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Using the multi-band $d-p$ model and unrestricted Hartree-Fock approximationwe investigate the electronic structure and spin-orbital order inthree-dimensional VO$_3$ lattice. The main aim of this investigation is testingif simple $d-p$ model, with partly filled $3d$ orbitals (at vanadium ions) and$2p$ orbitals (at oxygen ions), is capable of reproducing correctly nontrivialcoexisting spin-orbital order observed in the vanadium perovskites. We pointout that the multi-band $d-p$ model has to include partly filled $e_g$ orbitalsat vanadium ions. The results suggest weak self-doping as an importantcorrection beyond the ionic model and reproduce the possible ground states withbroken spin-orbital symmetry on vanadium ions: either $C$-type alternatingorbital order accompanied by $G$-type antiferromagnetic spin order, or $G$-typealternating orbital order accompanied by $C$-type antiferromagnetic spin order.Both states are experimentally observed and compete with each other in YVO$_3$while only the latter was observed in LaVO$_3$. Orbital order is induced andstabilized by particular patterns of oxygen distortions arising from theJahn-Teller effect. In contrast to time-consuming \textit{ab-initio}calculations, the computations using $d-p$ model are very quick and should beregarded as very useful in solid state physics, provided the parameters areselected carefully.

$d-p$ model and spin-orbital order in the vanadium perovskites