Slater's rules for finding approximate orbital exponents of K-, L-, and M-shell Slater AOs are as follows. The orbital exponent z is taken as (Z - snl)/n, where n is the principal quantum number and Z is the atomic number. The screening constant snl is calculated as follows: The AOs are divided into the following groups:
(1s) (2s, 2p) (3s, 3p) (3d)
To find snl, the following contributions are summed: (a) 0 from electrons in groups to the right of the one being considered; (b) 0.35 from each other electron in the group considered, except that 0.30 is used in the 1s group; (c) for an s or p orbital, 0.85 from each electron whose quantum number n is one less than the orbital considered and 1.00 from each electron still further in; for a d orbital, 1.00 for each electron in a group to the left.
Calculate the orbital exponents according to Slater's rules for the atoms H, He, C, N, O, S, and Ar. The optimum values of ζ to use when approximating an AO as a single STO have been calculated and are given in E. Clementi and D. L. Raimondi, J. Chem. Phys., 8, 2686 (1963); E. Clementi et al., J. Chem. Phys., 47, 1300 (1967). Compare these optimum values with the above values found by Slater's rules. [For n = 4, Slater took ζ as (Z - snl/3.7; however, Slater's rules are generally unreliable for n ≥ 4.]