A single hydrogen (or deuterium) molecule consists of only two protons (deuterons) and two electrons and is perfectly symmetric. Linearly polarized photons are similarly symmetric. So one might think that the angular distribution of photoelectrons resulting from photoionization of the molecule by the photon accompanied by dissociation into a hydrogen atom and a hydrogen ion would itself be symmetric. However, an international team of researchers from Germany, Spain, and the U.S. has now shown that this need not be the case. When there are multiple quantum paths for the process, interference between waves in the coherent superposition of electron states (which exists when the molecular fragments are still close together) skews the distribution by breaking the molecular symmetry.

Molecular hydrogen is the most fundamental and one of the most basic molecules we can think of as well as the four-body system that is to date the best described mathematically. A particularly elegant way to dissect this molecule experimentally is to probe with a single photon, since the photon deposits only energy and angular momentum, unlike particles such as electrons, ions, and neutrons. Moreover, the linear polarization makes the photon—the driving force in the photoionization/molecular dissociation process—perfectly symmetric as well.

In their studies with low-energy linearly polarized light at ALS Beamline 9.3.2, the researchers investigated the simple reaction where a single photon knocks out one electron and leaves behind an excited positively charged molecular ion, which then breaks apart into one proton and one hydrogen atom, resulting in an oriented molecule with one end distinguishable from the other. The team asked the question: Would we expect any asymmetric outcome in our reaction, e.g., an unequal electron emission pattern with respect to the molecular axis? An intuitive answer to this question is "no," since the electron leaves the molecule in a symmetric final state of well-defined parity—either the even (gerade) 1sσ_g or the odd (ungerade) 2pσ_u state. Neither one of these final states should trigger a nonsymmetric electron emission pattern.

In fact, "no" is the right answer if there exists only one pathway in any photo fragmentation processes of homonuclear diatomic molecules like hydrogen and deuterium. But the microcosm of atoms and molecules is quantum, not classical. In particular, an electron can be in the superposition of two different states, so the actual final state represents the coherent sum of the two possible outcomes 1sσ_g and 2pσ_u, which are degenerate (undistinguishable in energy) but of different symmetry. The relative weight in the superposition of the two different pathways represented by the gerade and ungerade states depends on the molecular dynamics, that is, the changing distances between the nuclei. An experimental fingerprint of this dynamics is the kinetic energy release (KER) of the heavy fragments, i.e., the net energy of the proton and the hydrogen atom.

Energy-level diagram and pathways to dissociative ionization of molecular hydrogen showing the total energy of the H₂ and H₂⁺ systems as a function of internuclear distance. The red and blue curves indicate the resonant ionization through the lowest states of two series (Q1 and Q2) of doubly excited states of H₂ with ¹Π_u symmetry leading to H₂⁺(1sσ_g) or to H₂⁺(2pσ_u). At large internuclear distances, the Q1 states dissociate into H(n = 1) + H(n = 2,...,∞) and the Q2 states into H(n =2, l = 1) + H(n = 2,...,∞), where n and l are, respectively, the principal and angular momentum quantum numbers of the state. The orange and green lines indicate the interfering pathways for dissociative ionization by absorption of one 33-eV photon.

To investigate the photoelectron angular distribution with respect to the orientation of the molecule and the polarization of the incoming light as a function of the KER, the team used a coincident-electron-and-ion momentum-imaging apparatus (COLTRIMS, see ALSNews, Vol. 247, November 24, 2004). Applying a state-of-the art quantum mechanical calculation without any semiclassical approximations for the nuclear motion enabled them to understand why the symmetry breaking is most apparent for a KER of 9 eV: it is here that the two possible outcomes of gerade and ungerade symmetry contribute equally, resulting in a strong mix of the two pathways of different parity.

Top: Angular distribution (radial distance in arbitary units) of the electrons as a function of kinetic energy release (KER) for dissociative ionization of deuterium, D₂ with linearly polarized light at a photon energy of 33.25 eV. The panels (a–f) represent KER = 0.2 eV, 6.3 eV, 7.8 eV, 9.2 eV, 11 eV, and 14 eV, respectively. The axis of the molecule, indicated by colored circles (blue, deuteron; green, deuterium), at 90° to the polarization vector, and the polarization vector define a common plane; the electron is restricted to this plane by ±45°. The curves represent theory (solid red line), experiment (circles with error bars representing standard deviation), and fit of the experimental data with spherical harmonics (dotted line). The small three-dimensional plots in the upper right are also theoretical results. Bottom: The angle-integrated KER spectrum, showing theory (red) and experiment (black). The blue bars at KER values labeled a–f correspond to the KER values in the top panels.

The team considers symmetry breaking in a completely symmetric molecule to be a general molecular manifestation of autoionization when several (at least two) decay channels are effectively accessible. Combining symmetry and coherence also provides an elegant way to probe the electron dynamics that drive chemical reactions.

Calculated D⁺ kinetic energy distribution in dissociative ionization of D₂ by absorption of a 33.25-eV photon, showing why the symmetry breaking is most apparent for a KER of 9 eV: it is here that the two channels [1sσ_g with gerade (solid line) and 2pσ_u with ungerade symmetry dashed line)] contribute equally, resulting in a strong mix of the two pathways of different parity. The inset is a magnification of the region.

 

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Research conducted by F. Martín and J. Fernández (University of Madrid, Spain); T. Havermeier, L. Foucar, K. Kreidi, M. Schöffler, L. Schmidt, T. Jahnke, O. Jagutzki, A. Czasch, R. Dörner, and H. Schmidt-Böcking (University of Frankfurt, Germany); Th. Weber, T. Osipov, M.H. Prior, and A. Belkacem (Berkeley Lab); E.P. Benis and C.L. Cocke (Kansas State University); and A. Landers (Auburn University).

Research funding: Dirección General de Investigación; European Cooperation in the Field of Scientific and Technical Research (COST); Bundesministerium für Bildung und Forschung; Deutsche Forschungsgemeinschaft; Deutscher Akademischer Austauschdienst; U.S. Department of Energy, Office of Basic Energy Sciences (BES). Operation of the ALS is supported by BES.

Publication about this research: F. Martín, J. Fernández, T. Havermeier, L. Foucar, Th. Weber, K. Kreidi, M. Schöffler, L. Schmidt, T. Jahnke, O. Jagutzki, A. Czasch, E.P. Benis, T. Osipov, A.L. Landers, A. Belkacem, M.H. Prior, H. Schmidt-Böcking, C.L. Cocke, and R. Dörner, "Single photon–induced symmetry breaking of H₂ dissociation," Science 315, 629 (2007).