Electronic, Structural, and Vibrational Properties of α-Sn Nanocrystals Built From Diamondoid Structures: Ab Initio Study

Sn diamondoids are suggested as building blocks of α-Sn nanocrystals. Density functional theory at the generalized gradient approximation level of Perdew, Burke, and Ernzerhof is used to investigate the electronic structure of these diamondoids. Results show that energy gap and bond lengths generally decrease with shape fluctuations as the number of tin atoms increases. Bond lengths, tetrahedral angles, highest occupied molecular orbital, and lowest unoccupied molecular orbital of Sn diamondoids show that Sn diamondoid molecules are the closest molecular structures to ideal diamond structure. Electronic and structural properties are in a very good agreement with both previous experimental and theoretical results. Vibrational Sn diamondoid modes converge to the Sn experimental bulk limits. This includes radial breathing mode (RBM) and highest force constant mode that encounter red and blue shifts, respectively at their diamondoid and nanocrystal sizes with respect to the bulk. The surface hydrogen related vibrational modes in the Sn diamondoids show little variation with size and could be used to identify such structures experimentally. Other modes that vary with diamondoids size such as the RBM can be used (at least theoretically) to estimate the size of these diamondoids.