Spectrochemical Series and the Dependence of Racah and 10Dq Parameters on the Metal−Ligand Distance: Microscopic Origin

Abstract

The origin of the spectrochemical series and the different dependence of crystal-field splitting (10Dq) and Racah parameters on the metal-ligand distance, R, is explored through ab initio calculations on Cr(3+)-doped K2NaScF6, Cs2NaYCl6, Cs2NaYBr6, and Cs2NaYI6 lattices. For this purpose both periodic and cluster calculations have been performed. An analysis of ab initio results proves that 10Dq values mostly come from the small admixture of deep nLs ligand orbitals present in the antibonding eg(∼ x(2)-y(2),3z(2)-r(2)) level and not from the dominant covalency with valence nLp ligand orbitals, which is actually responsible for the reduction of Racah parameters. This study thus reveals the microscopic origin of the stronger dependence upon R of 10Dq when compared to that observed for Racah parameters, thus explaining why electronic transitions which are 10Dq-independent give rise to sharp optical bands. As a salient feature, while the covalency with nLp levels increases significantly on passing from CrF6(3-) to CrI6(3-), the nLs admixture in eg is found to be practically unmodified. This fact helps to understand the progressive decrease of 10Dq through the series of CrF6(3-), CrCl6(3-), CrBr6(3-), and CrI6(3-) complexes embedded in the corresponding host lattices when compared at the corresponding equilibrium distance at zero pressure. The growing importance of the nLs admixture is well-depicted using deformation density diagrams on passing from the ground state (4)A2(t2g(3)) to the (4)T2(t2g(2)eg) excited state depicted at several R values.

First-principles study of pressure-induced magnetic transition in siderite FeCO3

“…As a result of the competition among CF splitting, on-site Coulomb correlation effects and intra-atomic Hund's rule exchange coupling, the Fe 2+ (3d 6 ) ion can adopt three possible electronic configurations, i.e., LS (t 6 2g e 0 g , S = 0), intermediate spin (IS) (t 5 2g e 1 g , S = 1) and HS (t 4 2g e 2 g , S = 2) states. Though these relevant energy scales are important for the spin states of Fe 2+ ion, only the CF splitting is extraordinary sensitive to pressure [25]. It has been established that the spin state transition is primarily controlled by competition between the CF splitting and the intra-atomic exchange coupling.…”

Crystal fields of porphyrins and phthalocyanines from polarization-dependent 2p-to-3d multiplets

“…46,47 The crystal field parameters 10Dq, Ds, and Dt can be used to calculate the 3d manifold in the one-electron picture, 3,48 as shown in Figure 2. We do not include the electron occupancy of the orbitals here, because the crystal field is not the only factor determining the total energy versus occupancy.…”

Effects of Cr3+ concentration on the optical properties of Cs2NaAlF6 single crystals

“…Neutron diffraction experiments realized with the 0.5 at% sample [27] showed that the metal-ligand distances between Al-F ions are 1.8189(5)Å and 1.8304(5)Å for S1 and S2 sites, respectively. Although some authors assume that the Dq parameter depends on R À 4.5 [29][30][31], in this work we consider that the Dq value depends on R À 5 , where R is the distance impurity-ligand [17][18][19]. Nevertheless in both approaches, the site with the shortest metal impurity-ligand distance will present the strongest crystalline field.…”