The geometric, energetic, and electronic properties of charged phosphorus-doped silicon clusters, PSi _n ⁺/PSi _n ⁻ (n = 1–8)

Abstract

Charged phosphorus-doped small silicon clusters, PSi _n ⁺/PSi _n ⁻ (n = 1−8), have been investigated using the B3LYP/6-311+G* level Kohn–Sham density functional theory (KS-DFT) method. For comparison, the geometries of neutral PSi _n clusters were also optimized at the same level, though most of them have been previously reported. According to our results, cationic PSi _n ⁺ clusters have ground state structures similar to those of pure silicon clusters Si _n+1, with the exception of n = 5. For anionic PSi _n ⁻, most of the lowest-energy structures are in accord with Wade’s 2N+2 rule for closed polyhedra: PSi₄ ⁻, PSi₅ ⁻, PSi₆ ⁻, and PSi₈ ⁻, respectively, favor the trigonal bipyramid, tetragonal bipyramid, pentagonal bipyramid, and tricapped trigonal prism (TTP) structures, corresponding to Wade’s 2N+2 rule with N = 5, 6, 7, and 9. The structures tend to contract when the cationic species is reduced initially to the neutral species and subsequently to the anionic species, implying a strengthening interaction between atoms within the clusters on one and two electron reductions of the cationic species to the neutral and anionic species, respectively. The relative order of stability of the PSi _n ⁺/PSi _n ⁻ isomers differs from that of the PSi _n isomers. Cluster stability was also analyzed by adiabatic ionization potentials (AIP), adiabatic electron affinities (AEA), binding energies (BE), second-order energy differences (∆₂E), and HOMO-LUMO gap values. The results indicate that PSi₄ ⁻ and PSi₇ ⁻ clusters are more stable than their neighboring anionic clusters and would be potential species for further mass spectrometric measurements.