d Orbitals in the sp3d, sp2d2, and p3d2 Configurations of Phosphorus

Wavefunctions and energy matrices for spectroscopic terms of phosphorus in the ${\mathrm{sp}}^{3}d$ configuration are reported. Using a two‐term Slater function for $\text{3d}$ orbitals and orthogonalized Slater functions for other orbitals, term energies are optimized with respect to $\text{3s, 3p}$ , and $\text{3d}$ orbital parameters. The core wavefunction is kept unchanged. Calculations on the lowest terms and configuration averages of ${\mathrm{sp}}^2{d}^2$ and $p^3{d}^2$ of phosphorus are also reported. $d$ Orbitals for the multiplets of phosphorus in the ${\mathrm{sp}}^{3}d$ configuration are diffuse and have mean radii upwards of 3.66 Å ${(}^6{D}^0)$ , while in the lowest terms of ${\mathrm{sp}}^2{d}^2$ and $p^3{d}^2$ they are compact, the mean radius being 2.03 Å. $d$ Orbitals in the excited configurations of phosphorus are compared with those of sulfur. The applicability of Slater's rules to excited configurations is examined. A computer method for performing all the calculations, including the algebra, is given in an Appendix.