Structural Evolution of Small-Sized Phosphorus-Doped Boron Clusters: A Half-Sandwich-Structured PB15 Cluster

Abstract

The present study is a theoretical investigation into the structural evolution, electronic properties, and photoelectron spectra of phosphorus-doped boron clusters PB_n^0/- (n = 3-17). The results of this study revealed that the lowest energy structures of PB_n^- (n = 3-17) clusters, except for PB₁₇^-, exhibit planar or quasi-planar structures. The lowest energy structures of PB_n (n = 3-17), with the exceptions of PB₇, PB₉, and PB₁₅, are planar or quasi-planar. The ground state of PB₇ has an umbrella-shaped structure, with C_6V symmetry. Interestingly, the neutral cluster PB₁₅ has a half-sandwich-like structure, in which the P atom is attached to three B atoms at one end of the sandwich, exhibiting excellent relative and chemical stability due to its higher second-order energy difference and larger HOMO-LUMO energy gap of 4.31 eV. Subsequently, adaptive natural density partitioning (AdNDP) and electron localization function (ELF) analyses demonstrate the bonding characteristics of PB₇ and PB₁₅, providing support for the validity of their stability. The calculated photoelectron spectra show distinct characteristic peaks of PB_n^- (n = 3-17) clusters, thus providing theoretical evidence for the future identification of doped boron clusters. In summary, our work has significant implications for understanding the structural evolution of doped boron clusters PB_n^0/- (n = 3-17), motivating further experiments regarding doped boron clusters.

Keywords: boron clusters; geometrical structures; phosphorus-doped; spectra.

Figure 1

Structures of PB_n, where pink balls represent boron atoms and orange ball represents phosphorus atom. (a) PB₃ C_2V; (b) PB₄ C_S; (c) PB₅ C_S; (d) PB₆ C_S; (e) PB₇ C_6V; (f) PB₈ C_2V; (g) PB₉ C_S; (h) PB₁₀ C₁; (i) PB₁₁ C₁; (j) PB₁₂ C_S; (k) PB₁₃ C₁; (l) PB₁₄ C_S; (m) PB₁₅ C_S; (n) PB₁₆ C₁; (o) PB₁₇ C_S.

Figure 2

Structures of PB_n⁻, where pink balls represent boron atoms and orange ball represents phosphorus atom. (a) PB₃⁻ C_2V; (b) PB₄⁻ C_2V; (c) PB₅⁻ C_S; (d) PB₆⁻ C_S; (e) PB₇⁻ C_2V; (f) PB₈⁻ C_2V; (g) PB₉⁻ C_S; (h) PB₁₀⁻ C₁; (i) PB₁₁⁻ C_S; (j) PB₁₂⁻ C_S; (k) PB₁₃⁻ C₁; (l) PB₁₄⁻ C_S; (m) PB₁₅⁻ C₁; (n) PB₁₆⁻ C₁; (o) PB₁₇⁻ C₁.

Figure 3

Average binding energy (E_b), second-order energy differences (Δ²E), and HOMO–LUMO gaps (E_gap) of doped boron clusters PB_n^0/− (n = 3−17). Red represents the neutral cluster, blue represents the anion cluster, and n represents the number of boron atoms in the cluster.

Figure 4

AdNDP analysis of PB₇. ON is the occupation number, and the yellow ball is the P atom.

Figure 5

AdNDP analysis of PB₁₅. ON is the occupation number, and the yellow ball is the P atom.

Figure 5

AdNDP analysis of PB₁₅. ON is the occupation number, and the yellow ball is the P atom.

Figure 6

ELF at the PBE0 level. (a) C_6v PB₇; the isovalue is 0.8. (b) C_S PB₁₅; the isovalue is 0.8.

Figure 7

Photoelectron spectra at the PBE0/6-311+G * level: (a) PB₃⁻; (b) PB₄⁻; (c) PB₅⁻; (d) PB₆⁻; (e) PB₇⁻; (f) PB₈⁻; (g) PB₉⁻; (h) PB₁₀⁻; (i) PB₁₁⁻; (j) PB₁₂⁻; (k) PB₁₃⁻; (l) PB₁₄⁻; (m) PB₁₅⁻; (n) PB₁₆⁻; (o) PB₁₇⁻.