Gallium clusters Gan (n=1-6):: Structures, thermochemistry, and electron affinities

Eight different density functional theory (DFT) and hydrid Hartree-Fock/DFT methods have been employed for studying the structures, electron affinities, and dissociation energies of the Ga-n/Ga-n(-) (n = 1-6) species. The basis set used in this work is of double- plus polarization quality with additional s- and p-type diffuse functions, denoted DZP++. The geometries were fully optimized with each DFT method independently. Located were 22 different structures for the neutral clusters and 15 structures for the anionic clusters, and the results are in broad agreement with the limited experimental results. High-spin electronic states appear to be preferred in the Ga-n, clusters when n < 4. Triangular and planar rectangular structures are the global minima for Ga-3 and Ga-4, respectively, while the global minima for Ga-5 and Ga-6 are low-spin nonplanar structures. The three types of neutral anion energy separations reported in this work are the adiabatic electron affinity (EA(ad)), the vertical electron affinity (EA,,,), and the vertical detachment energy (VDE). As in previous studies, the HF/DFT hybrid methods predict shorter and more reliable bond lengths than the pure DFT methods, and the BHLYP method appears to be the best for predicting geometries. The BP86 method-predicted VDE values for the anionic gallium clusters are in reasonable agreement with the experimental values. The BP86-predicted EA(ad) values, which are also considered to be reliable, are 1.51 (Ga-2), 1-81 (Ga-3),2.14 (Ga-4), 2.27 (Ga-5) and 2.31 eV (Ga-6). The first dissociation energies for the neutral gallium clusters predicted by the B3LYP method are 1.30 (Ga-2), 1.58 (Ga-3) 1.98 (Ga-4), 1.80 (Ga-5), and 2.29 eV (Ga-6)- Only the dissociation energy for Ga-2 (1.10 eV) is known from the experiment. The anion dissociation energies are predicted for both the Gan-1 + Ga- and the Ga-n-1(-) + Ga dissociation limits. The harmonic vibrational frequencies are also reported. Since most of the structures, bond dissociation energies, and vibrational frequencies for the neutral and anionic gallium clusters are experimentally unknown, it is hoped that this work will stimulate further explorations in the laboratory.