Numerous experimental and theoretical data indicate that small molecules coordinated to the metal centers or adsorbed on the surfaces undergo, as a rule, structural changes leading to distortion of their high-symmetry nuclear configurations. Earlier [1] we have proposed a new approach to handle instabilities and structural changes in molecular systems due to their interaction with another molecular systems or with a solid based on an approximate evaluation of the Jahn-Teller effect (JTE), pseudo JTE (PJTE), and Renner-Teller effect (RTE) in systems with fractional charges that occur due to orbital charge transfers (OCT). In the present work the predictive power of the theory and its efficiency in rationalization of the experimental data is demonstrated by means of ab initio calculations revealing the vibronic coupling constants and distortions of coordinated molecules in a series of coordination systems. It is shown that in all the cases distortions of coordinated and adsorbed molecules are due to the JTE, PJTE or RTE induced by the OCTs to and from molecular orbitals of coordinated ligands. As an example of the JTE in the coordinated molecules the white phosphorus (P4) coordination in [(triphos)RhH(η1 :η2 -P4)] complex is considered. It is shown that the butterfly geometry of the coordinated P4 molecule is due to the JTE induced by the OCT q=0.68e to its triple degenerate excited state. The PJTE instability in coordinated systems is analyzed by the example of the N2H2 molecule coordinated in the [M(N2H2)(dmpe)2] (M=Fe, Ru) (dmpe=Me2PCH2CH2PMe2) complexes, in which the η2 -coordinated N2H2 molecule distorts from a trans-planar to a nonplanar (C2) shape due to OCTs to and from its frontier orbitals. Calculations show that the curvature of the APES of the N2H2 molecule (in the au direction) becomes negative in both complexes, that explains the origin of the geometry of coordination of this molecule. The RTE effect in coordinated systems is demonstrated by the distortion of the acetylene molecule from its linear configuration to the non-linear cis-form by its coordination in Y-η 2 - C2H2 and Pd-η 2 -C2H2 systems. The same approach is employed to explain the origin of the bending distortion of FCN and FNC molecules adsorbed on Si (100)-(2×1) surface. It is shown that this bending can be explained as due to the Renner-Teller effect induced by the orbital charge transfers by adsorption.