconsistency of the shifted scheme observed by Silver in the ground state of He 2 . A possible advantage of the shifted scheme is its faster convergence for excited states.