Hund's Rules
Note: Some references, such as Haken & Wolf, use Hund's Rule #1 to apply to the nature of full shells and subshells. Full shells and subshells contribute nothing to the total angular momenta L and S. If you call this Hund'e Rule #1, then the above rules will be bumped up one in number. I don't know which is the more common practice.
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Hund's Rule #1The term with the maximum multiplicity lies lowest in energy.
These sketches are conceptual only. No attempt has been made to do any realistic scaling. Note that the energies we are discussing here are electric potential energies, so that a negative electron in the vicinity of a positive nucleus will have a negative energy leading to a bound state. Any force between the electrons will tend to counter that, contributing a positive potential energy which makes the electrons less tightly bound, or higher in potential energy.
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Index Atomic structure concepts Reference Rohlf Ch 9 | |||||||||
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Hund's Rule #2For a given multiplicity, the term with the largest value of L lies lowest in energy. The basis for this rule is essentially that if the electrons are orbiting in the same direction (and so have a large total angular momentum) they meet less often than when they orbit in opposite directions. Hence their repulsion is less on average when L is large. These influences on the atomic electron energy levels is sometimes called the orbit-orbit interaction. The origin of the energy difference lies with differences in the coulomb repulsive energies between the electrons.
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Hund's Rule #3For atoms with less than half-filled shells, the level with the lowest value of J lies lowest in energy. When the shell is more than half full, the opposite rule holds (highest J lies lowest). The basis for the rule is the spin-orbit coupling. The scalar product S·L is negative if the spin and orbital angular momentum are in opposite directions. Since the coefficient of S·L is positive, lower J is lower in energy.
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Exceptions to Hund's RulesHund's rules presume L-S coupling and presume that the electrons can be considered to be in a unique configuration. Neither is always true. For heavier elements, the "j-j coupling" scheme often gives better agreement with experiment.
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