Dissociative recombination by frame transformation to Siegert pseudostates: A comparison with a numerically solvable model

Abstract

We present a simple two-dimensional model of the indirect dissociative recombination process. The model has one electronic and one nuclear degree of freedom and it can be solved to high precision, without making any physically motivated approximations, by employing the exterior complex scaling method together with the finite-elements method and discrete variable representation. The approach is applied to solve a model for dissociative recombination of H + 2 and the results serve as a benchmark to test validity of several physical approximations commonly used in the computational modeling of dissociative recombination for real molecular targets. The second, approximate, set of calculations employs a combination of multi-channel quantum defect theory and frame transformation into a basis of Siegert pseudostates. The cross sections computed with the two methods are compared in detail for collision energies from 0 to 2 eV.

Coupled nuclear–electronic decay dynamics of O2 inner valence excited states revealed by attosecond XUV wave-mixing spectroscopy

“…Here the overall lifetimes of the vibrational levels, v ( ), are of interest, and they arise from two effects, tunneling through the barrier indicated in Figure 1 and electronic autoionization. To calculate them directly we apply another venerable computational method, the method of exterior complex scaling (ECS) 69 The ECS calculation is implemented using the grid-based discrete variable representation using methods described at length previously 70 and used many times in ECS calculations of the complex energies of both electronic and vibrational metastable states [71][72][73][74] . In these grid-based calculations, it is a simple matter to converge the complex resonance eigenvalues so that they have no dependence on the complex scaling angle θ to many significant figures and thus represent the essentially exact solution of Eq.…”

Validity of the Born-Oppenheimer approximation in the indirect-dissociative-recombination process

“…The 2D Hamiltonian partitioning is adopted from Ref. [23] and it is somewhat different from the original notation of Houfek et al [24,25]. The present system, with two different modes of fragmentation, associated with the competing dissociation and ionization (or detachment) channels, will be described by the timeindependent Schrödinger equation…”

“…The explicit form of the two potentials can be found in Ref. [23]. The charge parameter is Z = 0 for neutral target molecules, while Z = 1 for target cation.…”

“…In order to assess the accuracy of the Born-Oppenheimer approximation, the cornerstone of the vibrational frame-transformation theories [15,[20][21][22], we propose a numerically solvable two-dimensional (2D) model for the indirect dissociative recombination of H 2 in the singlet ungerade channels 1 Σ u . This model was recently devised by Hvizdoš et al [23] to test the accuracy of the energy independent frame transformation into a nuclear basis of Siegert pseudostates. That study thus provided a first numerical estimate for the accuracy of the underlying approximations.…”

“…The ECS approach was originally developed to address the dissociative electron attachment and the vibrational excitation channels in collisions of electrons with neutral molecules [24,25]. For the target cations the ECS method still provided accurate and converged results for most of the collision energies [23] , but at comparatively high computational cost due to necessity of using extensive long-range electronic grids to confine the countless number of Rydberg states involved in the closed-channel resonances.…”