Low-lying Shape Resonances Research Articles

Electron scattering by the hydrocarbons C4H6,C5H8 , and C6H10

We report calculated elastic integral and differential cross sections for electron collisions with the hydrocarbons 1,3-butadiene (${\mathrm{C}}_{4}{\mathrm{H}}_{6}$), 2-methyl-1,3-butadiene (${\mathrm{C}}_{5}{\mathrm{H}}_{8}$), and 2,3-dimethyl-1,3-butadiene (${\mathrm{C}}_{6}{\mathrm{H}}_{10}$) for impact energies up to 15 eV. Our calculations were performed with the Schwinger Multichannel Method with pseudopotentials, in the static-exchange and static-exchange plus polarization approximations. These molecules differ for the presence of one methyl group, in the case of ${\mathrm{C}}_{5}{\mathrm{H}}_{8}$, and two methyl groups, in the case of ${\mathrm{C}}_{6}{\mathrm{H}}_{10}$ in substitution of one and two hydrogen atoms in ${\mathrm{C}}_{4}{\mathrm{H}}_{6}$, respectively (methylation effect). For the polar molecule 2-methyl-1,3-butadiene, we included the Born closure procedure in order to account for the long-range potential. We found two ${\ensuremath{\pi}}^{*}$ shape resonances in the integral cross section of each one of the molecules studied. The present results are also compared with the experimental values for the resonances positions and with total cross sections available in the literature. In particular, we show that the minimum in the total cross section of ${\mathrm{C}}_{5}{\mathrm{H}}_{8}$ located at around 1.6 eV and assigned by the authors as a Ramsauer-Townsend minimum is, actually, a valley between the two ${\ensuremath{\pi}}^{*}$ shape resonances. Also for the ${\mathrm{C}}_{5}{\mathrm{H}}_{8}$ molecule, the enhancement in the total cross section below 1.6 eV is the tail of the low-lying shape resonance and not an effect due to its permanent dipole moment, as suggested by the authors. We discuss the influence of the methylation effect in the shape and magnitude of the elastic cross sections and also in the location of the ${\ensuremath{\pi}}^{*}$ shape resonances of these hydrocarbons.

The complex-scaled multiconfigurational spin-tensor electron propagator method for low-lying shape resonances in Be−, Mg− and Ca−

We further apply the complex scaled multiconfigurational spin-tensor electron propagator method (CMCSTEP) for the theoretical determination of resonance parameters with electron-atom systems including open-shell and highly correlated (non-dynamical correlation) atoms and molecules. The multiconfigurational spin-tensor electron propagator method (MCSTEP) developed and implemented by Yeager and his coworkers for real space gives very accurate and reliable ionization potentials and electron affinities. CMCSTEP uses a complex scaled multiconfigurational self-consistent field (CMCSCF) state as an initial state along with a dilated Hamiltonian where all of the electronic coordinates are scaled by a complex factor. CMCSTEP is designed for determining resonances. We apply CMCSTEP to get the lowest 2P (Be−, Mg−) and 2D (Mg−, Ca−) shape resonances using several different basis sets each with several complete active spaces. Many of these basis sets we employ have been used by others with different methods. Hence, we can directly compare results with different methods but using the same basis sets.

Interaction of low-energy electrons with dimethyl sulfide and dimethyl disulfide

We report elastic integral cross sections for low-energy electron scattering by gas-phase dimethyl sulfide and dimethyl disulfide, obtained with the Schwinger multichannel method with pseudopotentials. Our symmetry-resolved cross sections for dimethyl sulfide reveal that the single broad structure at $3.25\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ observed in the electron transmission spectrum (assigned as a ${\ensuremath{\sigma}}_{\mathrm{CS}}^{*}$ shape resonance) would actually arise from two superimposed anion states in the ${B}_{2}$ and ${A}_{1}$ symmetry components of the ${C}_{2v}$ point group. We also obtained two low-lying shape resonances for dimethyl disulfide, in good agreement with the available electron transmission data. In view of the recently reported measurements on dissociative electron attachment to dimethyl disulfide [C. Matias, A. Mauracher, P. Scheier, P. Lim\~ao-Vieira, and S. Denifl, Chem. Phys. Lett. 605-606, 71 (2014)], we also calculated cross sections for stretched S--S bond lengths, which indicate a fast stabilization consistent with the experimental data.

