A model of interaction of the hydrogenated vacancy with silicon interstitial and different dopants (B, P and As) in crystalline silicon is considered. Quantum chemical calculations show that hydrogenation of the vacancy leads to a decrease of mechanical stresses of the silicon crystalline lattice near vacancy and consequently to a considerable decrease of the energy barrier height for the interstitial atom incorporation into the vacancy site of the crystalline lattice. The potential barriers for incorporation of the interstitial into the site and for leaving the atoms from the site has been calculated as a function of hydrogen localization in the vicinity of the vacancy (inside and outside of the vacancy), the charge state of hydrogen localized outside the vacancy (H-0 and H+), and the transport direction ([111], [110] and [100]) of the atoms both in and out of the vacancy. The theory is compared with the experimental results.