Signatures of attosecond electronic–nuclear dynamics in the one-photon ionization of molecular hydrogen: analytical model versusab initiocalculations

Abstract

We present an analytical model based on the time-dependent WKB approximation to reproduce the photoionization spectra of an H 2 molecule in the autoionization region. We explore the nondissociative channel, which is the major contribution after one-photon absorption, and we focus on the features arising in the energy differential spectra due to the interference between the direct and the autoionization pathways. These features depend on both the timescale of the electronic decay of the autoionizing state and the time evolution of the vibrational wavepacket created in this state. With full ab initio calculations and with a one-dimensional approach that only takes into account the nuclear wavepacket associated to the few relevant electronic states we compare the ground state, the autoionizing state, and the background continuum electronic states. Finally, we illustrate how these features transform from molecular-like to atomic-like by increasing the mass of the system, thus making the electronic decay time shorter than the nuclear wavepacket motion associated with the resonant state. In other words, autoionization then occurs faster than the molecular dissociation into neutrals.

Reconstruction of the time-dependent electronic wave packet arising from molecular autoionization

“…As a consequence, the populated doubly excited states can efficiently ionize over a wide range of internuclear distances, from the Franck-Condon region up to well outside this region, thus leading to a broad distribution of H 2 + (1sσ g ) vibrational states. In general, the slower the autoionization, the higher the vibrational state in which H 2 + is left, because the rapidly evolving nuclear wave packet in momentum space can more efficiently overlap with higher vibrational states of H 2 + (1sσ g ) ( 35 ). Therefore, by vibrationally resolving the final state of the remaining H 2 + ion, one gains access to the dynamics of the autoionization decay: The nuclear motion acts as an internal clock that can be used to extract dynamical information about this decay.…”

“…Full lines: Ab initio calculation. Dashed lines: Fit to the experimental data by using the extended Fano model described in the text [see also ( 35 )].…”

“…In this formalism, molecular rotation is not taken into account because it is orders of magnitude slower than autoionization (picoseconds versus femtoseconds) so that the orientation barely changes during the electron emission process. The resonant contribution to the photoelectron wave packet correlated to the v-state of the H 2 + cation can be approximately written ( 35 ) where C is a constant, is the nonresonant background cross section, ϵ is the energy of the emitted electron, R is the internuclear distance, χ v is the final vibrational state of H 2 + with vibronic (electronic plus vibrational) energy E v , Γ is the autoionization width of the Q resonance, and χ Q is the nuclear wave packet evolving along the potential energy curve of this resonance, described within the semiclassical WKB approximation [see, for example, ( 45 ) for an introduction to WKB]. We note that, for each final vibrational state of H 2 + , the photoelectron energy and the photon energy E are related by the formula E + E g = E v + ϵ, where E g is the H 2 ground-state energy.…”

“…Although no resonance features are visible in the total nondissociative photoionization spectra of H 2 , theory has long ago predicted ( 28 ) that photoionization spectra in which the vibrational state of the remaining H 2 + ion is resolved (hereafter called v-spectra) do show resonance features associated with the H 2 doubly excited states (although they vanish when summing over all H 2 + vibrational states). Furthermore, it has been recently demonstrated ( 35 ) that these v-spectra provide a time-energy mapping of autoionization dynamics. Ultrafast nuclear motion is the clock that maps these dynamics into the final population of the bound vibrational states of H 2 + , allowing one to image H 2 autoionization without the need for ultrashort probe pulses as are used in current attosecond pump-probe experiments ( 36 ).…”

The quantum chemistry of attosecond molecular science

“…In general, the slower the autoionization, the higher the vibrational state in which is left, because the rapidly evolving nuclear wave packet accumulates higher momentum, thus ionizing into higher vibrational states of (1s σ g ). Therefore, the nuclear motion acts as an internal clock of autoionization and the line shapes of the peaks observed in vibrationally resolved photoelectron spectra provide snapshots of the autoionization dynamics through a direct time‐energy mapping …”