Vibronic superexchange

The aim of this work is to elucidate these problems. To this end, we calculate the effective spin Hamiltonian of the 5f2—5f2 superexchange interaction between the neighboring U4+ ions in the cubic crystal lattice of UO2 and we calculate T5 <%> eg, rs f2g(l) ancl r5 f2g(2) linear vibronic coupling constants. These data are then used to draw a more definite conclusion about the driving force of the phase transition and especially about the actual mechanism of the spin and orbital ordering in U02. 

It should be mentioned that while in the Hamiltonian of the superexchange interaction at orbital degeneracy there are no vibrational operators, the vibronic interaction as a rule plays a decisive role in the ordering of the orbitals in the JT crystals. 

It is usually assumed that the electronic coupling matrix element is a constant across the reaction coordinate. Since the electronic wavefunction is a function of both the electronic and nuclear coordinates, even in the Born-Oppenheimer approximation, it is not surprising that in some systems the assumption that the nuclear and electronic coordinates are independent (the Condon approximation) is not appropriate. The most obvious example of the failure of this approximation is for a system in which the matrix element is dominated by superexchange contributions, since the vertical energies, Adb and Eba. vary with the nuclear coordinates. There are other, probably less obvious kinds of such vibronic coupling ... 

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