Singlet-Triplet Interval Ratios forsp,sd,sf,p5sandd9sconfigurations

A systematic comparison of the known data on the singlets and triplets arising from $\mathrm{sp}$, $\mathrm{sd}$, $\mathrm{sf}$, $p^{5}s$ and $d^{9}s$ configurations with the theory of Houston shows that the theory gives a good account of the deviations from the Landé interval rule which accompany departure from Russell-Saunders coupling. There are numerous significant discrepancies, however. Writing ${}_{}{}^1{}_{}{}^{}L_l^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}L_{l+1\mathrm{}}^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}L_l^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}L_{l-1\mathrm{}}^{}{}_{}{}^{}$ with $L=P, D, F$ when $l=1, 2, 3$ for the term values, we plot as abscissa $\frac{({}_{}{}^3{}_{}{}^{}L_{l-1\mathrm{}}^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}L_{l+1\mathrm{}}^{}{}_{}{}^{})}{|{}_{}{}^3{}_{}{}^{}L_l^{}{}_{}{}^{}-{}_{}{}^1{}_{}{}^{}L_l^{}{}_{}{}^{}|}$ and $\frac{({}_{}{}^3{}_{}{}^{}L_{l-1\mathrm{}}^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}L_l^{}{}_{}{}^{})}{({}_{}{}^3{}_{}{}^{}L_l^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}L_{l+1\mathrm{}}^{}{}_{}{}^{})}$ as ordinate if ${}_{}{}^3{}_{}{}^{}L_l^{}{}_{}{}^{}-{}_{}{}^1{}_{}{}^{}L_l^{}{}_{}{}^{}$ is positive, otherwise the reciprocal of this quantity. Houston's equations (12) give functional relations between these interval ratios which are compared with the experimental values.