From double-slit interference to structural information in simple hydrocarbons Rajesh Kumar Kushawahaa,b, Minna Patanenc, Renaud Guillemina,b, Loic Journela,b, Catalin Mironc, Marc Simona,b, Maria Novella Piancastellia,b,d,1, C. Skatese, and Piero Declevae,f,g aLaboratoire de Chimie Physique-Matière et Rayonnement, Université Pierre et Marie Curie, 75231 Paris Cedex 05, France; bLaboratoire de Chimie Physique-Matière et Rayonnement (Unité Mixte de Recherche 7614), Centre National de la Recherche Scientifique, 75231 Paris Cedex 05, France; cSynchrotron SOLEIL, l’Orme des Merisiers Saint-Aubin, 91192 Gif-sur-Yvette Cedex, France; dDepartment of Physics and Astronomy, Uppsala University, 75120 Uppsala, Sweden, eDipartimento di Scienze Chimiche, Universitá di Trieste, 34127 Trieste, Italy; fConsorzio Interuniversitario Nazionale per la Scienza e Tecnologia dei Materiali Unitá di Trieste, 34127 Trieste, Italy; and gDemocritos Modeling Center for Research in Atomistic Simulation, Consiglio Nazionale delle Ricerche-Istituto Officina dei Materiali, 34149 Trieste, Italy Edited by R. Stephen Berry, The University of Chicago, Chicago, IL, and approved August 8, 2013 (received for review April 9, 2013) Interferences in coherent emission of photoelectrons from two on a rapidly decreasing cross-section. The cleanest observation is equivalent atomic centers in a molecule are the microscopic analo- expected by measuring the ratio of two cross sections, corre- gies of the celebrated Young’s double-slit experiment. By consider- sponding to symmetrical (g) and antisymmetrical (u) combina- ing inner-valence shell ionization in the series of simple hydrocarbons tions of 1s orbitals, which are expected to give oscillations in C2H2,C2H4,andC2H6, we show that double-slit interference is wide- antiphase, thus magnifying the interference pattern. For the spread and has built-in quantitative information on geometry, orbital same reason, no oscillation is present in the unresolved g/u cross- composition, and many-body effects. A theoretical and experimental section. Unfortunately, the g/u splitting of core orbitals is gen- study is presented over the photon energy range of 70–700 eV. A erally too small to be observable, due to the dominating natural – strong dependence of the oscillation period on the C Cdistanceis lifetime broadening. However, in N2 (17) and C2H2 (18, 19), it is observed, which can be used to determine bond lengths between of the order of 100 meV, owing to the very short interatomic selected pairs of equivalent atoms with an accuracy of at least 0.01 Å. distance associated with the triple bond, and beautiful inter- Furthermore, we show that the observed oscillations are directly in- ference patterns have been observed (13, 14). Another possibility formative of the nature and atomic composition of the inner-valence that has been exploited recently is to observe the interferences molecular orbitals and that observed ratios are quantitative meas- from the ratios of individual vibrational components, and clear ures of elusive many-body effects. The technique and analysis can be patterns have been observed in both the valence shell and core immediately extended to a large class of compounds. regions (20, 21). This method has some advantages but requires vibrational resolution, which is often not achievable in more coherent state and molecular photoemission | interference phenomena complex systems. Beyond the fundamental interest in observing quantum in- ave-particle duality, nowadays considered as a milestone terference between electron waves coherently emitted, many CHEMISTRY Win the development of quantum mechanics, is the revolu- important questions remain to be addressed by a broader study tionary concept that was experimentally demonstrated by Young’s of these interference patterns: ’ double-slit experiment in 1801. In Feynman s words, wave-particle A strong geometrical dependence of the interference patterns “ ... duality is a phenomenon which is impossible to explain in any is expected, as also predicted by the Cohen–Fano formula (5). ” classical way, and which has in it the heart of quantum mechanics This dependence may provide a means of accurate determi- (1). Once the wave nature of light was revealed in such an exper- nation of molecular geometries, especially when photoemis- iment, similar experiments were carried out with several particles, sion is the primary investigation tool. including electrons (2, 3) and even heavy species such as C60 (4), in which a beam passed through two slits separated by a distance Significance comparable to their associated de Broglie wavelength. In 1966, Cohen and Fano (5) interpreted the oscillatory be- Electrons emitted from equivalent centers in isolated molecules havior of the photoabsorption