Singlet-triplet energy differences calculated from generalized oscillator strengths

Abstract

Using a one‐electron model, the difference in energy, E_S — E_T, between a singlet state (obtained by exciting one electron from a nondegenerate closed‐shell ground state) and the corresponding triplet is shown to be (in atomic units) equal to ${\mathrm{(\pi \; gW)}}^{\text{−1}}{\int }_0^{00}{K}^2\mathrm{f\hspace{0.17em}dK}$ where f is the generalized oscillator strength for excitation to the singlet state, W is the excitation energy, g is the degeneracy of the excited singlet state, and K is the change in wave vector on collision. This relationship is tested for several states in helium and carbon monoxide for which both E_S — E_T and f are known. Calculated and observed values of E_S — E_T differ, on the average, by about 15%, the discrepancy being due no doubt to the one‐electron approximation. Where high accuracy is not required (and singlet‐triplet energy differences are difficult to obtain in other ways) the method may be of value since the position of the triplet is obtained from experimental measurements performed exclusively on the singlet excitation at high kinetic energies.