Stable negative ions and shape resonances in a series of organic molecules

We report on the theoretical determination of low-lying shape resonances in a selected set of seven molecules. The finite element discrete model method is used and the absolute differences between calculated and experimental values, where known, are ≲0.15 eV for the resonances lowest in energy. Difficulties expected with the higher calculated values are discussed. This article reports results for ortho-benzyne, benzene, naphthalene, anthracene, styrene, formamide, and acetamide. Comparisons are made with a few other calculations, again where available.

Dissociative electron attachment to HCN and HNC

Previous experimental and theoretical studies on HCN and HNC have indicated the presence of both $\ensuremath{\sigma}$ and $\ensuremath{\pi}$ low-lying shape resonances. The energy and autoionization width of these resonant states depend on the stretching and bending of the molecule and lead primarily to a $({\text{CN}}^{\ensuremath{-}}+\text{H})$ product. In this work, we present a comparative study of the dissociation mechanism of these isomers. We carried out electron scattering calculations using the complex-Kohn variational method as a function of the three internal degrees of freedom to obtain the resonance energy surfaces and autoionization widths. We then use these data as input to form the Hamiltonian relevant to the nuclear dynamics. The multidimensional wave equation is solved using the multiconfiguration time-dependent Hartree approach. We compute the relative dissociative electron attachment cross sections and examine the isotope effect relative to each isomer.

Recent developments in electron-molecule scattering

Over the past few years a wealth of new information on the properties of temporary negative ions has become available through various electron scattering techniques. The present paper focuses on recent work involving electron transmission spectroscopy to probe low-lying shape resonances in polyatomic systems. Emphasis is placed on new findings concerning the relative positions of π* and σ* resonances and dissociative attachment (e− + AB AB− A + B−) channels in unsaturated compounds. The theoretical questions raised by the experimental results are discussed.

R -matrix calculation of low-energy electron collisions with uracil

R-matrix calculations on electron-uracil collisions are presented within the static exchange, static exchange plus polarization, and close-coupling approximations. Particularly as input for the close-coupling calculations, a series of target calculations is performed which considers low-lying singlet and triplet excited states of the uracil target. The scattering calculations find three low-lying shape resonances of (2)A(") symmetry and three higher-energy Feshbach resonances of (2)A(') symmetry. In both symmetries the precise resonance parameters are found to be sensitive to the treatment of polarization effects employed. Cross sections are presented for both elastic scattering and electronic excitation. Comparisons are made with energy-dependent, differential cross section measurements at 90 degrees angle and good agreement is found for scattering energies above 0.5 eV.

Dissociative electron attachment and electron energy-loss spectra of phenyl azide

Electron-induced chemistry—dissociative electron attachment (DEA)—was studied for phenyl azide. The major fragment corresponded to the loss of N2 and formation of the phenylnitrene anion. This process has an onset already at zero kinetic energy of the incident electron and is interpreted as proceeding via the A″π* electronic ground state of the phenyl azide anion. Other fragments, N3− and CN−, were observed at higher energies and interpreted as proceeding via low-lying shape resonances or higher lying core-excited resonances. The interpretation of the dissociative attachment spectra was supported by an investigation of the excited electronic states of neutral phenyl azide by electron energy-loss spectroscopy and DFT/MRCI calculations, and a study of shape and core-excited resonances of the phenyl azide anion by means of electron transmission spectroscopy and of cross sections for vibrational and electronic excitation by electron impact. Interesting parallels and differences are found by comparing DEA of phenyl and benzyl azides with the corresponding chloro compounds.

Enhanced spin polarization of elastic electron scattering from alkaline-earth-metal atoms in Ramsauer-Townsend and low-lying shape resonance regions.

Spin polarizations (SP's) of elastic electron scattering from alkaline-earth-metal atoms in Ramsauer-Townsend (RT) and low-lying shape resonance (SR) regions are calculated using a relativistic method. The detailed SP distributions both with scattering angle and with electron energy are presented via the energy- and angle-dependent surfaces of SP parameters. It is shown that the SP effects of the collisions of electrons with Ca, Sr, and Ba atoms in the RT region are significant in a considerable area on the energy-angle plane and that the spin-orbit interaction is well increased around the low-lying p-wave SR states of Be and Mg and the d-wave SR states of Ca, Sr, and Ba.

