Sequential dissociation of H$_2$O$^{++}$ following double photoionization*

A recent analysis of momentum imaging experiments on the dissociation of the H$_2$O$^{++}$ ion following one-photon double ionization [Phys. Rev. A 98, 053429 (2018)] elucidated the dynamics of direct three-body dissociation to H$^+$ + H$^+$ + O, but also suggested that in one ionization channel a sequential mechanism is involved. Analysis of the momentum imaging data in the native frames of reference associated with each break step confirms sequential dissociation dynamics. A previous study of three-body breakup of H$_2$O$^{++}$ showed sequential dissociation of the $2 ^1A_1$ state by H$_2$O$^{++}$($2 ^1A_1$) $\rightarrow$ OH$^+$($^1\Sigma^+$) $+$ H$^+$ followed by spin-orbit coupling of the $^1\Sigma^+$ and the $^3\Pi$ hydroxyl cation states leading to OH$^+$($^3\Pi$) $\rightarrow$ O($^3$P)$ + $H$^+$. Here we present a theoretical determination of the rovibrational populations of the OH$^+$($^1\Sigma^+$) state from classical trajectories on the H$_2$O$^{++}$($2 ^1A_1$) surface. For two-body dissociation, the resulting internal energy distribution of the OH$^+$($^1\Sigma^+$) cation is binned quasiclassically. The resulting vibrational distribution and coupling to the dissociative OH$^+$($^3\Pi$) state allow comparison with the experimental native frames analysis.