Ultrafast nuclear dynamics in the doubly-core-ionized water molecule observed via Auger spectroscopy

We present a combined experimental and theoretical study of the Auger-emission spectrum following double core ionization and excitation of gas-phase water molecules with hard-x-ray synchrotron radiation above the O $K^{-2}$ threshold. We observe an indication of ultrafast proton motion occurring within the 1.5 fs lifetime of the double-core-hole (DCH) states in water. Furthermore, we have identified symmetric and antisymmetric dissociation modes characteristic for particular DCH states. Our results serve as a fundamental reference for state-of-the-art studies of DCH dynamic processes in liquid water both at synchrotron and free-electron-laser facilities.

Figure 1

Oxygen $KLL$ Auger spectrum in water at 2.3 keV photon energy (black, left axis) and an enlarged view of the satellite and hypersatellite Auger lines recorded with higher statistics (red, right axis).

Figure 2

(a) Comparison of an experimental hypersatellite Auger spectrum of water measured at 2.3 keV (black circles) with the Auger spectra calculated including the nuclear dynamics. The total Auger spectrum (thick solid red line) is composed of various hypersatellite contributions: $K^{-2}$ (dash-dotted green), $K^{-2}V$ (thin solid magenta), $K^{-2}{L}^{-1}$ (dotted cyan), and $K^{-2}{L}^{-1}V$ (dashed blue) states. (b) Comparison of the experimental HS Auger spectra (black circles) to the calculation with fixed molecular geometry (dashed black) and with the nuclear dynamics included (solid red).

Figure 3

Comparison of calculated Auger line profile for one of the dominant Auger channels ($K^0\to K^{1}1b_1^{-2}$) employing the Gaussian approximation in Eq. (9) and without. The solid red line shows the full calculated Auger spectrum, the dash-dotted green and dashed blue lines show the instantaneous ($t=0$ fs) Auger line profile for a single Auger channel. For the dash-dotted green line, the broadening due to finite lifetime was incorporated through a Lorentzian, and for the dashed blue line by employing a corresponding Gaussian. The inset shows a magnified region around the tail of the peak.

Figure 4

Resulting Auger spectra (a) with and (b) without the effects of nuclear dynamics in the core-ionized state. The weights of the individual satellites are described in Table 1, column B. (b) The vertical orange lines show the Auger transitions for the $K^{-2}$ satellite at the optimized ground-state geometry.

Figure 5

Comparison of calculated Auger line profile for the dominant Auger channel ($1b_1^{-2}$) employing the Gaussian approximation in Eq. (9) (dashed blue line) and employing the PCI lineshape as given in Eq. (14) with $\xi =-0.46$ (dash-dotted green line). The solid red line shows the full calculated Auger spectrum, the green and blue lines show the instantaneous ($t=0$ fs) Auger line profile for a single Auger channel. The inset shows a magnified region around the tail of the peak.

Figure 6

Dynamics of the water molecule in the (a) $K^{-2}$, (b) $K^{-2}4a_1$, and (c) $K^{-2}2a_1^{-1}4a_1$ states. The crosses mark the peak of the Wigner distribution of the vibrational wave packet. The squares indicate the atom positions at $t=0$ fs in the neutral ground state optimized geometry. The green dots indicate the spatial Wigner distribution of the vibrational wave packet. (d) Evolution of the average O–H bond distance as a function of time for the three electronic states.

Figure 7

Auger decay spectrum for the double $K$-shell ionized water molecule. The solid red line shows the assembled Auger spectrum according to Eq. (7). The dash-dotted/dashed/dotted lines show the instantaneous Auger spectra for different snapshots in time weighted by $exp(-\mathrm{\Gamma }t)$.