Interplay of electronic and geometry shell effects in properties of neutral and charged Sr clusters

The optimized structure and electronic properties of neutral, singly, and doubly charged strontium clusters have been investigated using ab initio theoretical methods based on density-functional theory. We have systematically calculated the optimized geometries of neutral, singly, and doubly charged strontium clusters consisting of up to 14 atoms, average bonding distances, electronic shell closures, binding energies per atom, the gap between the highest occupied and the lowest unoccupied molecular orbitals, and spectra of the density of electronic states (DOS). It is demonstrated that the size evolution of structural and electronic properties of strontium clusters is governed by an interplay of the electronic and geometry shell closures. Influence of the electronic shell effects on structural rearrangements can lead to violation of the icosahedral growth motif of strontium clusters. It is shown that the excessive charge essentially affects the optimized geometry of strontium clusters. Ionization of small strontium clusters results in the alteration of the magic numbers. The strong dependence of the DOS spectra on details of ionic structure allows one to perform a reliable geometry identification of strontium clusters.

Figure 1

(Color online) Optimized geometries of neutral strontium clusters ${\mathrm{Sr}}_2\text{–}{\mathrm{Sr}}_{14}$ calculated in the $\mathrm{B}3\mathrm{PW}91∕\mathrm{SDD}(6D,10F)$ approximation. The interatomic distances are given in angstroms. The label above each cluster image indicates the point symmetry group of the cluster.

Figure 2

(Color online) Same as in Fig. 1, but for singly charged strontium clusters ${\mathrm{Sr}}_2^{+}\text{–}{\mathrm{Sr}}_{14}^{+}$.

Figure 3

(Color online) Same as in Fig. 1, but for doubly charged strontium clusters ${\mathrm{Sr}}_2^{2+}\text{–}{\mathrm{Sr}}_{14}^{2+}$.

Figure 4

(Color online) Average bonding distance as a function of cluster size for neutral, singly, and doubly charged strontium clusters. Open squares present the results of the work by Wang et al. [44].

Figure 5

(Color online) Binding energy per atom for the most stable neutral (filled squares), singly charged (filled circles), and doubly charged (filled triangles) strontium clusters as a function of cluster size. Crosses present the results of the work by Wang et al. [44].

Figure 6

(Color online) Second differences of total energy for neutral (filled squares), ${\Delta }^2{E}_N=E_{N+1}-2E_N+E_{N-1}$, and singly charged (filled circles), ${\Delta }^2{E}_N^{+}=E_{N+1}^{+}-2E_N^{+}+E_{N-1}^{+}$, strontium clusters.

Figure 7

(Color online) Gap between the highest occupied and the lowest unoccupied eigenstates (HOMO-LUMO gap) for neutral, singly, and doubly charged strontium clusters as a function of cluster size. Open squares represent the HOMO-LUMO gap calculated for Mg clusters [26].

Figure 8

Density of states for neutral strontium clusters. Gaussian broadening of half-width $0.15\mathrm{eV}$ has been used. The zero level of energy is chosen equal to the Fermi level $E_f$ (vertical line).

Figure 9

Same as in Fig. 8, but for singly charged strontium clusters.

Figure 10

Same as in Fig. 8, but for doubly charged strontium clusters.

Figure 11

Density of states for three different isomers of ${\mathrm{Sr}}_{13}$. From left to right: Isomers of $I_h$, $C_s$, and $C_{2v}$ point symmetry groups, respectively. Gaussian broadening of half-width $0.15\mathrm{eV}$ has been used. The zero level of energy is chosen equal to the Fermi level $E_f$ (vertical line).