Stable Ti_n (n = 2−15) Clusters and Their Geometries:  DFT Calculations

Abstract

We present a detailed structural analysis for small Tin (n = 2-15) clusters based on ab initio quantum mechanical calculations of their binding energies, frontier orbital gaps, and second energy derivatives. Local density approximation calculations revealed that while the smaller clusters (n < or = 8) prefer hexagonal atomic arrays with bulklike crystal symmetry, the bigger clusters prefer pentagonal atomic arrays. From the stability criteria of the magic number clusters we could identify three magic number clusters Ti7, Ti13, and Ti15. While the most stable configuration of Ti7 is a decahedral bipyramid induced by tetrahedral atomic arrays, the most stable configuration of Ti13 is an icosahedron. The other stable cluster Ti15 takes a closed-shell icosahedron-like configuration with both pentagonal and hexagonal symmetries. The stability of the Tin clusters strongly depends on their geometries and charge states. The HOMO-LUMO gap of the Tin clusters approaches its bulk value for n > 8. While there is not much difference between the HOMO and LUMO isosurface charge distributions for the Ti7 and Ti13 clusters in their most stable configurations, they are very different in the case of Ti15. Such a distinct charge distribution in Ti15 indicates its singular chemical selectivity over the other two magic number clusters.

An all-electron density functional theory study of the structure and properties of the neutral and singly charged M12 and M13 clusters: M = Sc–Zn

“…The geometrical structure of the lowest total state of neutral Ti 13 is found to be a slightly distorted icosahedron (ICO) in agreement with the previous assignments. [34][35][36][37][38][39][40][41][42][43] Our value of 6 μ B for the total spin magnetic moment of Ti 13 is also in agreement with the result of a recent study. 44 The effective electron configuration of the central Ti atom in Ti 13 is 4s 0.40 3d 4.41 4p 1.38 4d 0.19 , which means that the central atom carries a negative charge of −2.4e.…”

Geometric and electronic structures of hydrogenated transition metal (Sc, Ti, Zr) clusters

“…21,22 Electronic structures of isolated and hydrogen-loaded titanium clusters have been the topic of a number of recent investigations. [46][47][48][49][50][51] To the best of our knowledge, effects of hydrogen adsorption and saturation have not been investigated for zirconium or scandium clusters. However, electronic structures of isolated zirconium and scandium clusters have been the focus of some recent theoretical studies.…”

Theoretical study on the interaction of neutral and charged Tin (n = 1–7) clusters with one oxygen molecule

“…The only exception is Ti 7 O 2 , whose E gap is instead higher by 0.1 eV than the bare Ti 7 . The reason can be seen from reference 23, in which the authors conclude that the Ti n ( n = 7, 13, 15, 19, and 23) clusters are magic ones, which have much larger E gap values than their neighboring clusters.…”

“…In these studies, O 2 is dissociative on Ba n clusters and Pd n clusters but still keeps a molecular state on Cu n and Ag n clusters. Ti n clusters have been extensively investigated both experimentally 18, 19 and theoretically 20–25. However, there are few studies on the interaction of O 2 molecule with Ti n clusters being reported yet based on our best knowledge.…”