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 Cr3+-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 ills ligand orbitals present in the antibonding e(g)(similar to x(2)-y(2),3z(2)-r(2)) level and not from the dominant covalency with valence n(L)p 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 n(L)p levels increases significantly on passing from CrF63- to CrI63-, the n(L)s admixture in e(g) is found to be practically unmodified This fact helps to understand the progressive decrease of 10Dq through the series of CrF63-, CrCl63-, CrBr63-, and CrI63- complexes embedded in the corresponding host lattices when compared at the corresponding equilibrium distance at zero pressure. The growing importance of the n(L)s admixture is well-depicted using deformation density diagrams on passing from the ground state (4)A(2)(t(2g)(3)) to the T-4(2)(t(2g)(2)e(g)) excited state depicted at several R values.