**4. Electronic properties and the origin of intense luminescence**

Validated by various research groups, the photophysical properties of metal clusters encaged in zeolite matrices are strongly dependent on numerous factors like ligand, spatial confinement, charge state, water content, electrostatic charge of the cavity or co-cation type [11]. Perhaps one of the largest scientific debates among scientist in this field is understanding the size dependent properties of a metal cluster [9]. Although the strong quantum confinement of the electrons separating the continues density of states into discrete energy levels is generally recognized as the origin of the optical transition, the fundamental photophysical mechanisms underlying their emission are poorly understood [61]. Metal clusters in various size regimes display molecule-like optical characteristics featuring HOMO-LUMO bandgap with transition to metal properties at high nuclearity. Obtaining well-defined clusters often remains questionable in designing nanostructures with specific functional properties. An understanding of both structural and electronic features by invoking their familiar aspects like the discrete electronic shell has led to a few concepts which attempt to rule the characteristics of the molecular-like entity. Substantial theoretical and computational efforts were made to understand and predict the fundamental properties associated with the existing and emerging metal clusters and develop a general valid theory [4, 7, 16].

In the examples presented earlier, the intense or dim luminescence has been attributed to various phenomena occurring in the excited state, effects mainly related to intersystem crossing (leading to phosphorescence), charge transfer and recombination, ion migration or structural changes [12, 62, 63]. Intriguingly enough, limited time-resolved spectroscopy experiments have shown that the luminescence decays on time scales ranging from fs to ms, a characteristic similar to molecules undergoing a complex excited-state dynamics. Several kinetic schemes have been proposed indicating luminescence either as a spin forbidden radiative transition to the ground state (phosphorescence) or recombination of electrons and holes trapped in the zeolite matrix (fluorescence) [2, 13, 59, 64].

The electronic configuration of the main constituent atoms Cu, Ag, and Au is situated at 3d, 4d, and 5d period, respectively. When a silver atoms with an electronic configuration of 4d105s1 forms a cluster, the electronic properties are determined by the frontier orbitals resulted from a linear combination of the 5 s orbitals [50, 54]. The 5 s orbitals can be regarded within the concept of "super atom" in analogy to the orbitals in hydrogen-like atoms. In gas-phase, clusters are assumed to behave like giant atoms and obey the same rules as atoms. Similarly, principles like orbital hybridization or Hund's rule can be applied. Inspired by the Jellium model, the confined electrons move within a smeared positive region that is evenly distributed over about the cluster volume [65]. In this model, the frontier orbitals with different numbers of nodes can be classified as S, P, and D and have an angular momentum quantum number L = 0, 1, and 2 for the S, P, and D orbitals, respectively) corresponding to the number of nodes of the 5 s-based orbitals. 67,72 In this light, the magic number of bare silver clusters and the selection rule in their electronic transitions (ΔL = ±1) can be resolved [7, 66].

Utilizing the super-atom orbital concept to understand properties of silver clusters inside ZSM-5 zeolite, Yumura *et al*. investigated the energetic properties of Agn clusters by using DFT and TD-TDF calculations [54]. TD- DFT optimized geometries of Agn–ZSM-5(Alm), where 3 < n < 6 and 1 < m < 5, showed an intense oscillator strength at the electronic transition between 5 s-based orbitals from the totally symmetric orbital (S-orbital) to that with one node (P-orbital). The S → P electronic transitions obeys the selection rule for cluster in gas-phase. Previously, DFT calculations of the Ag3 and Ag4 clusters inside a 10-membered ring of the ZSM-5 zeolite showed that photon absorption is due to a transitions from a completely symmetric 5 s-based orbital to a 5 s-based orbital with one node [67]. The absorptions spectra are "modulated" or strongly affected by the encapsulations as this induces cluster distortion leading to interactions between clusters and the framework oxygen atoms. The optical properties of Ag4 and Ag6 encapsulated inside the sodalite cavity of LTA zeolite were investigated using similar DFT and TD-DFT methods by Cuong *et al*. [50] Hydrated quadruply charged silver hexamer features a strong absorption band at 420 nm which is very sensitive to its charge. In the case of hydrated doubly charged silver tetramer cluster, the absorption band shifts slightly and steadily to lower energy with the increasing amount of interacting water molecules. The presence of water molecules pushes the silver tetramer away from the cavity center. Water molecules take the role as ligands and induce a splitting of the energy levels of excited states of both Ag4 2+ and Ag6 4+ clusters. As we will see bellow, this splitting causes the optical properties of the clusters to change significantly.

In a remarkable study, Grandjean *et al* investigated the structure and electronic properties at the origin of the luminescence of Ag4 clusters confined in Ag-LTAzeolite by a unique combination of XEOL-EXAFS, (TD)-DFT calculations and time-resolved spectroscopy [5]. XEOL experiments showed that the species at the origin of the bright green luminescence observed in Ag3K9-exchanged LTA zeolites are Ag4 clusters with short Ag-Ag distances of 2.82 Å in which each Ag atom is bonded in average to 2 water molecules at 2.36 Å. This results suggested the presence of two isomers Ag4(H2O)4 and Ag4(H2O)2 clusters with a 40/60 ratio in this Ag3K9-LTA sample. DFT calculations confirmed the presence of the two stable isomers. The best agreement between both the calculated structures and absorption spectra with those measured experimentally were obtained when applying a + 2 charge preferentially localized on the Ag4 cluster. The calculated frontier orbitals for both Ag4(H2O)4 2+ and Ag4(H2O)2 2+ isomers are a superposition of 50% from Ag 5 s atomic orbitals and of up to 25% from the oxygen states of the surrounding framework oxygens and water molecules. The lowest cluster configuration is formed from a doubly occupied <sup>1</sup> S0 HOMO of totally symmetric s-type and two sets of three singlet 1P and three triplet 3P LUMOs of p-type character with one node which corresponds to the assumed two electron model cluster. The coordination with water molecules lifts the degeneracy of the LUMOs orbitals. As a result LUMOs in Ag4(H2O)4 2+ and Ag4(H2O)2 2+ clusters are split into six excited states i.e. three singlet <sup>1</sup> P(S = 0, L = 1, ml = −1, +1 or 0) and three triplet 3 P(S = 1, L = 1, ml = −1, +1 or 0) states. Due to the quasi isoenergetic position of the high-energy triplet <sup>3</sup> P(S = 1, L = 1, ml = 0) state with the 1 P singlet states corroborated to a silver large *spin-orbit* coupling, an intersystem crossing takes place. Photon absorption promotes the clusters in the excited singlet state. A fraction of <sup>1</sup> P singlet states population is transferred to the high-lying triplet state that finally decays via internal conversion into the low-lying 3 P(S = 1, L = 1, ml = −1 or + 1) triplet state. Although a spin forbidden process, the bright green emission takes place as a radiative transition from the lowest triplet excited state <sup>3</sup> P(S = 1, L = 1, ml = −1) to the ground singlet state <sup>1</sup> S0.
