Abstract
For the complex in KNi we have constructed molecular orbitals (MO) which are linear combinations of the and Hartree-Fock atomic orbitals. These LCAO-MO, introduced by Van Vleck, are of the form in which is the function and a linear combination of the suitable functions. The orbitals were assumed to be solutions of Schrödinger's equation , where the Hamiltonian was . The terms and describe the Coulombic and exchange interactions with the metal ion and ligands, respectively. Matrix elements of the form were evaluated numerically on an IBM 7090. Assuming and the overlap between and to be small, the energy was minimized and the parameters were determined. For the bonding and the bonding the calculated values were and which agreed very well with the values and determined in the nuclear magnetic resonance experiment. The molecular orbitals were used to calculate the cubic crystal field splitting which is the promotion energy of an electron from a orbital to an orbital. The calculated value of agreed quite well with the observed value of considering the accuracy of the calculation. Furthermore, the reduction of the spin-orbit parameter and the Racah parameter from their free-ion values are satisfactorily explained by the molecular orbital approach. The physical interpretation of these results is emphasized. In particular, the only contributions to with the correct sign come from the off-diagonal matrix elements associated with the covalency; the amount of electron admixture is shown to be large; one novel physical mechanism partly responsible for the large bonding is the crystal field splitting of the and levels by the ions; expanding the radial function is shown to be unnecessary for some purposes and incorrect for the remainder. Details of the calculation are presented and implications of the LCAO-MO model discussed.
- Received 14 December 1962
DOI:https://doi.org/10.1103/PhysRev.130.517
©1963 American Physical Society