Quantum-chemical investigations of the interlayer interactions in vitreous g-B2O3 were carried out in terms of the cluster approach using the semiempirical MNDO and MINDO-3 methods. It is established that the formation of metastable hypervalent structures containing fourfold-coordinated boron atoms and threefold-coordinated oxygen atoms can occur in these glasses. The changes in geometric and electronic structures turn out to be closely similar for both the branched network of the BO3 triangles and the boroxol rings. Additional interlayer interactions are realized due to the breaking of the pi-component of the interlayer B-O bonds. This leads to a significant weakening of the bonds: the orders of bonds decrease approximately by a factor of one and a half, and their lengths increase by 0.15 - 0.20 Angstrom. The features of the interlayer and intralayer bonds in the active region become virtually the same, and rearrangement of the B-O bonds can be accomplished without substantial energy consumption at the points of ''joining'' the layers. The presence of the weaker bonds confirms the existence of the ''soft atomic configurations'' (SAC). Comparison between the revealed hypervalent structures and the real properties of g-B2O3 is made.