Quantum chemical modeling of the structure and properties of SnO2 nanoclusters

Abstract

By the method of density functional theory with exchange-correlation functional B3LYP and basis set 3‑21G (d), the structural and energy characteristics have been considered of the molecular models of SnO2 nanoclusters of different size and composition with the number of Sn atoms from 1 to 10. Incompletely coordinated surface tin atoms were terminated by hydroxyl groups. It has been shown that the Sn–O bond length in nanoclusters does not depend on the cluster size and on the coordination number of Sn atoms, but is determined by the coordination type of neighboring oxygen atoms. Namely, the bond length Sn–O(3) (@ 2.10 Å) is greater than that of Sn–O (2) (@ 1.98 Å). The calculated values of Sn–O (3) bond lengths agree well with the experimental ones for crystalline SnO 2 samples (2.05 Å). The theoretically calculated width of the energy gap decreases naturally with increasing cluster size (from 6.14 to 3.46 eV) and approaches the experimental value of the band gap of the SnO 2 crystal (3.6 eV). The principle of additivity was used to analyze the energy characteristics of the considered models and to estimate the corresponding values for a cassiterite crystal. According to this principle, a molecular model can be represented as a set of atoms or atomic groups of several types that differ in the coordination environment and, therefore, make different contributions to the total energy of the system. The calculated value of the atomization energy for SnO2 is 1661 kJ/mol and corresponds satisfactorily to the experimentally measured specific atomization energy of crystalline SnO2 (1381 kJ/mol). It has been shown that a satisfactory reproduction of the experimental characteristics of crystalline tin dioxide is possible when using clusters containing at least 10 state atoms, for example, (SnO2)10×14H2O.