Please cite this article in press as: V. Kimberg, C. Miron, Molecular potentials and wave function mapping by high-resolution electron spectroscopy and ab initio calculations, J. Electron Spectrosc. Relat. Phenom. (2013), http://dx.doi.org/10.1016/j.elspec.2013.11.003 ARTICLE IN PRESS G Model ELSPEC-46193; No. of Pages 6 Journal of Electron Spectroscopy and Related Phenomena xxx (2013) xxx–xxx Contents lists available at ScienceDirect Journal of Electron Spectroscopy and Related Phenomena j ourna l ho me page: www.elsevier.com/locate/elspec Molecular potentials and wave function mapping by high-resolution electron spectroscopy and ab initio calculations Victor Kimberg a , Catalin Miron b,∗ a Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany b Synchrotron SOLEIL, l’Orme des Merisiers, Saint-Aubin, BP 48, FR-91192 Gif-sur-Yvette Cedex, France a r t i c l e i n f o Article history: Available online xxx PACS: 33.80.-b 31.15.A 32.80.Aa 33.20.Rm Keywords: Inner-shell excitation X-ray spectra Resonant photoemission Ab initio calculations Vibrational wavefunction a b s t r a c t The recent development of high brightness 3 rd generation soft X-ray sources and high energy resolu- tion electron spectrometers made it possible to accurately trace quantum phenomena associated to the vibrational dynamics in core-excited molecules. The present paper reviews the recent results on map- ping of vibrational wave functions and molecular potentials based on electron spectroscopy. We discuss and compare the mapping phenomena in various systems, stressing the advantages of the resonant X- ray scattering for studying of the nuclear dynamics and spectroscopic constants of small molecules. The experimental results discussed in the paper are most often accompanied by state-of-the-art ab initio cal- culations allowing for a deeper understanding of the quantum effects. Besides its fundamental interest, the vibrational wave function mapping is shown to be useful for the analysis of core- and valence-excited molecular states based on the reflection principle. © 2013 Elsevier B.V. All rights reserved. 1. Introduction One of the fundamental concepts of modern chemical physics and quantum chemistry is the Born–Oppenheimer (BO) approx- imation, which allows considerable simplification of ab initio calculations and of the analysis of experimental molecular spec- troscopy data. The BO approximation assumes that the total molecular wave function may be represented as a product of elec- tronic and nuclear wave functions, thus decoupling the electronic and nuclear degrees of freedom. This wave function splitting allows one to employ a two-step approach. In the first step, one solves an electronic Schrödinger equation at fixed nuclei positions. The dependence of the electronic energy on nuclei’s positions forms a potential energy surface or, in the one-dimensional case, a poten- tial energy curve (PEC). In the second step, the nuclear dynamics is determined from the solution of the nuclear Schrödinger equa- tion with a Hamiltonian which includes the nuclear kinetic energy and the electronic energy of a particular electronic state. This step may additionally involve separation of the vibrational, rotational ∗ Corresponding author. Tel.: +33 169359605. E-mail addresses: victor.kimberg@pks.mpi.de (V. Kimberg), miron@synchrotron-soleil.fr (C. Miron). and translational degrees of freedom. In the high-energy electron spectroscopy studies presented here, the translational and rota- tional motions have only minor effects observed in the spectral broadening of the lines [1,2], while the vibrational motion plays a crucial role in the spectra formation. The eigenfunctions of the vibrational Hamiltonian – the vibrational wave functions (VWFs) – and the PECs are well known quantum concepts, which are widely used in the interpretation of the modern ultrahigh resolution spec- troscopic data tracing complex molecular dynamics. However, the question arises how these quantum concepts are related to the experimental observables, and if they can be mapped directly from the measurements? The experimental scheme to address this question was proposed almost twenty years ago based on the theoretical prediction of the vibrational wave function mapping phenomena in the framework of the resonant X-ray scattering theory applied to the excita- tion/decay processes involving dissociative final states [3]. Indeed, the resonant scattering cross section was shown to be propor- tional to the square of the wave function of the vibrational sublevel involved in the scattering process [3–5], thus mapping its spatial distribution and the nodal structure according to the reflection principle [6]. In spite of the recent progress in vibrational motion tracking by pump-probe approaches using ultrashort laser pulses [7–11], only very few experimental studies have tried to address 0368-2048/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.elspec.2013.11.003