Continuum Orbitals Research Articles

Low-energy electron scattering by the NO molecule

Eigenphase sums and resonance positions and widths are calculated for low-energy elastic impact of electrons on NO molecules using the R-matrix method with numerically defined continuum orbitals. Calculations are performed using both the simple close-coupling and the close-coupling plus short-range polarisation models using up to six electronic states or pseudostates of the NO target. The open-shell, 2 Pi , target is found to show increased sensitivity to polarisation effects which are better represented by coupled-states calculations than by a one-state model with an optical potential. Comparison is made with the available experimental data on e-NO scattering.

Resonance effects in the 5σ photoionization of CO

We report vibrational branching ratios and vibrationally resolved photoelectron angular distributions for resonant photoionization of the 5σ level of CO leading to X 2Σ+CO+. These results were obtained using frozen-core Hartree–Fock photoelectron continuum orbitals. These studies provide a clear quantitative picture of the role of the kσ shape resonance in the observed non-Franck–Condon behavior and useful insight into the interplay between this shape resonance and a valence-like autoionizing resonance around 23 eV.

Shape resonances in the photoionization of cyanogen

We have studied the photoionization cross sections and photoelectron asymmetry parameters for ionization of the 1πg(X 2Πg), 5σg(A 2Σ+g), and 4σu(B 2Σ+u) levels of cyanogen using frozen-core Hartree–Fock photoelectron continuum orbitals. The main purpose of these studies has been to extend our understanding of the dynamics of shape resonances from earlier studies of diatomic and smaller polyatomic molecules to a larger polyatomic system. The results do, in fact, reveal a rich shape resonant structure in the electronic continuum of this polyatomic system. There is a low-energy σu resonance which, as expected, is the C–C analog of the l=3 shape resonance seen in N2(3σ−1g) and several other diatomics. In contrast to this diatomic-like behavior, the presence of the two CN groups in C2N2 results in a second σu and a σg resonance corresponding to linear combinations of a l=3 shape resonance localized on the CN sites. Moreover, our results also show a pronounced shape resonant behavior in the πu continuum, which, to our knowledge, has not been seen in smaller molecules.

Relativistic and Coulomb autoionisation in low-lying excited states of fluorine

By applying a state-specific many-electron approach to the Breit-Pauli Hamiltonian, the authors have computed the relativistic autoionisation rate of the F 1s22s2p4(1S)3s 2S state whose lifetime was measured recently by the beam-foil technique and found to be tau =0.31+or-0.1*10-9 s. They find Gamma =1.7*109 s-1, which is about three times the theoretical prediction for the radiative transition rate to the ground state. The sum of the two contributions yields tau =0.45*10-9 s. Another Rydberg state F 2s22p4(1D)3d 2P, has a Coulomb autoionisation rate of 4.8*1011 s-1. However, its relativistic mixing with 3s 2S is very small and thus does not affect its lifetime. The present calculation has taken into account the following major effects: relaxation of orbitals of different states, non-orthonormality, electron correlation in initial and final states, core (K-shell)-valence interactions via the two-body spin-orbit operator, valence-valence relativistic interactions and term-dependent continuum orbitals.

Electronic excitation of the b3Σustate of H2by electron impact in the linear algebraic approach

The authors have performed two-state close-coupling calculations on the X 1 Sigma g to b 3 Sigma u transition for e-H2 scattering within the linear algebraic, effective optical potential approach. The strong orthogonality constraint between bound and continuum orbitals is relaxed by including correlation-type configurations. These correlation terms prove to be very important in the 2 Sigma g and 2 Sigma u symmetries and lead to an increase in the total cross section of a factor of two over earlier approaches, which neglected these terms. The authors obtain good agreement with recent R-matrix and Schwinger variational calculations.

Cross sections for electron impact excitation of the b3Σu+state of H2: an application of the Schwinger multichannel variational method

In this and two accompanying letters, the results of calculations of the cross sections for electron impact excitation of the b^3Σ_u^+ state of H_2, for collision energies from near threshold to 30 eV, are presented. The results are obtained using a multichannel extension of the Schwinger variational principle at the two-state level. The quantitative agreement between the integral cross sections of these three studies is very good. Inclusion of correlation terms in the scattering wavefunctions, which relax the orthogonality between bound and continuum orbitals is seen to affect the cross sections substantially. Although a comparison of these calculated cross sections with available experimental data is encouraging, some serious discrepancies exist.

