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 9.3.2.1, 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) 1sσg or the
odd (ungerade) 2pσu 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 1sσg and 2pσu, 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 1Πu symmetry
leading to H2+(1sσg) or to H2+(2pσu).
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 [1sσg with gerade
(solid line) and 2pσu 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.
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).
ALSNews Vol. 278, July 25, 2007 |