Correlational autodetachment of the low-lying shape resonances in C-, Si- and Ge- photodetachment

The photodetachment cross sections are calculated for the outer np and nearby ns subshells of the C- 2p3 4S, Si- 3p3 4S and Ge- 4p3 4S negative ions. The prominent interference feature with deep minimum is discovered for the np photodetachment in the vicinity of the ns threshold at omega approximately=6 eV. This structure is due to the strong interaction of the np continuum with the ns to in p shape resonance. This resonance corresponds to the transition of the ns electron to the quasi-bound 'np' state with the width Gamma (1 eV. The shape resonance undergoes rapid decay into the np continuum that is analogous to the super-Coster-Kronig transition. The asymmetry parameter for the np photoelectron angular distribution is calculated, showing abrupt changes in the same energy region. The calculations are performed using the spin-polarized version of the random phase approximation with exchange.

Relativistic effects and spin polarization on the low-energy shape resonances of electron scattering with magnesium, zinc and cadmium atoms

The scattering of low energy electrons from Mg, Zn and Cd atoms is calculated with the Dirac equation while paying attention to the spin polarization enhanced by the low-lying shape resonance states. It is found that the spin polarization effect is considerably increased at the resonance energy even for a light target such as the magnesium atom.

Elastic scattering of low-energy electrons with Sr atoms.

Static-exchange, plus correlation-polarization-potential calculations are performed for elastic low-energy electron scattering from Sr atoms while paying attention to the low-lying shape resonances. The correlation potential is calculated both with and without a scaling factor. A $^{2}$D-shape resonance is produced at 1.0 eV with a parameter-free, and at 1.25 eV with a scaled, correlation potential. No $^{2}$P-shape resonances are predicted, but evidence to support the existence of a stable negative ion ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$ in the 5${\mathit{s}}^{2}$5p electron configuration is given from the viewpoint of electron scattering. The bound energy of the extra electron in the negative ion is estimated by transforming the phase shift of the corresponding partial wave into the polarization quantum-defect number and extrapolating the number from positive to negative energies.

The low-lying shape resonances in low-energy electron scattering with Be, Mg and Ca atoms

Static exchange (plus correlation-polarisation potential) calculations are performed for elastic low-energy electron scattering from Be, Mg and Ca atoms with attention to the low lying 2P and 2D shape resonances. The correlation potentials are calculated with and without a scaling factor. The scaling factor is adjustable as the alpha parameter in the X alpha theory, and is adjusted to produce the 2P resonance energy of e-Mg scattering in agreement with the experiment. The predictions with the parameter-free correlation-polarisation potential are a 2P resonance at 0.15 eV with width of 0.19 eV for Be, a 2P resonance at 0.065 eV with width of 0.05 eV for Mg and a 2D resonance at 1.5 eV for Ca with width of 3.0 eV. The 2P resonances of Be and Mg and the 2D resonance of Ca are produced at 0.24 eV, 0.14 eV and 1.75 eV with widths of 0.33 eV, 0.17 eV and 3.2 eV respectively, by using the scaled correlation potential. No 2P resonances are produced in the calculations for e-Ca scattering using either the parameter-free or scaled correlation potential, i.e. the authors give evidence for the existence of a stable negative ion of Ca in the 4s24p 2P state by using the theory used for electron scattering.

Vibration-induced narrowing of electron scattering resonances near threshold

Resonant scattering of electrons from molecules is discussed in the context of an exactly solvable model. There is a strong non-adiabatic entanglement of electronic and nuclear motions for resonances near threshold. The calculations show that the interaction of the electronic and vibrational motions can lead to a dramatic reduction of the resonance width. The limits of applicability of the so-called compound state formula, which has been used so far to analyse low-lying shape resonances in molecules, are pointed out.

A low-lying resonance in the spectrum of H -

It was proved by Pekeris (1) that the singly excited states of H - lie exactly at, or slightly above, the ground state of hydrogen. Using a theory of Fano, (2) these fictitious states will have a configuration interaction with the H - continuum. The strength of this configuration interaction is computed for the mixing of a 1 s2p 1 P 0 state with the H - continuum for different values of the fictitious binding energy of the 2 p valence electron. In every case, the effect of the configuration interaction is to induce a rapid change of the phase shift of the continuum wave function by a quantity of π/2 over an energy range of a few times 0.01 eV, at an energy somewhat above the hydrogen ground state. The variation from π/2 to π is much slower. Such a swift change of the phase shift may be identified with the occurrence of a low-lying shape resonance.