Photochemistry and spectroscopy of small hydrated magnesium clusters Mg+(H2O)n, n = 1–5

Hydrated singly charged magnesium ions Mg+(H2O)n, n ≤ 5, in the gas phase are ideal model systems to study photochemical hydrogen evolution since atomic hydrogen is formed over a wide range of wavelengths, with a strong cluster size dependence. Mass selected clusters are stored in the cell of an Fourier transform ion cyclotron resonance mass spectrometer at a temperature of 130 K for several seconds, which allows thermal equilibration via blackbody radiation. Tunable laser light is used for photodissociation. Strong transitions to D1–3 states (correlating with the 3s-3px,y,z transitions of Mg+) are observed for all cluster sizes, as well as a second absorption band at 4–5 eV for n = 3-5. Due to the lifted degeneracy of the 3px,y,z energy levels of Mg+, the absorptions are broad and red shifted with increasing coordination number of the Mg+ center, from 4.5 eV for n = 1 to 1.8 eV for n = 5. In all cases, H atom formation is the dominant photochemical reaction channel. Quantum chemical calculations using the full range of methods for excited state calculations reproduce the experimental spectra and explain all observed features. In particular, they show that H atom formation occurs in excited states, where the potential energy surface becomes repulsive along the O⋅⋅⋅H coordinate at relatively small distances. The loss of H2O, although thermochemically favorable, is a minor channel because, at least for the clusters n = 1-3, the conical intersection through which the system could relax to the electronic ground state is too high in energy. In some absorption bands, sequential absorption of multiple photons is required for photodissociation. For n = 1, these multiphoton spectra can be modeled on the basis of quantum chemical calculations.


Benchmark of computational methods, electronic states character
Table S1 -Excitation energies (in eV) and oscillator strengths (in parenthesis) using the EOM-CCSD method with various basis sets, in the structures optimized at the MP2/def2TZVP level of theory. Only the most stable isomers were considered.  Table S3 analyzes the character of the four lowest electronic states in Mg + (H2O)n isomers and its correlation to the states of the bare Mg + ion, i.e. 3s and 3p. For the smallest clusters, the assignment is clear and almost quantitative, with a 3s the ground state and three 3p electronically excited states, whose degeneracy is lifted by the lower symmetry. The s and py,z atomic orbitals (AOs) are often the dominant contributions to the respective molecular orbital (MO). For the correlating pz states, only a limited contribution of the Mg AOs to the total MO are observed. For larger clusters with H2O in the second solvation shell (IVb, Vb, Vc), all Mg + s and p orbitals contribute to the respective states, making the qualitative analysis less clear. However, all excitations into the first band can be described as, at least partial, 3s-3p transitions as the 3s component always dominates the ground state and there is always a strong 3p component in the excited state. Table S3 -Analysis of the character of the first four electronic states of various Mg + (H2O)n isomers, calculated at the TD-CAM-B3LYP/aug-cc-pVTZ level of theory in the structure optimized at the MP2/def2TZVP level. The character of the state was calculated by summing the square of the AO coefficients for MOs that compose the given electronic state. All MOs with contribution higher than 6% for the given state were included. "Mg contribution" shows the relative weight of Mg orbitals for the given state.

Calculation of the relative photodissociation cross sections
Relative intensities were calculated by determining the photodissociation cross sections according to Equation 1.
Here I0 is the parent ion's intensity and I1-n are the intensities of the n fragment ions. The laser wavelength is represented by, the number of pulses by p and the pulse energy by E. Planck's constant is h, c is the speed of light and A represents the irradiated area inside the cell. The constant for the BIRD rate is kBIRD and t is the time the ions were exposed to black body radiation.
The set up for the laser irradiation is shown in Figure S1. The number of pulses p is controlled by an electronically controlled shutter. The pulse energies E are measured by a power meter. Figure S2 shows some power spectra of the laser system in the relevant wavelength range. Figure S2: Power spectra of the laser system used for ion irradiation.
Measurements of the pulse energies were performed behind an aperture at a distance of 3.4m from the ICR cell and compared to measurements directly in front of the laser ( Figure S3) to get an estimate of the photon flux inside the cell.

Detailed figures with all dissociation channels
Figures S3 -S7 show the detailed photodissociation spectra of the investigated ions, along with their branching ratios.

Reconstruction of the single photon spectrum for Mg(H2O) +
A reconstruction of the single photon absorption spectrum for the Mg + H2O ion is shown in figure S8. Figure S8: Reconstructed Photodissociation spectrum of Mg + H2O for single photon absorption

Photon flux dependence
Figures S9 -S14 show the photon flux dependencies of the investigated ions at specific wavelengths.

Correction of jumps in the spectra
At the wavelength where the laser system switches from SFG/SH generation to idler beam, jumps appear in the relative photodissociation cross sections, most likely due to a spatial deviation of the two different beams. To correct this, the relative cross sections were adjusted to meet at the same level at this specific wavelength, by multiplying the intensities at lower wavelengths by a constant factor. For Mg + H2O no such correction was necessary as the whole spectrum is located in the wavelength range above 410 nm. For Mg + (H2O)2 a correction factor of 2.0 was used ( Figure S30).  Here IBIRD-Fragments is the intensity of fragments produced by BIRD and IPhoto-Fragments is the intensity of fragments produced by photodissociation. The photon flux is represented by Φ while tIR stands for the irradiation time and tp for the pulse length.
For Mg + (H2O)5 only one BIRD fragment MgOH + (H2O)4 was observed and it was completely independent from laser irradiation. Its intensity without laser irradiation was in the order of 10-20% in the timescale of the experiment. The correction is shown in Figure S34.
S24 Figure S34: BIRD correction in the spectrum of Mg + (H2O)5 For Mg + (H2O)4 two BIRD fragments were observed, MgOH + (H2O)3 and Mg + (H2O)3. Only a minor amount of about 4% of the parent ions dissociated via BIRD without laser irradiation on the timescale of the experiment. The intensity of the Mg + (H2O)3 fragment was thereby also completely independent form laser irradiation, while MgOH + (H2O)3 shows wavelength dependency in the range from 393 nm to 688 nm. In this region the ratio of the MgOH + (H2O)3 fragment created by BIRD was estimated to be 0.1 % of the Mg + (H2O)3 fragment. The correction is shown in Figure S35.  Figure S36 shows the photoabsorption spectra of the Mg + (H2O)2 cluster using a different number of random walkers within the PIMD sampling. It can be used that there are only limited changes between spectra produced from PIMD simulations with 10 and 20 random walkers, the most significant difference is the height of the peak at 3.75 eV. Otherwise, the shape of the spectrum is almost unaffected. Figure S36: Photoabsorption spectra of the Mg + (H2O)2 cluster calculated at the CC2/aug-cc-pVDZ level of theory with a different number of random walkers used within the PIMD sampling. Figure S37 compares relaxed potential at the EOM-CCSD and MRCI method. MRCI can quantitatively reproduce energy of first four states in doublet multiplicity, D0 and D1-D3. For the fourth excited state D4, EOM-CCSD and MRCI differ already slightly, the agreement is however still very good. Finally, the fifth excited state D5 state was included into the MRCI state average for completeness to avoid convergence of D4 into a wrong state. At the MRCI level, the D5 state is sometimes predicted to be too high in energy (e.g. for the O-H coordinate at 1.2 Å). This is happens when a higher state comes from the CASSCF calculations into the MRCI procedure.