Snapshots along a selected trajectory showing water molecules together with isosurfaces (at values of 0.01 and 0.001 au−3) of the spin density. (a) The system right after ionization (t = 0) when the system is in the neutral geometry and the hole is partially delocalized. (b) The system after the hole localizes almost entirely on a single water molecule, forming transient H2O+ (t = 40 fs). This species reacts almost instantaneously with a neighboring water molecule, forming an OH radical and a hydronium cation (highlighted in green), which eventually become separated by water molecules, as shown in (c) (t = 400 fs).
Maximum Mulliken spin population (as a measure of localization of the hole) on a single oxygen atom, shown as a function of time for all trajectories. The dashed line is at the value of 0.95, its intersection with each line marking the time when the localization is practically complete. DFT trajectories are depicted in blue and DFT-D trajectories are in red. The black line is the average over all trajectories.
The distance between the center of spin and the center of charge, shown as a function of time for all the trajectories. This distance between an oxygen atom with the highest Mulliken spin population and that to which the excess proton is the closest monitors the progress of the proton transfer reaction. It is zero initially, becoming non-zero after the first proton hop. DFT trajectories are depicted in blue and DFT-D trajectories are in red. The black line is the average over all trajectories.
Correlation between the time of localization and the time of reaction. The former is defined as the time when the maximum Mulliken spin population on a single oxygen atom reaches 0.95 (dashed line in Fig. 2). The latter is characterized by the reaction interval (depicted by a line) that starts at the moment of the first proton transfer (full circles) and ends when no more back transfer to the original hole occurs (open circles). DFT trajectories are depicted in blue and DFT-D trajectories are in red. The full line shows direct proportion between the two times for reference.
Correlations between the distance between the oxygen atoms involved in the proton transfer reaction and the distance between the transferring hydrogen atom and its new oxygen bonding partner along all simulated trajectories. Blue circles mark the initial conditions and blue lines denote the trajectory segments until the reaction starts. Red segments with red circles at their boundaries mark the reaction intervals (as defined in Fig. 4). Gray segments show the rest of the trajectories after the reaction.
Snapshots of the aqueous bulk system right after ionization (t = 0) for a selected trajectory using different electronic structure methods. Water molecules are shown together with isosurfaces of the spin density.
Water pentamer as a benchmark cluster system, calculated with different methods (see text for detail). Water molecules are shown together with isosurfaces of the spin density.
(a) Time evolution of electronic excitation spectrum for ionized bulk water. Average of 22 AIMD trajectories with excitations computed for core trimer at the EOM-IP-CCSD level (see text). Stick spectra for each trajectory are broadened with 0.6 eV FWHM Gaussian. Excitations shown only for 1–5 eV, the optically accessible range. (b) As panel (a) except that the computed spectral intensity is turned on for each trajectory only when the spin is 95% localized as judged by analysis of the BLYP-SIC density, see Fig. 4. Intensity scale bar in both the plots is the oscillator strength density relative to that of the corresponding gas phase OH radical transition (0.00312).
Comparing spectral predictions and experiment. (a) and (c) Experimental transient absorption spectra with a continuum probe and time resolution of 40–50 fs. Photoionization of pure liquid water achieved with 2 photons giving a total excitation energy ∼11 eV. Scale bar is transient absorbance in mOD. The signal aligned along zero delay is coherent pump + probe absorption and is observed in absence of ionization (see text). In (a), cross phase modulation between the pump and 800 nm driven probe continua is observed (see arrow)—this is minimized by driving the continuum at 1350 nm (c). Signal rising to maximum at 500 fs delay most prominently at 700 nm is from the solvated electron; when fully developed, the absorbance at 720 nm is 20 mOD. (b) and (d) Simulated spectrum for ground state cationic hole in bulk water, reproduced from Fig. 8(b) but now shown matching experimental range of probe wavelengths and normalized to peak spectral intensity. Recall that the spectral simulation shows only signals attributable to the ionized and localized hole. These signals are not apparent in the experimental datasets.
Spectral cuts from the four panels of Fig. 9 at four pump-probe delays comparing theoretical prediction (b and d) and experimental reality (a and c). No blue shifting feature is picked up experimentally.
Spin localization and proton hopping times in fs.
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