Ground electronic configuration for many-electron atoms

2 Ground electronic configuration for many-electron atoms 

By applying the Pauli Exclusion Principle, we can put each successive electron into the available lowest-energy orbital to yield the following electronic configurations for the first 30 elements in the periodic table (Table 2.3.1). 

In the last column of Table 2.3.1, [Ar] denotes that the first 18 electrons of these elements have the Ar configuration. For Sc (Z = 21), we have ls22s22p63s23p6 for the first 18 electrons. For electron no. 19, E(3d) (4s), and hence the electron enters into the 3d orbital. For electron no. 20, (4s) E(3d), so it enters into the 4s orbital. For electron no. 21, (4s) (3d), and thus it enters into the 4s orbital. Finally, we have the configuration [Ar 3d14s2 for Sc, as well as [Ar dUs1 and [Ar]3d1 for Sc+ and Sc2+, respectively. 

It is now clear that the energies of the atomic orbitals do not follow an immutable sequence. Rather, the energy ordering depends on both the nuclear charge and electronic configuration under consideration. For example, for electron no. 19 in both K (Z = 19) and Ca (Z = 20), we have (4s) (3d). For electron no. 19 in Sc (Z = 21), it becomes E(3d) E(4s). Furthermore, for electrons no. 20 and no. 21 of Sc, the ordering is reversed. 

Note that there are two anomalies in the first transition series [Ar]3d54s1 (instead of [Ar]3d44s2) for Cr and [Ar]3d104s1 (instead of [Ar]3d94s2) for Cu. These two configurations arise from the extra stability of a half-filled or completely filled subshell. Such stability comes from the spherically symmetric electron density around the nucleus for these configurations. Take the simpler case of p3 as an example. The angular portion of the density function is proportional to 

---