Models, Interpretations, and Calculations Concerning Resonant Electron Scattering Processes in Atoms and Molecules

The RVP Method—From Real Ab-Initio Calculations to Complex Energies and Transition Dipoles

“…In the RVP method, as a first step, the energy spectrum is calculated using Hermitian codes as a function of a generalized box quantization parameter, E(α) where α = η (with θ = 0 and η = αe iθ ). For example, the eigenvalues can be calculated as a function of the number of basis functions (BFs) [45] or when finite given BFs are scaled by a real factor [47,48,51]. In practice, to scale the BFs by a real factor, one can use Gaussian base functions and divide the exponents of the Gaussians by the real factor α (see Eq.…”

“…Standard NHQM methods commonly work directly in the complex plane in order to calculate the resonance eigenvalue [6,[25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. RVP belongs to a subgroup of methods, which move into the NHQM regime via analytical continuation [41][42][43][44] It is based on the stabilization technique [45][46][47][48][49], where the real energy levels are plotted as a function of a parameter (α as denoted above) that controls the diffuseness of the Gaussian basis functions (see details in Section 2.1). The stabilization calculation, which is computationally the most demanding step, is followed by a very "cheap" analytical continuation step [50] (see Section 3).…”

Ab Initio Complex Transition Dipoles between Autoionizing Resonance States from Real Stabilization Graphs

“…First, the real stabilization curves were generated using the EOM-CCSD method as implemented in the latest version of Q-Chem, a quantum chemistry package . A plot of the energy or transition dipole of the state(s) in question versus the real scaling parameter is known as a stabilization graph . We obtained stabilization plots by scaling the basis set exponents by a real scaling parameter (η = α) that can vary over a chosen range.…”

“…33 A plot of the energy or transition dipole of the state(s) in question versus the real scaling parameter is known as a stabilization graph. 34 We obtained stabilization plots by scaling the basis set exponents by a real scaling parameter (η = α) that can vary over a chosen range. In general, the stabilization curve is a function of the real scaling factor, η = αe iθ , where η = α and θ = 0.…”

Description of Two-Particle One-Hole Electronic Resonances Using Orbital Stabilization Methods

“…The eigenvalues involved in the avoided crossings are analytically continued to the complex plane to obtain the Siegert energy associated with a given resonant state. 21,22,28,29 The analytical continuation is performed by means of Generalized Padé Approximants (GPA). 30 The GPA used in this work is given by a quadratic polynomial:…”