Size-Resolved Photoelectron Anisotropy of Gas Phase Water Clusters and Predictions for Liquid Water

We report the first measurements of size-resolved photoelectron angular distributions for the valence orbitals of neutral water clusters with up to 20 molecules. A systematic decrease of the photoelectron anisotropy is found for clusters with up to 5–6 molecules, and most remarkably, convergence of the anisotropy for larger clusters. We suggest the latter to be the result of a local short-range scattering potential that is fully described by a unit of 5–6 molecules. The cluster data and a detailed electron scattering model are used to predict the anisotropy of slow photoelectrons in liquid water. Reasonable agreement with experimental liquid jet data is found.

Figure 1

Lines labeled $n=1$ to $n=20$: Experimental $\beta$ parameters for ${\mathrm{H}}_2\mathrm{O}$ monomer and ${({\mathrm{H}}_2\mathrm{O})}_n$ clusters with $2\le n\le 20$ recorded at $13.0\mathrm{eV}\le h\nu \le 35.0\mathrm{eV}$. (a),(b), and (c) correspond to ionization from the $1b_1$, $3a_1$, and $1b_2$ orbitals of water, respectively. Monomer values for $\text{eKEs}<25\mathrm{eV}$ from this work and for $\text{eKEs}>25\mathrm{eV}$ from Ref. [20]. For ${({\mathrm{H}}_2\mathrm{O})}_2$, separate traces are shown for ${\mathrm{H}}_3{\mathrm{O}}^{+}$ [full brown line; $n=2$ Eq. (2)] and for the intact dimer $({\mathrm{H}}_2\mathrm{O}{)}_2^{+}$ (brown crosses) [see Fig. 2]. Green triangles: monomer (open symbols) and a cluster ensemble (full symbols) with an average cluster size $⟨n⟩\sim 58$ from Ref. [15]. Blue squares: monomer (open symbols) and liquid water (full symbols) from the microjet study by Faubel et al. [16]. Calculated anisotropy parameters for liquid water microjets: Open black circles: ${\beta }_{n=1}^{\text{liquid}}$ calculated with monomer values ($n=1$) as input for the local anisotropy in the liquid. Open orange diamonds: ${\beta }_{n=6}^{\text{liquid}}$ calculated with the cluster values ($n=6$) as input for the local anisotropy in the liquid. Open black stars: ${\beta }_{\text{elastic}}^{\text{liquid}}$ calculated with gas phase elastic scattering cross sections alone [39].

Figure 2

Experimental photoelectron spectra of (a) water monomer and ${({\mathrm{H}}_2\mathrm{O})}_n$ clusters for (b) $n=2$ and (c) $n=6$. Selected VMI images are shown in Fig. S3 of the Supplemental Material [22]. The dimer spectrum has contributions from the intact dimer $({\mathrm{H}}_2\mathrm{O}{)}_2^{+}$ (red line) and from ${\mathrm{H}}_3{\mathrm{O}}^{+}$ (black line) formed after fast proton transfer. (d) Calculated photoelectron spectra for the liquid water microjet for two polarization directions $\theta =0°$ (blue line) and 90° (black line) of the light (Fig. S5, [22]) for monomer input ${\beta }_{n=1}$ (Fig. 1). The photon energies $h\nu$ are indicated in the figure.