Intensities of Electronic Transitions in Molecular Spectra IX. Calculations on the Long Wave-Length Halogen Spectra

The dipole strength D_NQ for the perpendicular‐type N→Q transitions in the long wave‐length spectra of the halogen molecules is computed theoretically according to each of two approximations (LCAO and AO) for the wave functions. The work illustrates the behavior of antisymmetrical wave functions in transition moment calculations, and justifies the ignoring (as an approximation) of closed shells. The overlapping and dipole moment integrals ${\displaystyle \int }{\mathrm{[\phi (np\sigma )][\phi (np\sigma }}^{\prime }\mathrm{)]dv\hspace{0.17em}}\mathrm{and}\hspace{0.17em}{\displaystyle \int }{\mathrm{[\phi (np\sigma )]y[\phi (np\pi }}_y^{\prime }\mathrm{)]dv}$ are evaluated using Slater's approximate atomic orbitals for the φ's. The calculated D_NQ values for both approximations show the same rapid variation with atomic number as do the observed values, except for iodine, where the anomalous smallness of the observed value may reasonably be attributed to strong case c effects. The LCAO calculated values are consistently much larger than the AO values; the latter agree surprisingly well with the experimental values (cf. Table I). The calculations show D_NQ to be very sensitive to variations of the internuclear distance r, and to variation of the effective charge Z^* in the Slater atomic orbitals used. It is pointed out that the former variation may require reconsideration of work in which repulsive potential energy curves are deduced from intensity data on absorption continua. A qualitative discussion is given of the effects on D_NQ of various possible improvements of the wave functions used. In connection with this, calculations have been made which show that the energy of the σ_u1s antibonding state of H₂⁺ in LCAO approximation is minimized when Z^* for 1s is (roughly) 0.84, for normal internuclear distance. This contrasts with Z^*=1.228 determined by Finkelstein and Horowitz for the σ_g1s bonding state, and suggests that to improve molecular wave functions Z^* should be increased for bonding but decreased for antibonding molecular orbitals.