Hund's rule

Friedrich Hund

Hund's rule is an empirical principle of 13 rules formulated in 1927 by the German physicist Friedrich Hund (1896-1997) from the study of atomic spectra and the distribution of elements in the periodic table. The rule is stated as follows:

By filling orbitals of equal energy (the three orbitals p, the five d, or the seven f) the electrons are distributed, whenever possible, with their parallel spins, filling the orbitals with the larger multiplicity. The atomic configuration is more stable (i.e., it has less energy) the more electrons (parallel spins) it has.

This is also the name given to the logical numbering of Hund's multiplicity.

When several electrons are described by degenerated orbitals, the greatest energy stability is that in which the electronic spins are disconnected (spine correlation).

The electrons are placed inside orbitals with the same energy so that they are maximally unpaired.

In atomic physics, Hund's rules refer to a set of simple rules used to determine the spectroscopic ground state of the studied atom. The three rules are:

1. for a given electronic configuration, the term of less energy is the one with the greatest total spin (St);
2. for a given total thorn, the lowest energy term is that which has the largest L number;
3. for a term of given spectroscopy, in an atom having its outer layer full or less, the lower level of energy will be the one with the least possible number J. In an atom that has its outer layer more than half full, the lower level of energy is the one with the highest number J possible.

These rules make it easy to find the fundamental term of spectroscopy.

To understand Hund's rule, one must know that all orbitals in a subshell must be occupied by at least one electron and must be pairable before a second is assigned to it. That is, all the orbitals must be filled and all the electrons must be in parallel before one orbital gains a second electron. And when an orbital gains a second electron, it must be paired with the first (opposite or antiparallel spins). For example:

3 electrons in orbital 2p; px1 py1 pz1 (vs) px2 py1 pz0

(px2 py1 pz0 = px0 py1 pz2 = px1 py0 pz2= px2 py0 pz1=....)

Thus, the electrons in an atom are assigned progressively, using an ordered configuration in order to assume the most stable energy conditions. The Aufbau principle explains the rules for filling orbitals in such a way that Hund's Rule is not violated.

It can also be expressed in another constructive way: <Since there are equivalent orbitals, first the maximum possible number of orbitals are completed with electrons and then the electrons that continue to be added are paired>.

Hund's rule complements the Pauli exclusion principle allowing the absolute elucidation of the electronic structure of atoms.