Probing the mechanism of guest–framework bonding interactions through a first-principles study on the structural and electronic properties of type-II clathrate AxSi136 (A = Na, K, Rb; 0 ≤ x ≤ 24) under pressure

Abstract

The role of noncovalent bonding, including multiatomic interactions (van der Waals-like forces) and ionic characteristics, in the intermetallic clathrate A_xSi₁₃₆ (A = Na, K, Rb; 0 < x ≤ 24) is qualitatively discussed. Using the local density approximation (LDA) to density functional theory (DFT), we investigated the effect of different guest filling and pressure parameters on the structural and electronic properties of these materials. In the context of the rigid-band model, we first noted that the competition between van der Waals-like multiatomic interactions and ionicity due to the extent of charge transfer responsible for guest–framework complexes accounts for the nonmonotonic structural response upon guest filling in A_xSi₁₃₆ (0 ≤ x ≤ 8), which is in good agreement with previous experimental findings as well as theoretical predictions. In comparison with computational work initiated under zero temperature and pressure conditions, the DFT calculations at high pressure (P = 3 GPa) show no apparent variation with respect to the electronic structure. Regarding the A₁₆Si₁₃₆ compound, the encapsulated sodium atoms residing in the 20-atom cage cavity act as centers of somewhat localized electrons compared with the alkaline metal sites inside Si₂₈ cage voids. Moreover, the substitution of heavier guest atoms (e.g., Rb) for all the Na atoms in Na₈Si₁₃₆ yields less significant charge transfer between the guest and framework constituents. The net effect of quickly increasing multiatomic interactions and slowly decreasing ionic bonding between the encapsulated atom and Si₂₈ cage may prevent the entire lattice configuration from contracting in a more rapid way when guest species are tuned from Na to Rb in A_xSi₁₃₆ (A = Na, Rb; 0 < x ≤ 8) with increased composition x. In other words, the coulombic attraction due to ionic bonding slightly outweighs the repulsive interaction between the Rb atom and Si₂₈ cage. In addition, the determined formation energy per conventional unit cell in K₈Si₁₃₆, Rb₈Si₁₃₆ and Na₁₂Si₁₃₆ attains a minimum value, demonstrating the stabilizing effect of guests incorporated into “oversized” cage cavities.