The electronic spectrum of AgBr 2: Ab initio benchmark vs. DFT calculations on the lowest ligand-field states including spin–orbit effects

Abstract

The X 2Π g, 2Σ g + and 2Δ g states of AgBr 2 have been studied through benchmark ab initio CASSCF + Averaged Coupled Pair Functional (ACPF) and DFT calculations using especially developed valence basis sets to study the transition energies, geometries, vibrational frequencies, Mulliken charges and spin densities. The spin–orbit (SO) effects were included through the effective hamiltonian formalism using the |ΛSΣ〉 ACPF energies as diagonal elements. At the ACPF level, the ground state is 2Π g, in contradiction with ligand-field theory and Hartree–Fock results. The ACPF adiabatic excitation energies of the 2Σ g + and 2Δ g states are 3825 and 20 152 cm −1, respectively. The inclusion of the SO effects leads to a pure Ω = 3/2 ( 2Π g) ground state, a Ω = 1/2 (97% 2Π g + 3% 2Σ g +) A state, a Ω = 1/2 (3% 2Π g + 97% 2Σ g +) B state, a Ω = 5/2 ( 2Δ g) C state and a Ω = 3/2 (99% 2Δ g) D state. The B97, B3LYP and PBE0 functionals, which were shown to yield accurate transition energies for CuCl 2, overestimate the X 2Π g– 2Σ g + T e by around 25% but provide a qualitative energetic ordering in agreement with CASSCF and ACPF results. The nature of the bonding in the X 2Π g ground state is different from that of AgCl 2 since the Mulliken charge on the metal is 0.95 while the spin density is only 0.39. DFT strongly delocalizes the spin density providing even smaller values of around 0.13 on Ag not only for the ground state, but also for the 2Σ g + state.