Single photon induced symmetry breaking of H2 dissociation Page: 2 of 15
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Symmetries are essential building blocks of our physical, chemical and biological models.
For macroscopic objects symmetries are always only approximate. By reducing the complex-
ity in the microcosm these symmetries often become strict. Thus, in any symmetric molecule
the ground state has a well defined parity. This property has far reaching consequences such
as truncation of rotational spectra or the existence of ortho and para molecular isomers [1].
An intriguing way to break the symmetry is isotopic substitution of one of the nuclei [2]. In
larger systems, symmetry breaking can also be achieved through selected vibrational modes,
e.g., asymmetric stretch, which lies at the origin of the Jahn-Teller and Rener-Teller effects
[3]. Alternatively, external fields can be used to favor a particular molecular direction, which
has been recently used by Kling et al [4] to induce asymmetric dissociation of the HZ molec-
ular ion into a proton and a hydrogen atom. Here we show that, in dissociative ionization
by absorption of a single photon (eq. 1)
hv+H2 --p+H+e , (1)
symmetry breaking is possible even in the absence of an external field. This is the smallest
and most fundamental molecular system for which such symmetry breaking is possible.
Symmetry operations in a molecule having a well-defined parity can change the sign of
the ground state wave function (odd parity, or ungerade, states). However, all observables
must be symmetric because they are squares of wave functions or transition matrix elements.
To achieve left-right asymmetry in an observable, the system must be put into a coherent
superposition of gerade (g, even), and ungerade (u, odd), molecular states. The relative
phase between the two states can then lead to a left or right localization of an electron.
Direct photoionization usually cannot induce this outcome, because the g and u states of
the remaining molecular ion have different energies. Therefore, two ionization pathways are
distinguishable by the electron energy and hence the coherence is lost.
Figure la shows the energy diagram for the H2 and HZ molecules. The energy difference
between the lowest g and u states in HZ, 2E+(isag) and 2Eu+(2pa-) respectively, is about
17eV in the Franck Condon region of H2. Thus if H2 is directly ionized in a vertical transition
by a photon of energy hv, the photoelectron will have an energy of about E = by - 16eV
when the remaining HZ is left in the g state, whereas it will have E = by - 33eV when
it is left in the repulsive u state. Both ionization paths are distinguishable by the energy
(fig. lb and ic). Because, in either path, HZ is in a state of well defined parity, it manifests2
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Martin, F.; Fernandez, J.; Havermeier, T.; Foucar, L.; Weber, Th.; Kreidi, K. et al. Single photon induced symmetry breaking of H2 dissociation, article, December 6, 2006; United States. (https://digital.library.unt.edu/ark:/67531/metadc893126/m1/2/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.