Key Role of Deep Orbitals in the d-d₃ Gap in Tetragonal Complexes and 10Dq

Using first-principles calculations, we show that the origin of the intrinsic a_1g(∼3z² - r²)-b_1g(∼x² - y²) splitting, Δ_int, in tetragonal transition-metal complexes and the variations of the cubic field splitting, 10Dq, with the metal-ligand distance, R, are much more subtle than commonly thought. As a main novelty, the key role played by covalent bonding with deep valence ligand levels and thus the inadequacy of too simple models often used for the present goal is stressed. Taking as a guide the isolated D₄ CuF₆^4- complex, it is proved that Δ_int essentially arises from bonding with deep 2s(F) orbitals despite them lying ∼23 eV below 2p(F) orbitals. This conclusion, although surprising, is also supported by results on octahedral fluoride complexes where the contribution to 10Dq splitting from bonding with 2s(F) orbitals is behind its strong R dependence, stressing that explanations based on the crystal-field approach are simply meaningless.