Electronic Configuration of d-block Elements

Building on the Aufbau principle and Hund's rule learnt in Class XI, the electronic configurations of the d-block elements follow a clear rule with two well-known exceptions. According to the Aufbau principle, for the fourth-period elements the 4s orbital is filled before the 3d orbital, because 4s is lower in energy at the point Sc is being built up. So the filling of the 3d orbital genuinely begins only from scandium, whose configuration is [Ar]3d¹4s². As successive protons and electrons are added moving across the row, the electrons of each new element are progressively added to the 3d orbital, one at a time, in accordance with Hund's rule (each of the five 3d orbitals gets one electron before any is paired), and this filling of the 3d sub-shell is finally completed at zinc, whose configuration is [Ar]3d¹⁰4s².

However, there are two well-documented exceptions to this otherwise smooth, progressive filling: chromium and copper. Where the normal Aufbau prediction would give Cr the configuration [Ar]3d⁴4s², its actual, experimentally observed configuration is [Ar]3d⁵4s¹ -- one electron has effectively 'jumped' from the 4s orbital into the 3d sub-shell to make it exactly half-filled. Likewise, where Aufbau would predict Cu as [Ar]3d⁹4s², its actual configuration is [Ar]3d¹⁰4s¹ -- again, one 4s electron has moved into 3d to complete the sub-shell. In both cases, whenever there is a chance for an atom to acquire a half-filled (d⁵) or fully-filled (d¹⁰) d sub-shell by promoting one electron from the ns orbital, nature takes that option, because half-filled and fully-filled configurations carry extra stability, arising from the symmetrical distribution of electrons across the five d orbitals and the associated exchange energy released when electrons of the same spin occupy different orbitals.

This extra stability can also be pictured geometrically: when all five d orbitals are considered together as a set, they combine to form an overall spherically symmetric electron cloud. A half-filled or fully-filled d sub-shell therefore gives a genuinely symmetric distribution of electron density around the nucleus. In contrast, a partially (but not half- or fully-) filled configuration gives an asymmetric electron distribution, which sets up an internal charge/potential imbalance across the atom. To relieve this imbalance and settle into a lower-energy, less 'strained' state, the atom preferentially adopts the symmetrical (half-filled or fully-filled) arrangement wherever the energy cost of promoting one electron is small enough to be repaid by this stabilisation. …