spectra of N2 and O2 molecules (6) by theorizing the possibility of realizing the double-slit experiment via the photoelectric effect interfere, providing an atomic-scale ’ in the photoionization of homonuclear, diatomic molecules, where equivalent of the celebrated Young s double-slit experiment. the electrons are emitted by two equivalent atomic centers. Due to We have developed a theoretical and experimental framework coherence in the initial molecular state, the absorption of a single to characterize such interference phenomena accurately, and photon by the homonuclear molecule gives rise to two coherent we have applied it to the simplest hydrocarbons with different electron waves, which naturally lead to interference oscillations. bond lengths and bonding types. We demonstrate that such Further theoretical studies were carried out on the coherent fundamental observations can be related to crucial structural + information, such as chemical bond lengths, molecular orbital emission of electrons from the H2 molecule and the H2 ion by photoionization (7) and by fast electron impact (8, 9). The in- composition, and quantitative assessment of many-body effects, with a very high accuracy. The experimental and theoretical tools terference in the D2 molecule was also studied using electron impact (10). Projectiles such as heavy ions have also been used to we use are relatively simple and easily accessible, and our method canreadilybeextendedtolargersystems, including molecules of study similar phenomena in diatomic molecules (11, 12). In- biological interest. terference phenomena were also found and studied extensively in the K-shell ionization of diatomic molecules, such as N (13, 2 Author contributions: M.S., M.N.P., and P.D. designed research; R.K.K., M.P., R.G., L.J., 14). Recently, the cold target recoil ion momentum spectroscopy C.M., M.S., M.N.P., and P.D. performed research; R.K.K., M.P., R.G., L.J., C.M., C.S., and (COLTRIMS) technique has been used to study the double-slit P.D. analyzed data; and R.K.K., M.S., M.N.P., and P.D. wrote the paper. interference effect in the double ionization of H2 induced by The authors declare no conflict of interest. synchrotron radiation (15, 16). This article is a PNAS Direct Submission. Direct observation of the interference pattern in photoioni- 1To whom correspondence should be addressed. E-mail: maria-novella.piancastelli@fysik. zation is often difficult, being a small modulation superimposed uu.se. www.pnas.org/cgi/doi/10.1073/pnas.1306697110 PNAS | September 17, 2013 | vol. 110 | no. 38 | 15201–15206 Downloaded by guest on September 25, 2021 Another source of oscillatory behavior in the photoionization cross-sections is the diffraction by neighboring centers, which is well known in extended X-ray absorption fine structure (EXAFS) spectroscopy and is obviously due to the underlying photoemission channels. A beautiful observation of such struc- tures has been reported recently for a series of gas-phase mol- ecules (26, 27). The recognized success of EXAFS in producing structural information, coupled to the much richer information available in photoemission by means of the ability to select a specific orbital or emission center, bears great promise for the study of high-energy structures in photoemis- sion. The interplay between interference and diffraction pat- terns is another uncharted territory, and it will constitute an obvious development of our present work. This interplay is expected to be prominent in outer-valence orbitals, which show similar patterns, but are generally more complex due to the extensive delocalization. Although the spectrally unresolved splitting of core orbitals Fig. 1. Schematic representation of double-slit interference in core and prevents the study of interferences in most systems, an in- inner-valence photoionization of a polyatomic molecule and its relationship teresting possibility is restored by studying the ionization of with the bond length. Interference cannot be observed in the C 1s core inner-valence σg and σu orbitals originating from the 2s AOs of levels, where it is impossible to resolve the g/u splitting due to the large fi natural lifetime. the rst-row atoms. They have much larger g/u splitting due to the stronger bonding interaction, and are thus easier to resolve experimentally. This opens the possibility of a direct study of Most molecular orbitals (MOs) are complex and delocali- interference patterns in a much broader range of molecular zed over several atoms. In fact, the focus in the past on analyz- systems and facilitates the exploration of most of the issues ing core orbitals is due to the complete localization of such previously considered. Often, ionizations of 2s-derived MOs are orbitals on the equivalent centers