Hydrogen release from a single water molecule on Vn+ (3 ≤ n ≤ 30)

Water and its interactions with metals are closely bound up with human life, and the reactivity of metal clusters with water is of fundamental importance for the understanding of hydrogen generation. Here a prominent hydrogen evolution reaction (HER) of single water molecule on vanadium clusters Vn+ (3 ≤ n ≤ 30) is observed in the reaction of cationic vanadium clusters with water at room temperature. The combined experimental and theoretical studies reveal that the wagging vibrations of a V-OH group give rise to readily formed V-O-V intermediate states on Vn+ (n ≥ 3) clusters and allow the terminal hydrogen to interact with an adsorbed hydrogen atom, enabling hydrogen release. The presence of three metal atoms reduces the energy barrier of the rate-determining step, giving rise to an effective production of hydrogen from single water molecules. This mechanism differs from dissociative chemisorption of multiple water molecules on aluminium cluster anions, which usually proceeds by dissociative chemisorption of at least two water molecules at multiple surface sites followed by a recombination of the adsorbed hydrogen atoms.

S-5      Table 6 Electronic states of the low-lying energy isomers of Vn + , VnH2O + , VnO + clusters (n=1-13) calculated at BP86-D3/def-2TZVP level.  In actual experiments, there is coexistence of cations and anions and electrons generated in the LaVa source. Thus, the subsequent cluster reaction products may undergo dissociation and neutralization processes in the collision cell. In view of this, we examined the adiabatic ionization energies (I.E.) of the neutral VnH2O clusters, as shown in Supplementary Figure 10, where the clusters V1,2H2O + show larger electron affinities than other sizes indicating likely neutralization under multiple collisions.   Supplementary Figure 12 A comparison of DFT-calculated O-binding energy, with a comparison with the previous experimental study. 10 The detailed values correspond to the above table.

Supplementary
S-20 By comparing the DFT-calculated O-binding energy with the previous experimental study on the bond energies of Vn + -O by dissociation threshold analysis, there is a general consistence except a few clusters such as V8 + and V11-13 + . The occasional inconsistence may be due to the following factors.
1) Vanadium clusters could radiate with a high recurrent fluorescence rate as established a long time ago, 5 while this radiative cooling effect was not considered by the mentioned literature in their data of the dissociation threshold analysis. 4,11 One simple estimate suggests a 20% change in the value of the fitted dissociation energy, 4 and so display the error bars of the mentioned literature. 10 2) Another effect that was not attracted sufficient attention is the thermal properties of metal clusters at high excitation energies. These are most likely not possible to describe by simple harmonic oscillator models. That is, the difference of the experimentally determined threshold values are likely associated with a variation of radiation-induced residual energy which could cause electronic excitation states or unthermalized geometric deformation /aggravated vibrations, as well as melting effect at reduced sizes. 12,13,14,15,16 Melting alone is enough to disprove the simplified harmonic oscillator hypothesis, such as that by the group of Haberland and von Issendorff on sodium clusters. 17 For vanadium clusters the consequences of this effect will most likely have an impact on numbers extracted from experiments but the magnitude is difficult to quantify before thermal properties of these clusters have been measured.
3) From the point of view of DFT calculations, a universally correct exchange and correlation functional is not yet available to the scientific community. Apart from that, the theoretical calculation method and basis set could also bring forth overall energy differences, although the size-dependent tendency is almost parallel. S-21

S7 Natural Population Analysis of Charges
Supplementary Figure 13 Natural population analysis (NPA) charge on H2O in VnH2O + clusters calculated at BP86-D3/def2-TZVP level using NBO6.0 method. 18 The red dot line at 0.11 is just drawn to guide the eye.
Supplementary Table 11 NPA charge distributions on the atoms of VnH2O + (n = 1-13) calculated at BP86-D3/def2-TZVP level using NBO6.0 method. 18 The vanadium atom adsorbing the water molecule is defined as V-1 and the other vanadium atoms connecting with V-1 are identified as V-2, V-3, V-4 and V-5, etc. Among them, the V-2 corresponds to the one with the largest positive partial charge, while V-3 aims at the minima.  The HOMO-LUMO gaps are often associated with the cluster stability and reaction inertness.
Displayed here, are the HOMO and LUMO patterns of V1,5,9,10 + and H2O, as well as their relative orbital energy levels. Considering that Vn + react with water by transfer of electron, the proximity of the HOMO of H2O relative to the LUMO of V5,9 facilitates electron transfer from oxygen lone pair of water to the vanadium cluster.

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Supplementary Figure 15 HOMO-LUMO gaps of Vn + and VnH2O + clusters. Energies are given in eV.

S9 Energy Decomposition Analysis
Energy decomposition analysis (EDA) based on natural orbitals for chemical valence (NOCV) 19 between Vn + and H2O in VnH2O + can be divided into three parts: where ∆ is the repulsion energy caused by the Pauli exclusion principle, and ∆ and ∆ are the attraction energies due to electrostatic and orbital interactions, respectively. As seen in Supplementary Figure 16 and Table 12 below, the contribution of ∆ to ΔEint is larger than that of ∆ ; also, the plots of ΔEint values show the same tendency of odd-even oscillations as that of the Ead value plots (Figure 3a). From the ADF-calculated EDA results, the electrostatic interaction contributes about 2/3 to the attractive Vn + -H2O interaction, while the orbital interaction does ~1/3 contribution.

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Supplementary Figure 16 Energy decomposition analysis for VnH2O + showing the contributions of electrostatic interactions and orbital interactions to the total bonding energies. Detailed energy values are given in Supplementary  Table 12 below.