Jahn–Teller, pseudo Jahn–Teller, and Renner–Teller effects in systems with fractional charges

It is shown that modeling a part of a molecular system by means of fractional charges is very useful in many situations when its interaction with the rest of the systems is relatively weak as, for instance, in some coordination systems, mixed-valence compounds, molecular adsorption on surfaces, early stages of interactions in chemical reactions, etc. The structural changes in such subsystems can be described by means of orbital charge transfers (OCT) that change the intramolecular vibronic coupling leading to instabilities and distortions of the Jahn–Teller effect (JTE), pseudo JTE (PJTE), and Renner–Teller effect (RTE). A molecular orbital theory of these effects in systems with fractional charges involving orbital vibronic coupling constants and orbital force constants is worked out in the approximation of small OCT. The efficiency of the theory is demonstrated by means of ab initio calculations revealing the vibronic coupling constants and distortions of coordinated molecules in coordination systems and showing how the JTE, PJTE, and RTE allow one to predict and rationalize experimental data. The PJTE instability in coordinated systems with fractional charges is analyzed by considering three coordination compounds, [M(N2H2)(dmpe)2] with M = Fe, Ru (dmpe = Me2PCH2CH2PMe2), and [(N2H2)Ru2DPB(Im)2] (DPB = diporphyrinato-biphenylene tetraanion, Im = imidazole), in which the η2-coordinated N2H2 molecule distorts from a trans-planar to a nonplanar (C2) shape due to OCT to and from its frontier orbitals. As an example of the induced JTE in coordinated molecules the [(triphos)RhH(η1: η2-P4)] complex is considered, and it is shown that the white phosphorus (P4) distortion from tetrahedron to butterfly geometry by coordination is due to the OCT to its excited degenerate t1 orbital. 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-η2-C2H2 and Pd-η2-C2H2 systems.