Utilizing super-atom orbital ideas to understand properties of silver clusters inside ZSM-5 zeolite

Abstract

The energetic properties of Ag_n clusters in ZSM-5 zeolite were investigated using density functional theory (DFT) calculations with the B3PW91 functional. Several optimized geometries (Ag_n–ZSM-5(Al_m), 3 ≤ n ≤ 6 and 1 ≤ m ≤ 5) were obtained using this method, where m is the number of Al atoms substituted for Si atoms of a ten-membered ring of ZSM-5. DFT calculations found that an Ag_n cluster is well stabilized within a ZSM-5(Al_m) cavity at n = m + 2. The stabilization conditions can be explained by frontier orbital theory because the HOMO of Ag_m+2–ZSM-5(Al_m) zeolites is composed by totally symmetric 5s-based orbitals on silver atoms. The totally symmetric 5s-based orbital corresponds to a superatom S-orbital in cluster chemistry. Accordingly, the Ag_m+2–ZSM-5(Al_m) zeolites have an S² electronic configuration, being similar to magic-number silver clusters in the gas phase. Time-dependent DFT calculations found significant oscillator strength at the electronic transition between 5s-based orbitals from the totally symmetric orbital (S-orbital) to that with one node (P-orbital). The S → P electronic transitions in Ag_m+2–ZSM-5(Al_m) follow the selection rule of electronic transitions of bare clusters. Because the excitation energies (λ_max) change with an increase in the number of contained silver atoms, the S → P electronic transitions of Ag_m+2–ZSM-5(Al_m) could be used to identify the state of the inner silver atoms.