Rotational branching ratios in (1+1) resonant-enhanced multiphoton ionization of NO via the A 2 Sigma + state.

The rotational branching ratios resulting from (1+1) resonant-enhanced multiphoton ionization of NO via the A 2Σ+ Rydberg state are analyzed. Theoretical results using ab initio molecular parameters agree reasonably well with recent experimental data. More importantly, the analysis underscores the importance of the molecular nature of the problem and its resulting complexities. It is shown that, for photoionization of a Σ state that leaves the ion in a Σ state, the allowed rotational states of the ion satisfy the selection rule ΔN+l=odd, where ΔN is the difference in (electronic + rotational) quantum numbers for the neutral and for the ion, and l is the partial wave of the electron. Based on this selection rule, it follows that the predominantly gerade 3sσ Rydberg orbital of the A 2Σ+ state couples only to the ungerade channel in the continuum (l odd), thereby suppressing the ΔN=±1 peaks, in agreement with experiment. The molecular nature of the ionic potential leads to strong l mixing in electronic continuum orbitals. In fact, the influence of a nearby shape resonance causes the f wave to be dominant in the σ channel.

Transition probability and photoionisation cross section calculations for CH4and HF by one-centre expansion and Stieltjes technique

Transition probabilities, partial and total photoionisation cross sections for CH4 and HF are obtained from a discrete basis set calculation by using the Stieltjes imaging technique for the continuum oscillator strength densities. Bound and continuum electronic eigenfunctions in the ground-state equilibrium geometry are described in the independent channel approximation using large basis sets of integrable functions centred on the heavy atom. Besides the usual STO functions, hydrogenic Rydberg functions and diffuse oscillatory functions are used to improve the description of the bound excited orbitals and the continuum orbitals respectively. The results in the discrete and continuous energy regions compare well with the available experimental data, confirming the validity of the approach for this class of molecules.

ChemInform Abstract: STUDIES OF THE PHOTOIONIZATION CROSS SECTIONS OF ACETYLENE

We have studied the photoionization cross sections and photoelectron asymmetry parameters for all molecular orbitals of acetylene. These cross sections were obtained using accurate frozen-core Hartree–Fock continuum orbitals in the final-state wave function. The Hartree–Fock continuum equations were solved using the iterative Schwinger variational method. These fixed-nuclei cross sections are compared with available experimental data and with results obtained using the Stieltjes moment theory approach and the continuum multiple scattering method. The possible role of a shape resonance in the 1piu-->kpig channel and the resonant structure of the sigmau continuum are discussed in some detail.

Emploi d′une fonction de continuum moleculaire bicentrique

A molecular orbital scheme has been developed for describing homonuclear molecules A 2 with ionized inner shells and continuum electrons: to represent the A 2 + + e system, elliptical continuum orbitals and LCAO-MOs obtained from an SCF calculation in terms of Slater basis functions for the ground state of A 2 are merged together into a many-electron wavefunction.

Calculations of the auger transition rates in CH4. II. Effect of the exchange interaction

The Auger transition rates in methane are calculated by using the molecular continuum orbitals and taking into account the exchange interaction between the ejected electron and the bound electrons. The exchange interaction considerably enhances the rate for the (2a 1 ) −2 1 A 1 process. Comparison is made with the rates obtained using some approximate exchange potentials and those using the exact exchange potential. Further, the approximation in which the MOs of the neutral molecule are used instead of those of the molecular ion (the initial state of the Auger process) is investigated.

Calculations of the auger transition rates in CH4. II. Effect of the exchange interaction

The Auger transition rates in methane are calculated by using the molecular continuum orbitals and taking into account the exchange interaction between the ejected electron and the bound electrons. The exchange interaction considerably enhances the rate for the (2a 1 ) −2 1 A 1 process. Comparison is made with the rates obtained using some approximate exchange potentials and those using the exact exchange potential. Further, the approximation in which the MOs of the neutral molecule are used instead of those of the molecular ion (the initial state of the Auger process) is investigated.

