Studies on Rydberg Orbitals. II. Calculation of the Rydberg Orbitals of Li(I)–F(I) and Their Isoelectronic Series

Abstract

The 3s, 3p, and 3d orbitals of the atoms Li(I)–F(I) and their isoelectronic ions were calculated by optimizing the one-electron energy with the core electrons being fixed. These orbitals are for the valence states of the lowest Rydberg excited configurations, e.g., 1s22s22p3l, V2 for the C(I) series. First, the wave-functions were expanded with Slater orbitals of the least basis (3—l STO). Except for the case of 3p orbitals of the Li(I)–B(I) series, they are different from hydrogenlike expansions in that the coefficients and orbital exponents are independently optimized. Secondly, a 3l-STO was added to improve the shape of the inner loop. These Rydberg wavefunctions satisfy the following restrictions: (i) normalization, (ii) orthogonalization to the core orbitals, and (iii) cusp condition. The orbital exponents of the terms for the inner loops were set equal to the values calculated by Slater's rule for the precursors (the core orbitals of the same l with the Rydberg orbital). “Energy-optimization” and “virial-optimization” were applied separately, case by case. The results are generally good with respect to the orbital energy or quantum defect when compared to the values observed and calculated by others, the error being in the order of d ≪ p < s. Perturbations of the core by the Rydberg electron were discussed. It was revealed that for d orbitals the Slater–Condon parameters are almost constant for the different spectroscopic terms and the calculated and observed values coincide with each other, while for 3p and 3s orbitals the Slater–Condon parameters change drastically from term to term and due caution is necessary for assigning their values.