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Home > Research Teams > Molecular systems, Astrophysics and Environment > Internship, PhD and post-doc offers > Wavepacket propagation applied to photoionization cross section calculation

M2 theoretical intership

Wavepacket propagation applied to photoionization cross section calculation


Photoionization spectroscopy is based on the detection of the electron emitted by a molecule subject to a visible or ultraviolet electromagnetic radiation with a frequency ν such that hν is larger than the first ionization potential. Photoionization spectroscopy allows us to characterize a neutral molecule and its cation. This state of the art technique gives rise to many theoretical problems. The most challenging one being the calculation of photoionization cross sections. The system molecular cation + Rydberg electron needs to be modeled and the overlap integral between the vibrational wavefunctions of the neutral and that of the cation need to be evaluated to obtain the so-called Franck- Condon factors. In the case of rigid molecules, where the nuclear motion is well accounted for by the harmonic approximation, there already exist dedicated approaches to compute these factors. Such is not the case of non-rigid molecules displaying large amplitude motions. In such molecules, the Schrödinger equation for nuclear motion should be solved explicitly, for the neutral as well as for the cationic species, to obtain the vibrational wavefunctions and ultimately the Franck-Condon factors.

This theoretical internship will be focused on the calculation of photoionization cross sections of non-rigid molecules. Molecules displaying a large amplitude bending motion, in addition to other stretching modes, will be dealt with. The list of target molecules includes the methylene (CH2) and isocyanic acid (HNCO) displaying large amplitude HCH and HNC bending angles, respectively. Photoionization cross sections will be computed numerically using an approach which, unlike the one outlined above, is based on wavepacket propagations and avoids diagonalization of the full multidimensional Hamiltonian. As shown by Reinhardt and Kerner [1], photoionization cross sections can be obtained from the time correlation function Fourier transform. Cross section evaluation reduces then to the propagation of the neutral vibrational ground state wavefunction.

The internship work will start by finding the best suited internal curvilinear coordinates describing the neutral and cationic species. For the target molecule CH2, these include the bending HCH angle and the two CH stretching coordinates; for the target molecule HNCO, only a few coordinates, including the HNC angle, will be selected. In the next step, the vibrational Hamiltonian will be derived. The potential energy part of this operator will be retrieved from previously published results. The wavefunctions will be expanded using basis set functions depending on the chosen coordinates and the effects of the Hamilonian will be numerically calculated using Gaussian quadratures. A computer program in either FORTRAN or C language will be written for this purpose. This result along with the multiconfigurational time dependent Hartree (MCTDH) approach [2] will allow us to numerically propagate the neutral ground state wavefunction and to obtain the time correlation function. These numerical results will be compared to experimental ones.

[1] Reinhardt and Kerner, AIP Conference Proceedings 205 (1990) 458
[2] Beck, Jäckle, Worth, and Meyer, Physics Reports 324 (2000) 1

View online : Systèmes Moléculaires, Astrophysique et Environnement