28
A. Palacios et al.
Facilities as FLASH in Hamburg or LCLS in Stanford nowadays produce pulses
in the x-ray region with durations as short as a few fs [7]. With the advent of
detection techniques such as recoil-ion and electron momentum spectroscopy [5],
it is possible to detect in coincidence all charged fragments arising from atomic
and molecular fragmentation processes. Combinations of these experimental set-ups
have recently provided a time-resolved picture of the Coulomb break-up of D 2 after
absorption of two XUV photons [33, 34]. On the other hand, HHG techniques have
demonstrated to be able to generate trains of attosecond (as) [10, 35] and isolated
as [12] XUV pulses. These pulses are ideal to trigger ionization processes in atoms
and molecules, whose field-free evolution can be subsequently tracked at the electronic time scale (hundreds of as). Experimental set-ups combining such sources
with IR fields have led to the first observations of time-resolved images of electron localization in single ionization of H 2 and D 2 [36–38]. Despite the relatively
large experimental efforts devoted to study molecular photoionization in hydrogen
molecules, further investigations should also shed light on a number of unexplored
processes, such as those involving the dynamics of highly correlated singly excited
states, or those involving DES that are not optically allowed in photoionization (i.e.,
that are not accessible by absorption of a single photon).
2.3 Theoretical Approach and Implementation
Solid ab-initio theoretical methods able to describe the interaction of pulsed radiation with molecules are still under development. A full treatment that accurately
accounts for all degrees of freedom (electronic and nuclear motion, including electron correlation) remains a challenge, even for the simplest molecules. As a consequence, apart from low dimensional models, most formalisms have been devoted
to H
+
2 (see [18, 19] and references therein). Few groups have reported electronic
correlated calculations on diatomic homonuclear molecules, and most of them have
tackled the problem by using methods within the fixed nuclei approximation (FNA)
[39–42], or assuming that the electronic dipole transition moments are independent
of the internuclear distance [43, 44]. The first fully correlated calculations accounting for the complete dimensionality of electronic and vibrational motions as well
as for interferences between all open direct and resonant ionization channels in H 2
and D 2 photoionization were performed within a time-independent approach [45–
48]. Although restricted to single photoionization with monochromatic radiation,
the methodology provided, for the first time, an accurate description of molecular autoionization (lifetimes, dissociative and photoionization cross sections, etc).
Recently, this method has provided solid theoretical support to a large variety of
experiments performed with synchrotron radiation [21–23, 30]. Its Feshbach-like
treatment [49] allows for a proper description of the electronic continuum of the
molecule and constitutes the skeleton for latter theoretical developments in the time
domain. In particular, the representation of molecular stationary states presented
below in this section is based on this formalism.
A. Palacios et al.
Facilities as FLASH in Hamburg or LCLS in Stanford nowadays produce pulses
in the x-ray region with durations as short as a few fs [7]. With the advent of
detection techniques such as recoil-ion and electron momentum spectroscopy [5],
it is possible to detect in coincidence all charged fragments arising from atomic
and molecular fragmentation processes. Combinations of these experimental set-ups
have recently provided a time-resolved picture of the Coulomb break-up of D 2 after
absorption of two XUV photons [33, 34]. On the other hand, HHG techniques have
demonstrated to be able to generate trains of attosecond (as) [10, 35] and isolated
as [12] XUV pulses. These pulses are ideal to trigger ionization processes in atoms
and molecules, whose field-free evolution can be subsequently tracked at the electronic time scale (hundreds of as). Experimental set-ups combining such sources
with IR fields have led to the first observations of time-resolved images of electron localization in single ionization of H 2 and D 2 [36–38]. Despite the relatively
large experimental efforts devoted to study molecular photoionization in hydrogen
molecules, further investigations should also shed light on a number of unexplored
processes, such as those involving the dynamics of highly correlated singly excited
states, or those involving DES that are not optically allowed in photoionization (i.e.,
that are not accessible by absorption of a single photon).
2.3 Theoretical Approach and Implementation
Solid ab-initio theoretical methods able to describe the interaction of pulsed radiation with molecules are still under development. A full treatment that accurately
accounts for all degrees of freedom (electronic and nuclear motion, including electron correlation) remains a challenge, even for the simplest molecules. As a consequence, apart from low dimensional models, most formalisms have been devoted
to H
+
2 (see [18, 19] and references therein). Few groups have reported electronic
correlated calculations on diatomic homonuclear molecules, and most of them have
tackled the problem by using methods within the fixed nuclei approximation (FNA)
[39–42], or assuming that the electronic dipole transition moments are independent
of the internuclear distance [43, 44]. The first fully correlated calculations accounting for the complete dimensionality of electronic and vibrational motions as well
as for interferences between all open direct and resonant ionization channels in H 2
and D 2 photoionization were performed within a time-independent approach [45–
48]. Although restricted to single photoionization with monochromatic radiation,
the methodology provided, for the first time, an accurate description of molecular autoionization (lifetimes, dissociative and photoionization cross sections, etc).
Recently, this method has provided solid theoretical support to a large variety of
experiments performed with synchrotron radiation [21–23, 30]. Its Feshbach-like
treatment [49] allows for a proper description of the electronic continuum of the
molecule and constitutes the skeleton for latter theoretical developments in the time
domain. In particular, the representation of molecular stationary states presented
below in this section is based on this formalism.