Electronic structure of the ${\mathrm{Tl}}^{+}$ center in KCl. I. Relation to the $A$, $B$, and $C$ bands

The $a_{1g}$ and $t_{1u}$ one-electron molecular orbital (MO) energy levels of KCl: ${\mathrm{Tl}}^{+}$ have been calculated by a charge-consistent extended Hückel method. The reliable ${\mathrm{Tl}}^{+}$ $6s$ and $6p$ and ${\mathrm{Cl}}^{-}$ $3p$ and $4s$ wave functions are used in constructing the MO's. The result of the MO calculation quantitatively gives a more consistent interpretation of the $A$, $B$, and $C$ absorption bands in KCl: ${\mathrm{Tl}}^{+}$ than the case of earlier MO calculation made by Bramanti et al. That is to say, the theoretical calculation is in sufficiently satisfactory agreement with experiment for the exchange and spin-orbit energies in the lowest-excited-state configuration $\left(a_{1g}^{*}\right)\left(t_{1u}^{*}\right)$, which is responsible for the $A$, $B$, and $C$ bands, and for the energy difference between the $\left(a_{1g}^{*}\right)\left(t_{1u}^{*}\right)$ and ground-state ${\left(a_{1g}^{*}\right)}^2$ configurations, giving a satisfactory agreement with experiment for the $A$-, $B$-, and $C$-band energies. An attempt is made to estimate the oscillator strength of the ${\left(a_{1g}^{*}\right)}^2\to \left(a_{1g}^{*}\right)\left(t_{1u}^{*}\right)$ transition. It is shown that the estimated value is close to the experimental value.