Knowledge Bank

The most general set of secular equations for a $kd3,7$, (k = 3, 4, 5), transition metal complex in a cubic environs which is allowed by the fundamental approximations of ligand field theory has recently been derived by Eisenstein and has been subsequently utilized by him to interpret the magnetic and optical properties, of $K2ReCl6$ and $IrF6.1$ As his final energy determinants have a more lucid form than the presently available (corresponding) unpublished energy matrix elements of $Weakliem2$ and of Recah, Schonfeld, and $Low3$ we have used those of Eisenstein in our present systematic study of the optical properties of the cubic $kd3,7$ transition metal systems. Proceeding as in our previous investigations of the $kd0$, (n = l, 2, 8, 9), $problems,4,5$ we have computed the variation of the energy as a function of the ligand field parameter Dq, the spin-orbit coupling constant $\lambda$, and the electron correlation integrals B and C. To simplify our problem and to save time on the Bell Telephone Laboratories I.B.M. 7090 data processing machine, we have employed the theoretical ratio of C/B of 4 in our calculations. The results obtained have been graphically and tabularly portrayed and will be presented in these forms. Particular attention will be paid to the spectral effects of spin-orbit interactions in a variety of $kd3,7$, (k = 3, 4, 5) compounds, and a general commentary on the future usefulness of this and other $works1-5$ will be given.