Vibronic interaction in multielectronic mixed-valence trimeric clusters

The problem of vibronic interaction in multielectronic trimeric clusters of transition metal ions is considered. The dynamic vibronic problems are solved numerically for the d1-d1-d0 and d1-d1-d2 trimers taking into account both the electron transfer (double exchange) and the isotropic (Heisenberg type) exchange interaction. For both types of system (i.e. d1-d1-d0 and d1-d1-d2) the joint action of the electron transfer and vibronic interaction is shown to lead to the (A1 + E) ⊗ e and (A2 + E) ⊗ e pseudo Jahn-Teller problems. For the d1-d1-d2 clusters the more complicated (A1 + A2 + E + E) ⊗ e dynamic problem also appears. The magnetic properties of the above mentioned systems are discussed in detail. Some comments concerning spin models of double exchange are given in connection with the problem of vibronic interaction in mixed-valence clusters. As distinguished from the microscopic quantum-mechanical approach the conventional spin-model is shown to meet difficulties in the solving of the vibronic problem of mixed-valence trimers (and systems of higher nuclearity as well). All the vibronic matrices in the symmetry-adopted bases are given in the Appendix for the d1-d1-d2-, d2-d2-d3-, d3-d3-d2- and d3-d3-d4-mixed-valence trimers. These matrices are necessary for the calculations of the vibronic spectra of systems of such type.