Density-functional study of small neutral and cationic bismuth clusters Bin and Bin+(n=2–24)

Abstract

Density-functional theory with scalar-relativistic pseudopotential and a generalized gradient correction is used to calculate the neutral and cationic Bi(n) clusters (2< or =n< or =24), with the aim to elucidate their structural evolution, relative stability, and magnetic property. The structures of neutral Bi clusters are found to be similar to that of other group-V elemental clusters, with the extensively studied sizes of n=4 and 8 having a tetrahedron and wedgelike structure, respectively. Generally, larger Bi clusters consist of a combination of several stable units of Bi(4), Bi(6), and Bi(8), and they have a tendency to form an amorphous structure with the increase of cluster sizes. The curves of second order energy difference exhibit strong odd-even alternations for both neutral and cationic Bi clusters, indicating that even-atom (odd-atom) sizes are relatively stable in neutral clusters (cationic clusters). The calculated magnetic moments are 1micro (B) for odd-atom clusters and zero for even-atom clusters. We propose that the difference in magnetism between experiment and theory can be greatly improved by considering the orbital contribution. The calculated fragmentation behavior agrees well with the experiment, and for each cationic cluster the dissociation into Bi(4) or Bi(7) (+) subclusters confirms the special stability of Bi(4) and Bi(7) (+). Moreover, the bond orders and the gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital show that small Bi clusters would prefer semiconductor characters to metallicity.

Structure and dynamics in liquid bismuth and Bin clusters: A density functional study

“…Isomers identified in studies by other groups have been tested where appropriate. [35][36][37] In addition to using simulated annealing and other standard methods for locating energy minima, we generated large numbers of random coordinates for each cluster size and optimized the resulting structures with DF methods. This procedure was carried out up to n = 20, but the rapid increase in the number of local energy minima with increasing n means that we have restricted the present analysis to n ≤ 14.…”

“…32 The results of coupled-cluster and density functional calculations have been compared for Bi 3 , 33 but almost all recent theoretical work on Bi n clusters and their ions have used DF methods. The most extensive include Sb − n and Bi − n to n = 13, 34 Bi n and Bi + n to n = 24, 35 Bi n and Bi − n to n = 13, 36 Bi n to n = 14, 37 and Bi + n to n = 14. 38 The DF/MD calculations for neutral Bi clusters and liquid Bi described here are the most extensive parameter-free calculations yet performed on either system, and we focus on the structures and dynamical properties.…”

Structures of small bismuth cluster cations

“…The global minimum structure (GM) of Bi 5 + (5-I) corresponds to a square pyramidal geometry (see Fig. 1) as has been predicted by Yuan et al 17 There is no doubt about the structure of the pentamer since the next higher-lying isomer, a trigonal bipyramid (5-II), is more than 0.5 eV above the GM. The ring (5-III), the favored anionic structure, is 1.6 eV above the GM as the cation.…”

“…They find that clusters in this size range "prefer semiconducting character" and that particularly the largest species studied have a tendency to form "amorphous structures". 17 So far, the structure of isolated bismuth clusters has not been directly probed by experiment. The aim of the present article is therefore to establish equilibrium structures for positively charged bismuth clusters of up to 14 atoms via a combination of ion mobility spectrometry and trapped ion electron diffraction measurements.…”

“…[11][12][13][14] More recently, larger neutral and charged bismuth clusters have been the focus of several theoretical studies. [15][16][17] Yuan et al have calculated structures, fragmentation behavior, and magnetic moments for bismuth clusters up to 24 atoms using density-functional theory. They find that clusters in this size range "prefer semiconducting character" and that particularly the largest species studied have a tendency to form "amorphous structures".…”