Solvation of cationic copper clusters in molecular hydrogen

Multiply charged superfluid helium nanodroplets are utilized to facilitate the growth of cationic copper clusters (Cun+, where n = 1–8) that are subsequently solvated with up to 50 H2 molecules. Production of both pristine and protonated cationic Cu clusters are detected mass spectrometrically. A joint effort between experiment and theory allows us to understand the nature of the interactions determining the bonding between pristine and protonated Cu+ and Cu2+ cations and molecular hydrogen. The analysis reveals that in all investigated cationic clusters, the primary solvation shell predominantly exhibits a covalent bonding character, which gradually decreases in strength, while for the subsequent shells an exclusive non-covalent behaviour is found. Interestingly, the calculated evaporation energies associated with the first solvation shell markedly surpass thermal values, positioning them within the desirable range for hydrogen storage applications. This comprehensive study not only provides insights into the solvation of pristine and protonated cationic Cu clusters but also sheds light on their unique bonding properties.

Measurements are done at conditions specified as "H 2 big clusters" in table S1.S1.Only complexes with n = 1-5 are compared, since bigger clusters were not produced with conditions "H 2 small clusters".The data points which do not follow the general trend are marked green.S1.The ion abundances are plotted for each separate cluster size as a function of H 2 (k).The measurement points highlighted in green were not verified by the reference measurements and therefore are not considered.S1.The ion abundances are plotted for each separate cluster size as a function of H 2 (k).

Simulation methods
In this work we have employed the evolutionary algorithm (EA) and a diffusion Monte Carlo (DMC) method to study both the energy and structure of the (H 2 ) k Cu + (k>4) clusters following the description discussed in the main text: The first four H 2 units are assumed as fixed as the global minimum shown in Figures 1 and 3.The other H 2 units are considered as pseudoatoms and their interaction with the inner (H 2 ) 4 Cu + core is described by means of the potential shown in Eqs. ( 3) -( 5)

Evolutionary Algorithm
The so called EA [1] provides insights of the minimum energy configurations of the (H 2 ) k Cu + clusters.This algorithm has already been used successfully for doped hydrogen [2] and helium [3] clusters.The method starts with M (equals to 30 in our calculation) parent populations which are confronted as in a natural selection procedure with offspring populations obtained after inducing some mutations in the original ones.The conformational space of the system is then explored through the optimization of a fitness function to search for the overall minimum energy.Groups of 10 individuals are confronted and the best fit (within an energy threshold of 10 -4 meV).In the present study we start generating initial populations of M clusters consisting of N H 2 units treated as pseudoatoms.surrounding the (H 2 ) 4 Cu + core.Each individual i is characterized by the pair of vectors (ẑ i , ῆ i ) representing the 3N Cartesian coordinates of the atoms and standard deviations for Gaussian mutations, respectively.We start with η i = 1 and with random selections for the position within a specific range (0, ∆).A single offspring (z' i , η' i ) is created for each parent following the conditions: z' i (j) = z i (j) + η i (j) η' i (j) = η i (j) exp[τ' N(0,1) + τ N j (0,1)] where j = 1, …, 3N; τ and τ' are adjustable parameters which depend on the value of N; N(0, 1) is a random number from a Gaussian distribution of mean μ = 0 and standard deviation σ = 1, and N j (0, 1) stands for a randomly generated number for each component j.
The following step is then to establish pairwise comparisons of the energy of each individual with q random choices as opponents over the union of 2M elements formed with parents (z' i , η' i ) and offsprings (z' i , η' i ).We select those M individuals from the total population formed both with parents and offsprings with a larger number of points awarded in the competition with some other opponents to search for the lowest energies.These survivors individuals thus become parents for a new iteration in the selection process which will be repeated until the difference between the potential energies of consecutive generations is lower than a certain selected tolerance value.

Diffusion Monte Carlo
We use the DMC approach [4,5] to obtain the ground state energies, and the corresponding probabilities and distributions.In this method the time-dependent Schrödinger Equation is transformed in a diffusion equation by the change τ=i t.The ground state will correspond with the last non vanishing term in the propagation of the diffusion equation.We have used FigureS1: H m Cu n + distributions as a function of the number of H atoms (m) adsorbed to each individual cluster size (n) at H 2 pressure in the hexapole chamber of 1.5×10 -3 (black) and 1.8×10 -3 (red) mbar.Measurements are done at conditions specified as "H 2 big clusters" in tableS1.

Figure S2 :
Figure S2: H m Cu n + distributions as a function of the number of H atoms (m) adsorbed to copper cluster cations with a size (n) between 1 and 5.The complexes are formed by introducing H 2 to the quadrupole chamber prior Cu cluster formation) to the same pressure as was used during measurements in figure S1.To shrink He droplets H 2 was replaced by the room temperature He.

Figure S3 :
Figure S3: The measurement from figure S1 obtained at a H 2 pressure of 1.8×10 -3 (red) mbar is verified with two different reference measurements measured with different conditions using H 2 (blue) and D 2 (brown).The conditions of all three measurements are listed in tableS1.Only complexes with n = 1-5 are compared, since bigger clusters were not produced with conditions "H 2 small clusters".The data points which do not follow the general trend are marked green.

Figure S4 :
Figure S4: Histograms for the separation distance R of the H 2 centers of mass from the Cu atom for the optimized geometries of the (H 2 ) k Cu + and (H 2 ) k HCu + (k = 1-5) clusters depicted in figure 2 of the main text.

Figure S5 :
Figure S5: Histograms for the separation distance R of the H 2 centers of mass from the Cu atoms for the optimized geometries of the (H 2 ) k Cu 2 + and (H 2 ) k HCu 2 + (k = 1-7) clusters depicted in figure 3 of the main text.

Figure S6 :
FigureS6: CID measurements of Cu + with 7, 12, 13 and 14 D atoms attached.For each complex three measurements were done at 0 eV (without any collision gas), 1 and 10 eV (with Ar as a collision gas).The main fragmentation path is represented in blue and the number of D atoms attached to Cu + are also indicated.The peaks originated from the complexes with D 2 O impurity are marked with the asterisk.

Figure S7 :
Figure S7: CID measurements of D 5 Cu 2 + complex at the energy of 10-60 eV in steps of 10 eV.The zoomin on the Cu + , D 2 Cu + and DCu 2 + fragments at energies >30 eV is also shown with the corresponding magnifying factor.

Figure S10 :
Figure S10: Ion abundances of Cu n + (black) and HCu n + (red) for n=1-5 solvated in the H 2 with corresponding error bars, similar to figure S7, but measured at the "H 2 small clusters" conditions from tableS1.The ion abundances are plotted for each separate cluster size as a function of H 2 (k).

Table S1 :
Experimental conditions used to obtain data in figureS3. H