Electronic structure of theTl+center in KCl. II. Relation to theDband

Abstract

It has been shown that the $D$ band in alkali halides containing $s^2$ ion (${\mathrm{Tl}}^{+}$, ${\mathrm{In}}^{+}$, ${\mathrm{Ga}}^{+}$, ${\mathrm{Sn}}^{2+}$) is composed of three bands (named $D_1$, $D_2$, $D_3$ in the order of increasing energy). Of the three bands, the $D_1$ band is the weakest whereas the $D_2$ band is the strongest. In KCl: ${\mathrm{Tl}}^{+}$, the $D_1$ band is observed at about 6.72 eV whereas the $D_2$ band is observed at about 7.23 eV. A theoretical calculation using molecular orbitals has been made on the charge-transfer-type transition ${\left(e_g\right)}^4\to {\left(e_g\right)}^3\left(t_{1u}^{*}\right)$ in a ${\left(\mathrm{T}\mathrm{l}{\mathrm{Cl}}_6\right)}^{5-}$ complex to clarify the origin of the $D$ band in KCl: ${\mathrm{Tl}}^{+}$. The configuration interaction with $\left(a_{1g}^{*}\right)\left(t_{1u}^{*}\right)$ configuration responsible for the $A$, $B$, and $C$ bands is taken into account in the calculation. Three absorption bands are theoretically derived; one is located at 7.74 eV, the others at 7.28 and 6.71 eV. It is shown that the latter two bands correspond well to the observed $D_2$ and $D_1$ bands, respectively. It is also demonstrated that the theoretically derived 7.74-eV band is not observed experimentally being hidden under the much stronger exciton band. The present calculation also gives a satisfactory agreement with experiment for the $A$ and $C$ band positions.