Vibronic coupling of electronic resonances

The Born-Oppenheimer approximation is one of the cornerstones of the electronic structure theory of molecules and solids allowing the interpretation of the vibrational dynamics in terms of potential energy surfaces. The situations where this approximation breaks lead to interesting phenomena like Jahn-Teller or Renner-Teller effect and the concept of the potential energy surface must be generalized to topologically much more interesting multivalued potential energy manifold subjected to conical intersections (or “diabolic points”). The subject is well studied in the case of bound states (see for example [1]) but to a large degree unexplored in the case of metastable resonance states.

In our group we developed methods [2] to study theoretically electron-molecule (and anion-atom) scattering mediated by resonances or virtual states by extending the methods proposed in 80’s by Domcke and collaborators [3]. The approach has been very successful in the case of diatomics [4] but it was difficult to apply it also to polyatomic molecules. In a recent breakthrough we managed to treat the CO 2 molecule with Renner-Teller crossing in continuum [5] and we also treated a model molecule with Jahn-Teller crossing of metastable states [6].

The aim of this project is to continue our effort to understand theoretically the inelastic and reactive electron scattering from polyatomic molecules and to model data that will be measured by our collaborators in Heyrovsky Institute of Physical Chemistry (also in Prague). One of the main tasks is to develop theoretical methodology to understand systematically 2D electron-energy-loss spectra [7].

We require that the candidate has a good background in atomic and molecular physics and quantum physics in general and also a good background in numerical methods and some programming skills. Direct experience with FORTRAN, Python and some quantum chemical packages would be also useful but not strictly required.

References:

[1] W.Domcke, D.Yarkony, H.Koppel, Conical Intersections: Electronic Structure, Dynamics & Spectroscopy, World Scientific 2004.
[2] M. Čížek, K. Houfek, Chapters 3 and 4 in Low-energy Electron Scattering from Molecules, Biomolecules and Surfaces, edited by P. Čárský and R. Čurík, CRC Press 2012.
[3] W. Domcke, Theory of resonance and threshold effects in electron-molecule collisions: The projection-operator approach, Phys. Rep. 208 (1991) 97.
[4] See for example:J. Phys. B 33 (2000) L209, Phys. Rev. Lett 89 (2002) 073201, Science 328 (2010) 69, Phys. Rev. A 81 (2010) 042702, Eur. Phys. J. D 72 (2018) 66.
[5] J. Dvořák et al. Phys. Rev. Lett. 129 (2022) 013401, Phys. Rev. A 105 (2022) 062821, Phys. Rev. A 106 (2022) 062807.
[6] M. Ćosićová, J. Dvořák, M. Čížek, Vibronic dynamics in electron continuum – iterative solvers, arXiv:2307.13483 [physics.chem-ph].
[7] See for example: Phys. Rev. Lett. 110 (2013) 203201, Eur. Phys. J. D 70 (2016) 123, M. Allan, https://homeweb.unifr.ch/allanm/pub/ma/Lectures.html Two-dimensional electron energy loss spectra reveal nuclear dynamics of negative ion resonances. (2019), Talk, Telluride, (unpublished), J. Chem. Phys. 157 (2022) 064302.