  "Realistic modeling" is a new direction of electronic structure calculations,
where the main emphasis is made on the construction of some effective
low-energy model entirely within a first-principle framework. Ideally, it is a
model in form, but with all the parameters derived rigorously, on the basis of
first-principles electronic structure calculations. The method is especially
suit for transition-metal oxides and other strongly correlated systems, whose
electronic and magnetic properties are predetermined by the behavior of some
limited number of states located near the Fermi level. After reviewing general
ideas of realistic modeling, we will illustrate abilities of this approach on
the wide series of vanadates RVO3 (R= La, Ce, Pr, Nd, Sm, Gd, Tb, Yb, and Y)
with distorted perovskite structure. Particular attention will be paid to
computational tools, which can be used for microscopic analysis of different
spin and orbital states in the partially filled t2g-band. We will explicitly
show how the lifting of the orbital degeneracy by the monoclinic distortion
stabilizes C-type antiferromagnetic (AFM) state, which can be further
transformed to the G-type AFM state by changing the crystal distortion from
monoclinic to orthorhombic one. Two microscopic mechanisms of such a
stabilization, associated with the one-electron crystal field and electron
correlation interactions, are discussed. The flexibility of the orbital degrees
of freedom is analyzed in terms of the magnetic-state dependence of interatomic
magnetic interactions.
