The electronic spectrum of AgBr2: Ab initio benchmark vs. DFT calculations on the lowest ligand-field states including spin-orbit effects

The X²Π_g, ²Σ_g⁺ and ²Δ_g states of AgBr₂ 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 CuCl₂, overestimate the X²Π_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 X²Π_g ground state is different from that of AgCl₂ 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.