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The equilibrium geometries, stabilities and electronic properties of Be n + 1 and Be n Li (n=2–12) clusters have been systematically investigated by using the density-functional approach at B3LYP/6-31G(d) level. The resulting geometries show that Li prefers to be on the periphery of Be clusters. We also report polarizabilities for both series of Be n + 1 and Be n Li clusters. Our calculations demonstrate that Li impurity increases the polarizabilities of Be n + 1 clusters.

The equilibrium geometries and electronic properties of Na m Si n ( m + n ⩽ 7 ) clusters have been studied by using density functional theory at the B3LYP/6-311+G(d) level. The ground state structures of Na m Si n clusters can be obtained by adding one Na atom to Na m - 1 Si n clusters, and the Na atom locates on the site which maximally tends to form Na Si bonds. The Si-rich clusters are more stable than Na-rich clusters with the same number of atoms. The Si Si bond is stronger than the Na Si bond, and the latter is stronger than the Na Na bond. The vertical ionization potentials of Na m Si n clusters obtained by B3LYP are in good agreement with the experimental values available. For such a certain cluster size ( m + n = 4 , 5 , 6 , 7 ) , the energy gaps of the most stable Na m Si n clusters show odd–even oscillation with changing m, the clusters with odd Na atoms exhibit stronger chemical reactivity than those with even Na atoms.

Determinations of the lowest energy structures and electronic properties of MgBen (n=2-12) clusters were carried out by using density-functional theory. It was found that MgBe3 and MgBe9 clusters with higher binding energy and larger HOMO-LUMO gap are more stable than the neighboring clusters. The electronic properties from van der Waals to covalent and bulk metallic behavior in MgBen (n=2-12) clusters are discussed with the evolution of the size, and the data indicates Magnesium-doped Beryllium clusters already early appear some metallic-like features than host Ben clusters. By analyzing electronic properties of MgBen (n=2-12) clusters, it can be concluded that Mg-doped reduces the stabilities of Be clusters.

The geometries, stabilities, and electronic and magnetic properties of Y(n)Al (n=1-14) clusters have been systematically investigated by using density functional theory with generalized gradient approximation. The growth pattern for different sized Y(n)Al (n=1-14) clusters is Al-substituted Y(n+1) clusters and it keeps the similar frameworks of the most stable Y(n+1) clusters except for Y(9)Al cluster. The Al atom substituted the surface atom of the Y(n+1) clusters for n9. Starting from n=9, the Al atom completely falls into the center of the Y-frame. The Al atom substituted the center atom of the Y(n+1) clusters to form the Al-encapsulated Y(n) geometries for n9. The calculated results manifest that doping of the Al atom contributes to strengthen the stabilities of the yttrium framework. In addition, the relative stability of Y(12)Al is the strongest among all different sized Y(n)Al clusters, which might stem from its highly symmetric geometry. Mulliken population analysis shows that the charges always transfer from Y atoms to Al atom in all different sized clusters. Doping of the Al atom decreases the average magnetic moments of most Y(n) clusters. Especially, the magnetic moment is completely quenched after doping Al in the Y(13), which is ascribed to the disappearance of the ininerant 4d electron spin exchange effect. Finally, the frontier orbitals properties of Y(n)Al are also discussed.

The geometries, stabilities, and electronic properties of TiSin (n=2-15) clusters with different spin configurations have been systematically investigated by using density-functional theory approach at B3LYP/LanL2DZ level. According to the optimum TiSin clusters, the equilibrium site of Ti atom gradually moves from convex to surface, and to a concave site as the number of Si atom increases from 2 to 15. When n=12, the Ti atom in TiSi12 completely falls into the center of the Si outer frame, forming metal-encapsulated Si cages, which can be explained by using 16-electron rule. On the basis of the optimized geometries, various energetic properties are calculated for the most stable isomers of TiSin clusters, including the average binding energy, the highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO) gap, fragmentation energy, and the second-order difference of energy. It is found that at size n=6,8,12 the clusters are more stable than neighboring ones. According to the Mulliken charge population analysis, charges always transfer from Si atoms to Ti atom. Furthermore, the HOMO-LUMO gaps of the most stable TiSin clusters are usually smaller than those of Sin clusters.

We have investigated the stability, electronic, and magnetic properties of transition-metal-doped $M{\mathrm{B}}_{n}$ clusters ($M=\mathrm{Cr},\mathrm{Mn},\mathrm{Fe},\mathrm{Co},\mathrm{Ni}$, $n\ensuremath{\leqslant}7$) using first-principles density functional theory with generalized gradient approximation. The equilibrium structures of $M{\mathrm{B}}_{n}$ $(n\ensuremath{\leqslant}5)$ clusters can be obtained by directly adding $M$ atoms to the ${\mathrm{B}}_{n}$ clusters, while for $n=6$, hexagon or near-hexagon geometries with a boron atom at the center ring are regarded as the ground-state structures. $n=7$ marks the onset of three-dimensional geometries for $M{\mathrm{B}}_{n}$ clusters. According to the second-order energy differences, gaps between the highest occupied molecular orbital and lowest unoccupied molecular orbital and vertical ionization potentials, we can conclude that $\mathrm{Cr}{\mathrm{B}}_{4}$, $\mathrm{Cr}{\mathrm{B}}_{7}$, $\mathrm{Mn}{\mathrm{B}}_{3}$, $\mathrm{Fe}{\mathrm{B}}_{3}$, $\mathrm{Fe}{\mathrm{B}}_{5}$, $\mathrm{Fe}{\mathrm{B}}_{7}$, and $\mathrm{Co}{\mathrm{B}}_{7}$ possess relatively higher stabilities. The relative orientation between the magnetic moments of the $M$ atom and those of its neighboring B atoms mainly exhibits an antiferromagnetic alignment for $\mathrm{Cr}{\mathrm{B}}_{n}$, $\mathrm{Mn}{\mathrm{B}}_{n}$, and $\mathrm{Fe}{\mathrm{B}}_{n}$, while it mainly shows a ferromagnetic alignment for $\mathrm{Co}{\mathrm{B}}_{n}$ and $\mathrm{Ni}{\mathrm{B}}_{n}$ clusters.