Molecular-Orbital Theory of the Excited-State Exchange Interaction

Abstract

An approximate molecular-orbital exchange theory is derived in which the various contributions to the exchange interaction are expressed explicitly as functions of the covalency amplitudes, overlaps, single-ion Coulomb and exchange integrals and charge-transfer excitation energies. The relative sizes of contributions of the same type to the different pairwise interactions between electrons occupying specific orbitals on neighboring sites can be evaluated fairly reliably from such a theory. Fixing over-all scale factors for the kinetic and potential exchange to produce agreement with ground-state exchange constants then has the effect of incorporating higher-order relaxation and correlation effects into the theory and making it relatively insensitive to some of the approximations which enter into its derivation. Application of the theory to the ground-state exchange constants of Mn${\mathrm{F}}_{2}$, KMn${\mathrm{F}}_{3}$, Ni${\mathrm{F}}_{2}$, and KNi${\mathrm{F}}_{3}$ not only determines the required scale factors, which prove to agree adequately with simple a priori estimates, but also produces interesting information on the relative sizes of different components of the covalent bonding: ${p}_{\ensuremath{\sigma}}$, ${p}_{\ensuremath{\pi}}$, and ${s}_{\ensuremath{\sigma}}$. Properties derived from the exchange interactions of the excited $^{4}E(I)$ multiplet in Mn${\mathrm{F}}_{2}$ are then deduced from the theory and compared to the experimental results. The agreement is fair to excellent for all quantities studied: two dispersion constants and two exciton-magnon coupling constants.