Electronic structure of rare-earth orthovanadates and its relation to photoelectron and optical spectra

The electronic structure of some rare-earth orthovanadates, RVO₄, where $R=La,{{0ex}{0ex}}Ce,{{0ex}{0ex}}Nd,{{0ex}{0ex}}Eu,{{0ex}{0ex}}Tb,{{0ex}{0ex}}Dy,{{0ex}{0ex}}or{{0ex}{0ex}}Yb$, has been studied using the discrete variational $X{α}$ method. Charge and spin densities and the derived potentials for clusters embedded in the crystal lattice were iterated to self-consistency with the use of the self-consistent charge procedure. The results are compared with experimental x-ray photoelectron spectra (XPS) and atomic calculations. Eigenvalues (or transition-state energies) are compared with XPS binding energies and the calculated exchange splittings of lanthanide $4s$, $5s$, and $4f$ levels are compared with experiment. For $4f$'s, the exchange splitting between the least-bound spin-up and spin-down states is measured. An analysis of optical and luminescent properties is made based on the cluster calculations. The results show that the lanthanide $4f$ orbitals play an active role in bonding, and that luminescence can be related to a resonant energy transfer from excited vanadate orbitals to the lanthanide $4f$ states.