Electron-molecule Potential Research Articles

An analytic approach to electron-molecule potentials using STOs

Using Guseinov's translation formula for a complex Slater-type orbital (STO) and Steinborn's overlap integral between two Slaters on different centers, an analytic approach to electron-molecule interaction potentials has been developed. The theory presented is restricted to diatomic molecules although it is easily generalized to multiatom systems. A general computer code based on this formalism has been written and ē-H2 interaction potentials have been produced for the X1Σ+g state of H2 using two target representations: (1) McLean's five-state (open-shell form) configuration interaction function and (2) Fraga and Ransil's single-configuration (closed-shell form) function. The results are compared with a numerical procedure due to Faisal.

The complex coordinate rotation method and exterior scaling: A simple example

The so-called complex coordinate rotation technique is applied to two simple one-dimensional piecewise-defined model potentials. The invariance of the bound and resonance energy levels of these potentials under coordinate rotation is analyzed. It is shown that a proper treatment of the coordinate rotation gives a natural and easily understood introduction of the so-called exterior scaling. Implications for application of the coordinate rotation method to physically reasonable electron-atom or electron-molecule potentials are also discussed. Finally, the relative merits of the rotation procedure and the direct Siegert search method proposed by Miller et al. are evaluated.

Moving adaptive grid methods for numerical solution of the time-dependent molecular Schrödinger equation in laser fields

We present a moving adaptive grid method for solving the time-dependent Schrödinger equation, TDSE, for molecules in intense laser fields, applicable in the nonperturbative nonlinear regime where dissociation ionization occurs. The method is based on a Lagrangian, moving coordinate system. In this representation, the reference system is moving with the laser pulse so that the classical movement of free particles in the field, i.e., in the asymptotic region where electron–molecule potentials are negligible but the laser field is still present, is exactly described. As a consequence, the asymptotic quantum wave functions are exact in presence of a laser pulse. We have tested several discrete propagator methods for the TDSE in different gauges in a Born–Oppenheimer simulation of H2+ in a short, intense laser pulse. Our comparison of convergence between the same discretization methods for different gauges have demonstrated the superiority of the present Lagrangian adaptive grid method to treat the response of molecules to intense time-dependent electromagnetic fields.

Generalized space translation and new numerical methods for time-dependent Schroedinger equations of molecules in intense laser fields

We present new numerical methods, based on a Generalized Space Translation representation (GST), for solving the Time-Dependent Schroedinger equation (TDSE), to treat the nonlinear, nonperturbative interaction of molecules with intense laser pulses. Adopting a Lagrangian, moving coordinate system, we generalize the previous Space Translation method (ST), used in atom–laser interaction problem. In this representation (gauge), the reference system is moving with the laser pulse so the classical movement of free particles in the field, i.e. in the asymptotic region where electron-molecule potentials are negligible but the laser field is still present, is exactly described. As a consequence, the asymptotic quantum wave functions are exact in presence of the laser pulse. To solve numerically the GST–TDSE, all standard discrete propagators for the time discretization and all efficient space discretization methods can be applied. In order to illustrate different possibilities for the choice of discretization methods, we have tested several types of split-operator (SO) and alternating direction implicit (ADI) methods combined with adaptive finite difference methods for the 3D Born–Oppenheimer simulation of H 2 + in a short intense laser pulse field. Our comparison of convergence between the same discretization methods for different gauges have demonstrated the superiority of the GST method. As examples, we present for the first time the ionization of H 2 + exposed to a circularly or linearly polarized intense laser pulse perpendicular to the internuclear axis by an exact 3D simulation.

PROGRESS IN SCF-SW-XALPHA AB INITIO XANES CALCULATIONS FOR CHROMIUM HEXACARBONYL BASED ON GENERAL NON-MUFFIN-TIN POTENTIALS

We describe progress towards the performance of SCF-SW-Xalpha calculations of photo-absorption cross-sections based on the theory of Natoli et al. for non-muffin-tin potentials. A crucial requirement is the accurate modelling of the electron-molecule potential using spherical harmonic expansions. We describe how this has been achieved and what difficulties are encountered. In the particular case of our model compound, chromium hexacarbonyl, we show what muffin-tin calculations produce and show that we may expect significant improvements from a non-muffin-tin calculation. Finally, we comment on the programming problems involved in these computations.

Electron-molecule potentials using the Gegenbauer addition theorem

Electron-molecule potentials using the Gegenbauer addition theorem

Elastic and rotational excitation of the oxygen molecule by intermediate-energy electrons

The Glauber-type eikonal amplitude for a fixed molecular orientation is used in the framework of adiabatic approximation to compute pure elastic excitation ($J=1\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=1$), rotational excitation ($J=1\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=3$), and orientationally averaged elastic cross sections of the oxygen molecule in its ground electronic and vibrational states with the use of electrons as incident particles. Both differential and integral cross sections are reported at electron energies 20-200 eV. The effect of target polarization is included in the effective electron-molecule potential used, but that of electron exchange is neglected. The results are compared with the available experimental data and theoretical calculations of other workers. A comparative study of the molecules ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, and ${\mathrm{O}}_{2}$ as targets is made.

Elastic and rotational excitation of the nitrogen molecule by intermediate-energy electrons

An adiabatic approximation in which the eikonal elastic amplitude for fixed molecular orientation is used as input is employed for the calculation of pure elastic scattering ($J=0\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=0$ and $J=1\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=1$) pure rotational excitation ($J=0\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=2$ and $J=1\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=3$), and orientationally averaged elastic cross sections of the nitrogen molecule in its ground electronic and vibrational states using electrons as incident particles. Both differential and integral cross sections are computed at electron energies 20-200 eV. Total momentum-transfer cross sections are also calculated. The effect of target polarization is considered in the effective electron-molecule potential. The effect of electron exchange is not taken into account. Results obtained are compared with those of other theoretical and experimental workers. The qualitative features of the rotational-excitation cross sections are found to resemble those of the hydrogen molecule. Small-angle experimental elastic cross sections are well reproduced.