Studies of the photoionization cross sections of acetylene

We have studied the photoionization cross sections and photoelectron asymmetry parameters for all molecular orbitals of acetylene. These cross sections were obtained using accurate frozen-core Hartree–Fock continuum orbitals in the final-state wave function. The Hartree–Fock continuum equations were solved using the iterative Schwinger variational method. These fixed-nuclei cross sections are compared with available experimental data and with results obtained using the Stieltjes moment theory approach and the continuum multiple scattering method. The possible role of a shape resonance in the 1πu→kπg channel and the resonant structure of the σu continuum are discussed in some detail.

A fixed core Hartree-Fock program for calculating bound and continuum orbitals

A fixed core Hartree-Fock program for calculating bound and continuum orbitals

Calculations of the Auger transition rates in molecules. I. Effect of the nonspherical potential: Application to CH 4

The Auger transition rate in methane is calculated. The calculation of the continuum orbitals consists of two steps. The first step is the calculation of the continuum orbitals under the spherical potential, and the second one is the solution of the coupled equation in which the nonspherical term representing the coupling of the continuum orbitals with different angular momenta appears. The calculated transition rates are in good agreement with experiment.

The Schwinger variational method in electron-atom and electron-molecule scattering theory with polarisation

A method of implementing the Schwinger variational expression in electron-atom and electron-molecule scattering calculations with polarisation included via an ab initio optical potential is described. The Schwinger expression is also used to obtain approximate molecular Hartree-Fock continuum orbitals at arbitrary energies which are needed to calculate the optical potential above the first electron excitation threshold. Explicit closed-form expressions of integrals required for a Gaussian orbital basis are given. The method is applied to low-energy electron-helium scattering with a second-order optical potential.

Photoionization of excited-state xenon

The photoionization cross section of Xe $5{p}^{5}^{2}P_{\frac{3}{2}}6p(J=0)$ is calculated near threshold. We use a $\mathrm{jjJM}$-coupling scheme to describe the excited-state spectrum of xenon. By transformation from $\mathrm{jj}$ to $\mathrm{LS}$ coupling, one set of cross-section results is obtained using bound and continuum orbitals generated in the Hartree-Fock approximation. Another set of cross-section results is obtained using orbitals generated in the Dirac-Fock approximation. The difference in the two sets of results, which represents the contribution from relativistic effects, is found to be as much as 25% at certain energies. On the other hand, differences in the cross-section results which arise from the choice of electromagnetic field gauge are found to be as much as 75%.

The emission of energetic electrons from atoms by fast ions considered as a charge-transfer process

The ejection of energetic electrons from atoms by fast ions is described using as final electron states the continuum orbitals in the field of the projectile. The electronic distribution in the first-order Born approximation is equal to the distribution for direct ionisation where the final electron state is described by a plane wave times the Coulomb factor centred on the projectile. In the second-order Born approximation the distribution of ejected electrons is significantly decreased, and it is shown that it is equivalent to the correct distribution for direct ionisation in first order times the Coulomb factor around the projectile. For the case of ejected electrons with negligible momentum in the frame of the projectile, it is shown that the electron distribution centred on the projectile is isotropic to order nu -12, while the double scattering term in nu -11 depends on the direction of motion of the electron.

Electron scattering by diatomic molecules: Iterative static-exchange techniques

Iterative techniques are developed and examined for the solution of the single-center, fixed-nuclei electron-molecule scattering equations. They are found to have wide application to scattering by both large and small homo- and heteronuclear diatomic molecules. It is found that enforcement of orthogonality of the bound and continuum orbitals is required for efficient convergence with iteration. Results are presented for the molecules ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, LiH, and CO.

Calculated Auger transition rates for HF

We report ab initio calculations of Auger transition rates for hydrogen fluoride, using Hartree-Fock molecular orbitals from finite-basis Slater-type-orbitals calculations. Continuum orbitals are calculated as spherical waves in the single-center expanded-molecular potential. Results show reasonable agreement with experiment and with previous calculations for neon. The effect of final-state configuration mixing is discussed, as well as the use of perturbation theory for improving the continuum orbitals.