  Electronic structure of strongly correlated transition metal oxides (TMOs) is
a complex phenomenon due to competing interaction among the charge, spin,
orbital and lattice degrees of freedom. Often individual compounds are examined
to explain certain properties associated with these compounds or in rare cases
few members of a family are investigated to define a particular trend exhibited
by that family. Here, with the objective of generalization, we have
investigated the electronic structure of three families of compounds, namely,
highly symmetric cubic mono-oxides, symmetry-lowered spinels and asymmetric
olivine phosphates, through density functional calculations. From the results
we have developed empirical hypotheses involving electron hopping,
electron-lattice coupling, Hund's rule coupling, strong correlation and d-band
filling. These hypotheses, classified through the point group symmetry of the
transition metal - oxygen complexes, can be useful to understand and predict
the electronic and magnetic structure of 3d TMOs.
