Average One-Center Two-Electron Exchange Integrals and Exchange Interactions

Abstract

We show how the introduction of the average one-center two-electron exchange integral, which is closely related to Jørgensens spin-pairing energy parameter, facilitates comparison of the Heisenberg-Dirac-van Vleck exchange parameter for different transition metal dimers. The formalism is illustrated on m-oxo-dimanganese(III) and m-oxo-dichromium(III) complexes in which the oxo bridge is the important exchange pathway.

Theoretical Insights into the Magnetostructural Correlations in Mn3-Based Single-Molecule Magnets

“… e normalσ = h pd normalσ 2 normalΔ = 4 t pd normalσ 2 normalΔ A value of the parameter I pp of the intraligand exchange (−5000 cm −1 ) has been deduced using data on atomic spectra of O . Finally, the parameter of Mn II intraatomic exchange I dd has been expressed as given in eq , with I = [ C + (5/2) B ], I dd = 5 I an average one-center two-electron exchange integral and the prefactor 5, the number of unpaired d electrons . Again, we use here spectroscopic data for the Racah parameters B and C ( B = 760 cm −1 and C = 3290 cm −1 ) to obtain the value I dd .…”

Effective Hamiltonian Crystal Field for Magnetic Interactions in Polynuclear Transition Metal Complexes. Sequential Derivation and Exemplary Numerical Estimates

“…( 45) indicates its special form as diagonal with respect to the l -system variables. This quantity is thus the relevant estimate for the effective MMCT energy as required in works [39,40,42,43,60] in the general case. One can easily check that the principal source of the renormalization of the MMCT energy is the electron-hole interaction g ij apparently omitted there.…”

“…One can easily check that the principal source of the renormalization of the MMCT energy is the electron-hole interaction g ij apparently omitted there. [39,40,42,43,60] Including the dependence of the ionisation potentials I(i) and electron affinities A(j) of the d -shells on the spins of the states produced and after assuming the smallness of the intrashell exchange K dd yields the final formulae [39,40,42,43] used for semiquantitative analysis. We do not expand either LMCT, MLCT, or MMCT energy denominators and use them for calculation in their precise form.…”