A new set of criteria for quantitative analysis of molecular interactions is proposed resulted from the investigation of crystal structures of 808 picomplexes of rare-earth atoms (Ln).The set is based on the conceptions of atomic and molecular Voronoi-Dirichlet polyhedra and comprises: I.The criteria of existence of agostic and van der Waals contacts Ln...H-L between the complexing atom Ln and a ligand L. II.A set of criteria for ligands, namely: ligand total, valent and agostic solid angles, which are to be calculated with the faces of Voronoi-Dirichlet polyhedron of the Ln atom corresponding to all, only valent or only agostic Ln-L contacts, respectively; and ligand residual solid angle which is the difference between total and valent solid angles.III.A set of criteria for complexes as a whole including similar terms as the previous set, but relating to entire complex particle, to be calculated by summation of corresponding ligand solid angles for all ligands in a given complex.It is shown that the criteria of the first set allow one to improve the conclusions about existence or missing of agostic contacts.Seven different numerical combinations of the second and third sets of criteria were singled out, with which one can predict the composition and sterical stability of complex groups, the existence of intra-and intermolecular agostic and van der Waals interactions, and can judge about the capability of a ligand L to screen the central atom and to form the agostic contacts Ln...H-L.