Indirect Dissociative Recombination of LiH+^+ Molecules Fueled by Complex Resonance Manifolds

The LiH$^{+}$ molecule is prototypical of the indirect dissociative recombination (DR) process, in which a colliding electron destroys the molecule through Rydberg capture pathways. This Letter develops the first quantitative test of the Siegert state multichannel quantum defect theory description of indirect DR for a diatomic molecular ion. The R-matrix approach is adopted to calculate ab-initio quantum defects, functions of the internuclear distance that characterize both Rydberg states and the zero-energy collisions of electrons with LiH$^{+}$ ions. The calculated DR rate coefficient agrees accurately with recent experimental data (S. Krohn et al, Phys. Rev. Lett. 86, 4005). We identify the doorways to fast indirect DR as complex resonance manifolds, which couple closed channels having both high and low principal quantum numbers. This sheds new light on the competition between direct and indirect DR pathways, and suggests the reason why previous theory underestimated the DR rate by an order of magnitude.Comment: Submitted to PR

Electron-impact vibrational excitation of cyclopropane

We report a very detailed test of the ab initio discrete momentum representation (DMR) method of calculating vibrational excitation of polyatomic molecules by electron impact, by comparison of its results with an extensive set of experimental data, covering the entire range of scattering angles from 10∘ to 180∘ and electron energies from 0.4 to 20 eV. The DMR calculations were carried out by solving the two-channel Lippmann-Schwinger equation in the momentum space, and the interaction between the scattered electron and the target molecule was described by exact static-exchange potential corrected by a density functional theory (DFT) correlation-polarization interaction that models target’s response to the field of incoming electron. The theory is found to quantitatively reproduce the measured spectra for all normal modes, even at the difficult conditions of extreme angles and at low energies, and thus provides full understanding of the excitation mechanism. It is shown that the overlap of individual vibrational bands caused by limited experimental resolution and rotational excitation must be properly taken into account for correct comparison of experiment and theory. By doing so, an apparent discrepancy between published experimental data could be reconciled. A substantial cross section is found for excitation of the non-symmetric HCH twisting mode ν 4 of A′′1 symmetry by the 5.5 eV A′2 resonance, surprisingly because the currently accepted selection rules predict this process to be forbidden. The DMR theory shows that the excitation is caused by an incoming electron in an f-wave of A′2 symmetry which causes excitation of the non-symmetric HCH twisting mode ν 4 of the A′′1 symmetry and departs in p- and f-waves of A′′2 symmetry

Vibrational excitation of methane by slow electrons revisited: theoretical and experimental study

We have calculated and measured differential and integral cross sections for vibrationally inelastic scattering of electrons by methane molecules. The calculations were carried out using the discrete momentum representation (DMR) method. We solved the two-channel Lippmann–Schwinger equation in the momentum space. The interaction between the scattered electron and the target molecule is described by the exact static-exchange potential. Correlation–polarization forces were included by a simple local density functional theory potential of Perdew and Zunger (1981 Phys. Rev. B 23 5048). The cross sections calculated in this way agree very well with our measurement and with other more recent experimental data, but are larger than some older experimental and theoretical results

Vibrational excitation of cyclopropane by electron impact: An experimental test of the discrete-momentum-representation theory with density-functional-theory approximation of polarization and correlation

The discrete-momentum-representation theory with short-range correlation and polarization approximated by local-density-functional theory has been augmented by connecting the short-range potential to an asymptotic polarization tensor. The capacity of this theory to correctly describe the coupling of a free electron with nuclear motion is tested by a detailed comparison of calculated and measured cross sections for vibrational excitation in cyclopropane. Absolute magnitudes of the cross sections, selectivity with respect to the vibrational modes excited, angular distributions in the entire angular range 0∘–180∘, and resonant structures dependent on the incident electron energy in the range from threshold to 16 eV are compared. The results are encouraging; the theory reproduces all these aspects quantitatively, even at low energies, down to about 1 eV. An important asset of this theory is that it is applicable to large molecules

Efficient solution of scattering equations by combination of R-matrix and Lanczos methods

We propose a fast and economical computational method for solving scattering Lippmann-Schwinger integral equation. Our approach benefits from the accurate construction of the Green's function based on the R-matrix theory combined with the Schwinger-Lanczos variational principle. No principal restrictions on the form of the potential are assumed. Theoretical description of our method in the first part of this paper is then followed by numerical examples. In particular we demonstrate how to adapt our method for computation of partial wave phase-shifts in the case of electron-hydrogen atom scattering. Then we also investigate the properties of a family of long-range potentials (emerging e.g. in the theoretical description of the Cs2 or 4He2 dimer ground state interaction). As demonstrated on these particular cases, our approach turns out to be very accurate in comparison with other computational methods