Ab Initio Study of the Geometries and Vibrational Properties of the Low-Lying Electronic States of Neutral and Anionic M₃ (M = P, As, Sb, and Bi):  The Photoelectron Spectroscopy of the Anions

Abstract

The geometries and vibrational properties of the low-lying electronic states of neutral and anionic of M 3 (M ) P, As, Sb, and Bi) are studied using the coupled-cluster singles, doubles, and noniterative triples (CCSD(T)) method as well as the density functional theory (B3LYP-DFT) method. For P 3 -, the 1 Σ g + and X 3 A′ 1 (D 3h ) states are almost degenerate. The X 3 A′ 1 (D 3h ) state, however, turns out to be the lowest state for As 3 -, Sb 3 -, and Bi 3 -, and the adiabatic excitation energies of the 1 Σ g + state are 0.6, 0.9, and 1.0 eV, respectively. In the anionic trimers of all four elements, another singlet state, 1 A 1 (C 2V ), is located about 0.3-0.4 eV above X 3 A′ 1 (D 3h ); the energy gap between these states is compared to the splittings between the first two peaks in the photoelectron spectra of these anions. For all of the neutral trimers, the adiabatic and vertical energetic splittings between the Jahn-Teller components of the X 2 E′′ and 4 E′ states are calculated to be only 0.04-0.08 eV. Another quartet state, 4 A′′ 2 , is 0.4 eV higher, almost equal, 0.2 eV lower, and 0.3 eV lower in energy than the 4 E′ state in P 3 , As 3 , Sb 3 , and Bi 3 , respectively. All of the features of the main peaks in the photoelectron spectra of the anions observed to date are explained by using calculated geometries, vibrational frequencies, and excitation energies. In addition, a number of peaks are predicted that have not yet been observed experimentally.

Structure and dynamics in liquid bismuth and Bin clusters: A density functional study

“…The 2 A 2 state (α = 63.9 • , shortest bond r = 2.91 Å) is slightly (0.02 eV) more stable than the 2 B 1 state (56.4 • , r = 2.86 Å). Similar structures were found by Choi et al, 33 although coupled cluster calculations favor the 2 B 1 state slightly. The linear structure (r = 3.04 Å) and a quartet D 3h state with r = 3.04 Å lie 1.64 eV and 2.41 eV, respectively, above the 2 A 2 state.…”

“…Previous vibration frequency calculations for clusters with n > 2 appear to be limited to the trimer. 33 While the results depend on choice of basis set and effective core potential, the results compare reasonably well with ours. In the 2 A 2 state, the present calculations give 79, 105, and 160 cm −1 , compared with 108 and 163 cm −1 ; C 2v : 58, 76, 89, 104, 124, and 142 cm −1 ) support the assignment of the T d structure as the most stable isomer.…”

“…It has been used frequently to test relativistic effects in molecular and solid state calculations, including wave function based calculations of the dimer 30,31 and trimer. 32 The results of coupled-cluster and density functional calculations have been compared for Bi 3 , 33 but almost all recent theoretical work on Bi n clusters and their ions have used DF methods. The most extensive include Sb − n and Bi − n to n = 13, 34 Bi n and Bi + n to n = 24, 35 Bi n and Bi − n to n = 13, 36 Bi n to n = 14, 37 and Bi + n to n = 14.…”

Density functional study of structure and dynamics in liquid antimony and Sbn clusters

“…Previous vibration frequency calculations for Sb n clusters with n > 2 appear to be limited to the trimer. 56 While the results depend on the choice of the basis set and effective core potential, the results compare reasonably well with ours. In the 2 A 2 state, the present calculations give 114, 152, and 230 cm 1 , compared with 149 and 229 cm 1 with CCSD(T) calculations.…”

“…49 Laser induced fluorescence provides the most detailed information about Sb 2 , 50 Raman spectra of the dimer and tetramer have been measured in neon matrices, 51 and the equilibrium dissociation energies of Sb 2 , Sb 3 , and Sb 4 have been measured in the gas phase. 52 Calculations using correlated wave functions have been performed on Sb 2 , 53,54 Sb 3 , 55,56 and Sb 4 , 57 but DF methods have been favored for larger clusters. They include Sb − n (n = 2-9), 49 Sb n (n = 2-8, 12), 58 and Sb n (n = 2-10).…”