FERM3D: A finite element R-matrix electron molecule scattering code

Abstract

FERM3D is a three-dimensional finite element program, for the elastic scattering of a low energy electron from a general polyatomic molecule, which is converted to a potential scattering problem. The code is based on tricubic polynomials in spherical coordinates. The electron-molecule interaction is treated as a sum of three terms: electrostatic, exchange. and polarisation. The electrostatic term can be extracted directly from ab initio codes (GAUSSIAN 98 in the work described here), while the exchange term is approximated using a local density functional. A local polarisation potential based on density functional theory [C. Lee, W. Yang and R. G. Parr, Phys.Rev. B 37, (1988) 785] describes the long range attraction to the molecular target induced by the scattering electron. Photoionisation calculations are also possible and illustrated in the present work. The generality and simplicity of the approach is important in extending electron-scattering calculations to more complex targets than it is possible with other methods.

Retrieval of interatomic separations of molecules from laser-induced high-order harmonic spectra

“…In particular, for our purpose, we do not need high-precision photoabsorption cross sections in a narrow energy region such as those measured with synchrotron radiation, but rather moderately accurate dipole matrix elements over a broad photon energy range. Thus simpler calculations based on the one-electron model along the line developed by Tonzani [21] is likely adequate for this purpose. Clearly further development along this line requires the input of experimental data in order to demonstrate the actual working of the iterative method.…”

Quantitative rescattering theory for high-order harmonic generation from molecules

“…A somewhat simpler approach, the finite-element R-matrix (FERM3D) by Tonzani [66] can also be employed to calculate transition dipoles and photoionization cross sections.…”

Theory of high-order harmonic generation from molecules by intense laser pulses

“…Furthermore, for the purpose of obtaining HHG spectra for molecules in the intense laser pulses, high-precision cross sections in a narrow energy region such as those measured with synchrotron radiation are not needed. Instead, moderately accurate results over a broad range of energy such as those based on the one-electron model developed by Tonzani [30] is likely adequate.…”