Estimates of electronic interaction parameters for La$M$O$_3$ compounds ($M$=Ti-Ni) from ab-initio approaches

We have analyzed the ab-initio local density approximation band structure calculations for the family of perovskite oxides, La$M$O$_3$ with $M$=Ti-Ni within a parametrized nearest neighbor tight-binding model and extracted various interaction strengths. We study the systematics in these interaction parameters across the transition metal series and discuss the relevance of these in a many-body description of these oxides. The results obtained here compare well with estimates of these parameters obtained via analysis of electron spectroscopic results in conjunction with the Anderson impurity model. The dependence of the hopping interaction strength, t, is found to be approximately $r^{-3}$.