THE HUND’S RULE OF MAXIMUM MULTIPLICITY

Hund’s rule is a series of principles developed by German physicist Friedrich Hund in 1927 for determining the word ideogram that correlates to a multiple-electron atom’s ground state. The very first rule is particularly essential in chemistry, which is commonly known as Hund’s Rule. 

There are three rules which are as follows:

• The word with the highest multiple has the least energy for a particular electron configuration. 2S+1 is the multiplicity, where S is the cumulative spin angular momentum of every electron. The multiplicity is the quantity of unpaired electrons multiplied by one. As a result, the word with the lowest energy also has the highest S and the most unpaired electrons.
• The word with the biggest cumulative orbital angular momentum quantum number L has the least energy for a given multiplicity.
• The layer with the least value of total angular momentum quantum number J (for J=L+S) in an atom with the outermost subshell half-filled or less has the lowest energy for a given term. The level having the greatest value of J has the lowest energy if the outermost shell is much more half-filled.

These rules describe how common energy communications determine whether the word carries the ground state in a straightforward manner. The rules presume that the force of repulsion among outer electrons is substantially stronger than the spin-orbit contact, which is more strong than remaining interactions. The LS coupling paradigm is what it’s called.

The quantum numbers for total S, total spin angular momentum, and total L, total orbital angular momentum, are not affected by full shells or subshells. It might be proven that the leftover electrostatic force (repulsion among electrons) and the spin-orbit contact can only move all of the energy levels at one place for complete orbitals and suborbital. Just the outer valence electrons should be taken into account when calculating the ranking of energy levels in general.

UNDERSTANDING THE HUND’S RULE OF MAXIMUM MULTIPLICITY- 

The least energy atomic state is the one that is maximising the cumulative spin quantum number of the electrons in the empty subshell, according to Hund’s first rule. Before the double occupation, the orbitals of the subshell are all filled individually with electrons of opposite spin. (This is sometimes referred to as the “bus seat rule,” because it is following the advice of bus passengers, who seem to be inclined towards filling all dual seats individually before double occupancy arises.)

The enhanced durability of high multiplicity situations has been attributed to two separate physical reasons. It was postulated in the initial periods of quantum mechanics that electrons in various orbitals are more apart, reducing electron-electron repulsion energy. However, precise quantum-mechanical simulations (beginning in the 1970s) reveal that the explanation is that electrons in singularly occupied orbitals are less efficiently screened or insulated from the nucleus, causing such orbitals to compress and the electron–nucleus attraction energy to increase (or declines algebraically).

EXAMPLE- 

Take into account the equilibrium state of silicon for instance. Si has the following electrical configuration: 1s2 2s2 2p6 3s2 3p2. None but the outer 3p2 electrons must be considered. It can be proved that the Pauli exclusion principle allows the words 1D, 3P, and 1S. According to Hund’s first rule, the ground state word is now 3P (triplet P), which has S = 1. The quantity of the multiplicity is denoted by the superscript 3: 2S + 1 = 3. With ML = 1 and MS = 1.

RULE NUMBER 2 OF HUND’S RULE- 

The goal of this rule is to reduce electron repulsion. The conventional figure shows that if all the electrons orbit in the similar direction (greater orbital angular momentum), they will collide less frequently than the ones orbiting in opposite ways. The repulsive force is increased in the latter situation, separating electrons. This increases their potential energy, resulting in a higher energy level.

EXAMPLE- 

As there is a single triplet word in silicon, this rule is unnecessary. Titanium (Ti, Z = 22), with electron configuration 1s2 2s2 2p6 3s2 3p6 3d2 4s2, is the atom having the least weight that uses this rule to find the ground state word. The non-closed-shell in this example is 3d2, and the words allowed are singlets (1S, 1D, and 1G) and triplets (3P and 3F). (The ideograms S, P, D, F, and G denote that the cumulative orbital angular momentum quantum integer has values of 0, 1, 2, 3, and 4, respectively, similar to how atomic orbitals are named.) 

RULE THREE OF HUND’S RULE- 

The energy shifts owing to a spin-orbit coping are taken into account by this criterion. L and S are still acceptable quantum numbers in scenarios in which the spin-orbit coupling is poor when compared with the remaining electrostatic interaction. The splitting is determined by: 

= ζL,SL.S

= (1/2)L,S{JJ+1-LL+1-SS+1}

For shells that are more than half full, the value zeta, S) goes from plus to minus. This word describes how the ground state energy is affected by the magnitude of J. 

EXAMPLE-

The lowest energy term for sulfur (S) is 3P with spin-orbit layers J=2,1,0, but the ground state is 3P2 since there are now four of the six available electrons in the shell.

Because L=0 when the shell is half-filled, there is only a single value of J (=S), which is the least energy state. The least energy state in phosphorus, for example, is S=3/2 L=0 for three unpaired electrons in three 3p orbitals. As a result, J=S=3/2 and 4S3/2 is the ground state.

CONCLUSION-

Before pairing up, electrons should always occupy an empty orbital, with the first rule. Because electrons are negatively charged, they repel one another. Electrons prefer to occupy their orbitals rather than splitting an orbital with some other electron to reduce repulsion. Quantum computations have also revealed that electrons in singularly filled orbitals are less efficiently screened or insulated from the nucleus. Unpaired electrons in singularly filled orbitals possess the same spins according to the second rule. The first electron in a sublevel might be “spin-up” or “spin-down,” in technical terms. However, once the spin of the first electron in a sublevel is decided, all of the other electrons in that sublevel’s spins are determined by that first spin.