Higher order decouplings of the dilated electron propagator with applications to P Be−2, P Mg−2 shape and S Be+2 (1s−1) Auger resonances

Abstract

The full third order (⌺ 3 ), quasi-particle third order (⌺ q 3 ) and Outer Valence Green's Function decouplings of the bi-orthogonal dilated electron propagator have been implemented for the first time and results from their application to 2 P Be Ϫ , 2 P Mg Ϫ shape and 2 S Be ϩ (1s Ϫ1 ) Auger resonances are presented and compared with energies and widths obtained using the zeroth order (⌺ 0 ), quasi-particle second order (⌺ q 2 ) and second order (⌺ 2 ) decouplings. The energies and widths from third order decoupling for shape resonances are close to those obtained using second order self-energy approximants. The energy and width calculated using the third order decoupling for Auger resonances provide better agreement with experimental results, with the much more economic quasi-particle third order decoupling being just as effective. The differences between FDAs from different decouplings are analyzed to elicit the role of correlation and relaxation in the formation and decay of shape and Auger resonances.

Application of higher order decouplings of the dilated electron propagator to Π2 CO−, Πg2 N2− and Πg2 C2H2− shape resonances

“…Our order analysis for the dilated electron propagator 17 is similiar to that for real unscaled electron propagator 2,42 and proceeds by expressing the exact N electron reference state ͉N͘ using a Rayleigh-Schrödinger perturbation expansion 2 with…”

“…15 The advent of faster CPUs and large memory and storage however has made it possible recently to apply the full third order and related decouplings to the treatment of atomic shape and Auger resonances 17 and it is our purpose in this paper to present some results from first application of the third order decouplings to some prototypical molecular resonances.…”

“…These are our systems of choice as well. The formal expressions for the third order decouplings have been detailed in a previous paper 17 and only a brief outline of the methodology is offered in the next section. A discussion of results from our application using the outer valence Green's function (⌺ OVGF 3 ), quasiparticle third order (⌺ q 3 ), and full third order (⌺ 3 ) decouplings to the study of 2 ⌸ CO Ϫ , 2 ⌸ g N 2 Ϫ , and 2 ⌸ g C 2 H 2 Ϫ shape resonances are offered in Sec.…”

Algebraic modifications to second quantization for non‐Hermitian complex scaled hamiltonians with application to a quadratically convergent multiconfigurational self‐consistent field method

“…Much of this has already been done for single-referencerestricted Hartree-Fock-based biorthogonal dilated electron propagator scheme previously used quite extensively [29,30].…”

“…Furthermore, recent investigations [29,30] have established that methods based on a single reference state are often inadequate for the accurate descriptions of resonances. The detailed algebraic modifications and demonstrative application to derive complex bivariational MCSCF equations will facilitate their extension to other L 2 techniques and computational packages using MCSCF-based bound-state techniques allowing for a simple, economic, and accurate treatment of shape, Feshbach and Auger resonances.…”