Correlated Dynamics of the Motion of Proton-Hole Wave Packets in a Photoionized Water Cluster

We explore the correlated dynamics of an electron hole and a proton after ionization of a protonated water cluster by extreme ultraviolet light. An ultrafast decay mechanism is found in which the proton-hole dynamics after the ionization are driven by electrostatic repulsion and involve a strong coupling between the nuclear and electronic degrees of freedom. We describe the system by a quantum-dynamical approach and show that nonadiabatic effects are a key element of the mechanism by which electron and proton repel each other and become localized at opposite sides of the cluster. Based on the generality of the decay mechanism, similar effects may be expected for other ionized systems featuring hydrogen bonds.

Figure 1

(a) Potential energy surfaces of the three lowest electronic states of $\mathrm{H}({\mathrm{H}}_2\mathrm{O}{)}_2^{++}$ for the $z$ (central proton position projected onto the oxygen-oxygen axis) and $R$ (oxygen-oxygen distance) coordinates and keeping the rest of the vibrational modes frozen. The dot marks the Frank-Condon nuclear geometry. The orbitals shown represent the highest occupied molecular orbitals at the Hartree-Fock mean field level, and they correspond to the electron hole in the leading configuration for each of the three lowest-energy electronic states of the dication in a multiconfigurational description. (b) Scheme of the hydrogen-bonded system indicating the location of the electron pairs that can be ionized and the corresponding potential energy surfaces as a function of the central proton position. Ionization leading to the electronic states under consideration can take place from lone electron pairs on each monomer (in red and blue, negative and positive slope curves, respectively) or from the electrons involved in the hydrogen bonding (in green, horizontal curve).

Figure 2

Schematic representation of the seven internal nuclear coordinates used in the wave packet propagations showing in each case the relevant atoms. The proton transfer coordinate used in this work was transformed as $z^{\prime }=z/(R-\delta )$ [28], where $\delta$ is a constant. In this work appearances of ($z$) refer to the ($z^{\prime }$) defined here.

Figure 3

Correlation function between proton and electron-hole positions obtained from the propagated wave packet.

Figure 4

Reduced probability densities in the $z$ (central proton position projected onto the oxygen-oxygen axis) and $R$ (oxygen-oxygen distance) coordinates obtained from the propagated wave packets after tracing over all other vibrational modes and electronic states. Snapshots (a)–(c) correspond to propagations with the full Hamiltonian in Eq. (1). Snapshots (d)–(f) correspond to propagation without nonadiabatic coupling in the Hamiltonian, Eq. (3).