Low-energy electron collisions with O2: Test of the molecularR-matrix method without diagonalization

Abstract

Electron collisions with O2 at scattering energies below 1 eV are studied in the fixed-nuclei approximation for a range of internuclear separations using the ab initio molecular R-matrix method. The 2 Πg scattering eigenphases and quantum defects are calculated. The parameters of the resonance and the energy of the bound negative ion are then extracted. Different models of the target that employ molecular orbitals calculated for the neutral target are compared with models based on anionic orbitals. A model using a basis of anionic molecular orbitals yields physically correct results in good agreement with experiment. An alternative method of calculation of the R-matrix is tested, where instead of performing a single complete diagonalization of the Hamiltonian matrix in the inner region, the system of linear equations is solved individually for every scattering energy. This approach is designed to handle problems where diagonalization of an extremely large Hamiltonian is numerically too demanding.

Total cross-section for low-energy and very low-energy electron collisions with O2

“…Therefore, the widths of Higgins et al may have been affected by the treatment of the R-matrix pole. Tarana and Greene also pointed out [42] that the use of an advanced treatment of electron correlation and polarization for the target description gives a much narrower resonance width compared to the results of earlier R-matrix studies [21,41,51], which supports the present results.…”

“…The resonance widths obtained by the R-matrix study of Higgins et al [41] also show rather wide values, close to the results of Ziesel et al [34]. Tarana and Greene [42] pointed out that the study of Higgins et al [41] was based on their earlier R-matrix calculations with a fixed-nuclei approximation [51] which failed to obtain an accurate energy of the resonances, and Higgins et al adjusted their earlier results by shifting the R-matrix poles for studying resonant vibrational excitation. Therefore, the widths of Higgins et al may have been affected by the treatment of the R-matrix pole.…”

“…The resonance widths obtained by the R-matrix study of Higgins et al [41] were close to the results of Ziesel et al [34]. However, much narrower resonance widths have been obtained in later theoretical studies [23,42]. As shown in the theoretical consideration of Parlant and Fiquet-Fayard [39], the absolute value of the electron scattering cross-section at around the resonance provides key information for this problem.…”

“…Since these calculations did not consider the effect of the nuclear motions of the target, the calculated cross-sections show an enhancement of the P 2 g resonance represented only at the equilibrium separation, and hence they are not comparable with the experimental cross-sections. However, the calculated resonance energies seem to be too high, considering that the series of the P ) rather than for neutral O 2 lowers the resonance energy of the P 2 g resonance efficiently.They obtained a resonance energy of 0.154 eV and a width of 3.6×10 −5 eV [42]. They also pointed out that employing the basis set of molecular orbitals optimized for neutral O 2 was not sufficient for reliable scattering calculations in the energy range of the P 2 g resonance, even if the polarization effects were taken account of much more than in earlier R-matrix calculations.…”

The impact of diffuse orbitals on low energy electron vibrational scattering from a nitrogen molecule

“…The interaction details between the projectile and the target are very important and the quantum effects are evident, so the scattering problem is an essentially complex quantum many body problem. In scattering theory, the wave function for the bound electrons of the target molecule is crucial and is usually treated in a cc-pVXZ basis, such as the R-matrix method [5,6], with a size usually up to cc-pVTZ. In the body frame vibrational close-coupling (BFVCC) [7][8][9] method, an accurate wave function of the bound electrons of the target is also the foundation to obtain the static, correlation/polarization, and exchange potentials [10].…”