# Stability of half-filled and completely filled orbitals

Symmetrical distribution of electrons allows half and completely filled subshells to become more stable. Two or more electrons with the same spin can exchange their position with the degenerate orbitals. The spinning of electrons introduces a new type of quantum mechanical interaction called Exchange energy, Eex. And, the exchange energy release is maximum in the half-filled or completely filled subshells which intern increases their stability. This is proportional to the no. of exchanges of positive by electrons of same spins from one orbital to another in the same sub-shell. Even though electrons in the same subshell have the same energy, they have different spatial distribution.. therefore, their shielding effect of one over another is relatively small. Hence, the electrons are more attracted to the nucleus. And the state of lowest total electronic energy always corresponds to the ground state electronic configuration of an element.

The s-orbital is spherical in shape, therefore the electronic charge is distributed uniformly in all directions. The three p-orbitals, px, py & pz are symmetrical along-x,y & z-axis respectively. In px’, the electronic charge is concentrated along the x-axis, whereas in py & pz configuration, the electronic charge is concentrated along ‘y’ & ‘z’ axis respectively. In px2 py’ pz’ configuration the electronic charge is more concentrated along the x-axis. In px2 py2 pz1 configuration, the electronic change is more in plane xy. The ununiform distribution of electronic charge results in the unsymmetrical configuration.

However, the distribution of charge in px1py1pz1 & px2py2pz2 configuration is symmetrical in all the directions. Hence, the symmetrical configuration decreases the exchange energy making the configuration higher in stability. Similarly, the configuration of d-orbitals such as d5 & d10 have symmetrical distribution of electronic charge. Greater the number of exchanges results in higher exchange energy and hence greater stability. As the number of exchanges that take place in the less filled and completely filled orbitals is maximum, thus exchange energy is maximum and hence maximum stability.

Thus, the exchange of energy forms the basis of Hund’s rule where extra stability of half/completely filled subshells is because of three reasons:

1. Relatively small shielding
2. Lower coulombic repulsion energy
3. Larger exchange energy

In certain elements such as Cu or Cr where the difference between 3dand 4s shell is small, electrons choose to shift from subshell of lower energy (4s) to subshell of higher energy level (3s) in cases where the shift facilitates in making the higher subshell half/completely filled and provide extra stability. Thus, configurations like p3, d5, d10, f7, f14 etc. are more stable than others (Figure 1) (Huheey, Keiter, Keiter, & Medhi, 2006).

Table 1: Expected and observed configuration of electrons in elements (Singh, 2011).

 Element Expected electron configuration Actual electron configuration Copper, Cu [Ar] 3d94s2 [Ar] 3d104s1 Silver, Ag [Kr]4d95s2 [kK]4d105s1 Gold, Au [Xe]4f145d96s2 [Xe]4f145d106s1 Oalladium, Pd [Kr]4d85s2 [Kr]4d10 Chromium, Cr [Ar]3d44s2 [Ar]3d54s1 Molybdenum, Mo [Kr]4d45s2 [Kr]4d55s1