Treatment of shape and Auger resonances using the dilated electron propagator

Abstract

An overview of the dilated electron propagator method based on operators defined on biorthogonal orbitals from bivariationally obtained complex scaled SCF procedure is presented and discussed. Results from applications to atomic and molecular electron attachment and detachment resonances using different decouplings of the dilated electron propagator are analyzed to adduce the role of correlation and relaxation effects in the formation and decay of shape and Auger resonances. FeynmanDyson amplitudes of the dilated electron propagator are examined to try and unravel the mechanistic underpinnings of these resonances.

Obtaining positions and widths of scattering resonances from a complex multiconfigurational self‐consistent field state using the M1 method

“…Nevertheless, the clear indication of a change in direction of the curves may be taken as an indication of stabilization in the latter 8. Notice that the plots in Figure 2 closely resemble those obtained by Mishra and coworkers 8, 13, 47 using single configuration‐based dilated electron propagator (EP) method. However, they did not see anything that resembles the plots in Figure 3.…”

“…For the past few decades, the challenge of theoretically investigating the resonances that occur in the electron‐atom and the electron‐molecule scattering experiments using low‐energy electron beam has attracted attention 1–16. Although the resonances lie in the continuum part of the Hamiltonian buried under the nonresonant scattering states, their quasi‐bound nature appealed to many theoreticians to apply bound state methods to study them.…”

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.…”

“…Square integrability of resonance functions in a certain domain of values has led to bound-state methods like linearly convergent SCF [20 -22], CI [23,24], and the usual perturbational electron propagator theory [25][26][27][28][29][30] being employed for investigating these scattering resonances after diverse algebraic modifications that stem from the nonhermiticity of H(). Prescription of a special scalar product (the c product [24]), complex scaling of only the diffuse functions in the primitive basis without any scaling of the core basis functions and the Hamiltonian [20,23], and accommodation of complex scaling as a perturbation [26] or use of an additional complex absorbing potential (CAP) in order to determine resonance positions and widths [31][32][33][34][35][36][37][38] are approaches that have provided very useful results, but they suffer from formal limitations discussed elsewhere [21,27].…”