Question

How does Hund's rule of maximum multiplicity suggest what one can predict for a stable configuration?

Answer 1

Hint: Hund's rule of maximum multiplicity rule is a formula for predicting the ground state of an atom or molecule having one or more open electronic shells based on atomic spectra. The rule says that the lowest energy term for a given electron configuration is the one with the highest spin multiplicity value. If two or more orbitals of equal energy are available, electrons will fill them individually before filling them in pairs.

Complete answer:
2S + 1 is the multiplicity of a state, where S is the total electronic spin. As a result, a high multiplicity state is the same as a high-spin state. Unpaired electrons with parallel spins are generally found in the lowest-energy state with the highest multiplicity. Because each electron has a half-spin, the total spin is equal to one-half the number of unpaired electrons, and the multiplicity is equal to the number of unpaired electrons + 1. The ground state of the nitrogen atom, for example, contains three unpaired electrons with parallel spin, resulting in a total spin of $\frac{3}{2}$ and a multiplicity of 4.
Because the high-spin state includes unpaired electrons with parallel spin, which must dwell in distinct spatial orbitals according to the Pauli exclusion principle, the atom has a lower energy and is more stable. Different occupied spatial orbitals generate a higher average distance between electrons, lowering e -e- repulsion, according to an erroneous explanation for the lower energy of high multiplicity states. However, quantum simulations using precise wave functions have revealed that the real physical cause for enhanced stability is a reduction in electron-nuclear attraction screening, allowing unpaired electrons to approach the nucleus more intimately and increasing electron-nuclear attraction.
The Aufbau principle imposes limitations on the way atomic orbitals are filled in the ground state as a result of Hund's rule. Other orbitals in the same subshell must each contain one electron before any two electrons may occupy an orbital in that subshell. Also, before the opposing spin electrons start filling up a subshell, the electrons filling it will have parallel spin (after the first orbital gains a second electron). As a result, the highest amount of unpaired electrons (and hence the largest total spin state) is guaranteed while filling up atomic orbitals.
The $$2p^4$$ subshell of the oxygen atom, for example, organizes its electrons as $$[\uparrow \downarrow ][\uparrow ][\uparrow ]$$ rather than $$[\uparrow \downarrow ][\uparrow ][\downarrow ]$$or $$[\uparrow \downarrow ][\uparrow \downarrow ]\left[\right]$$ The manganese (Mn) atom has a $3d^5$ electron configuration, which corresponds to a ${}^{6}S$ ground state, with five unpaired electrons all spinning in the same direction.
According to Hund's rule, the superscript 6 denotes the multiplicity value, which corresponds to five unpaired electrons with parallel spin.

Note:
The multiplicity of an energy level is defined as 2S+1 in spectroscopy and quantum chemistry, where S is the total spin angular momentum. Singlets, doublets, triplets, quartets, and quintets are states with multiplicities of 1, 2, 3, 4, and 5. The multiplicity is the number of unpaired electrons multiplied by one.