Structural, energetic and magnetic properties of small Tin (n = 2–13) clusters: a density functional study

The stabilization mechanism of titanium cluster

“…The computed spin multiplicities of the lowest energy structures for Ti n (n ¼3, 4, 5 and 7) agree with Castro et al [3] and Du et al [4]. For Ti 13 , the present result is consistent with Medina et al [6] and Wang et al [7]. However, almost no one explore the spin multiplicities of Ti 15 so far.…”

“…For Ti n opt (n ¼3, 4, 5, 7, 13, 15 and 19), each can be described as a distorted version of a higher symmetric structure, i.e., equilateral triangle (D 3h ), tetrahedron (T d ), triangular bipyramid (D 3h ), pentagonal bipyramid (D 5h ), icosahedron (I h ), sixfold icositetrahedron (D 6d ), two interpenetrating icosahedra (D 5h ) (Fig. 1), which agrees well with the previous results [2,3,6,7]. Based upon the standard structures, we have conducted comparative studies.…”

“…The occurrence of magnetism brings additional difficulties to obtain the ground states, for which we must consider the dense spin multiplicities to avoid trapping into local minima in the entire spin space. The understanding of geometric, electronic and magnetic properties of titanium clusters poses tremendous challenges both experimentally and computationally [1][2][3][4][5][6][7].…”

“…They came to a conclusion that distortion and spin polarization can reduce the total energy of Ti 13 cluster through lifting the degeneracy and the spin redistribution of the highly populated highest occupied molecular orbital (HOMO) region. Using DFT/the Becke, Lee, Yang, Parr (BLYP) or the Perdew, Burke, Ernzerhof (PBE) exchange correlation functional/double zeta valence plus polarization (DZVP) basis sets schemes, Medina et al [6] studied the effects of structural distortion on the total energy and magnetism of Ti 13 clusters and found that the structural distortion has no effect on the total magnetic moment. Despite the studies mentioned above further research about titanium clusters is needed in order to understand the underlying physical mechanisms of these phenomena.…”

The generation of ground‐state structures and electronic properties of ternary AlkTilNim clusters (k + l + m = 4) from a two‐stage density functional theory global searching approach

“…[54] Strong magnetic behavior is observed in dimers and some of the small aluminum clusters such as Al 3 , Al 6 , Al 7 , and Al 8 . [52] Since the turn of the millennium, experimental and computational methods [55][56][57][58][59] are widely used to study the geometric, electronic, and magnetic properties of the titanium clusters. As a typical transition element, titanium atom has a large number of vacant valence d orbitals, giving rise to a highly delocalized characteristic.…”