What is Hund's rules: Definition and 13 Discussions

In atomic physics, Hund's rules refers to a set of rules that German physicist Friedrich Hund formulated around 1927, which are used to determine the term symbol that corresponds to the ground state of a multi-electron atom. The first rule is especially important in chemistry, where it is often referred to simply as Hund's Rule.
The three rules are:
For a given electron configuration, the term with maximum multiplicity has the lowest energy. The multiplicity is equal to


{\displaystyle 2S+1\ }
, where


{\displaystyle S}
is the total spin angular momentum for all electrons. The multiplicity is also equal to the number of unpaired electrons plus one. Therefore, the term with lowest energy is also the term with maximum


{\displaystyle S\,}
and maximum number of unpaired electrons.
For a given multiplicity, the term with the largest value of the total orbital angular momentum quantum number


{\displaystyle L\,}
has the lowest energy.
For a given term, in an atom with outermost subshell half-filled or less, the level with the lowest value of the total angular momentum quantum number


{\displaystyle J\,}
(for the operator






{\displaystyle {\boldsymbol {J}}={\boldsymbol {L}}+{\boldsymbol {S}}}
) lies lowest in energy. If the outermost shell is more than half-filled, the level with the highest value of


{\displaystyle J\,}
is lowest in energy.These rules specify in a simple way how usual energy interactions determine which term includes the ground state. The rules assume that the repulsion between the outer electrons is much greater than the spin–orbit interaction, which is in turn stronger than any other remaining interactions. This is referred to as the LS coupling regime.
Full shells and subshells do not contribute to the quantum numbers for total S, the total spin angular momentum and for L, the total orbital angular momentum. It can be shown that for full orbitals and suborbitals both the residual electrostatic energy (repulsion between electrons) and the spin–orbit interaction can only shift all the energy levels together. Thus when determining the ordering of energy levels in general only the outer valence electrons must be considered.

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  1. Mr_Allod

    Hund's Rule for Determining Term Symbol Energy Order

    Hello there, for the above question I have no issue finding the term symbols but I am a little unsure about employing Hund's rules to the electron configuration, particularly those referring to the energies based on the total angular momentum J. These state: - In a less than ##\frac12##-filled...
  2. R

    I Hund's rules and Pauli's principle

    So as I can see from the literature there are two "methods" on how to apply Hund's rules to determine the ground state of an electron configuration. Method 1: One determines all possible states due to Pauli's principle (wave function must be totally antisymmetric) using angular momentum...
  3. C

    I In what cases (precisely) are Hund's rules valid?

    I can't find on any good source (such as a textbook) a precise specification about the cases when Hund's rules (especially Hund's third rule) for an electronic configuration of atom are valid (the rules help to select the lowest energy state of a configuration). As far as I understood: Hund’s...
  4. C

    Showing Consistency with Hund's Rules

    Homework Statement Show that the ground states for the first three elements in the “neon configuration” (Z=11 to 18) are consistent with Hunds rules. Homework Equations From Hyperphysics, the rules are: 1. The term with maximum multiplicity lies lowest in energy 2. For a given multiplicity...
  5. A

    A Hund's rule and strong spin-orbit interacion

    Hi, I have read that Hund's rules are valid for Atoms with low z. Because the third Hund's rule is build of Russell-Saunders coupling. Can I still use the first and second Hund's rule for heavy atoms and jj-coupling( for the third rule)? Or how can I know the groundstate for an atom with large...
  6. astrocytosis

    Using Hund's rules to find ground state L, S, J

    Homework Statement Using Hund's rules, find the ground state L, S and J of the following atoms: (a) fluorine, (b) magnesium, and (c) titanium. Homework Equations J = L + S The Attempt at a Solution I'm having trouble understanding what L, S and J mean on a basic level. I read the textbook...
  7. M

    I Understanding Hund's Second Rule: What is a Singlet or Triplet?

    Can anyone explain the second rule, because the Wikipedia page is not very clear? Hund's zeroth rule - Ignore all inner shells and focus on the outermost shell. Hund's first rule - Put the electrons such that they maximize spin, ##s##. So far so good. Hund's second rule appears to be simply...
  8. S

    Solving Erbium's Ground State w/ Hund's Rules

    I have the solution for this problem but don't understand it. 1. Homework Statement Use Hund's rules to calculate the ground state of erbium with electron configuration [Xe]4f126s2 Homework Equations Hunds Rules: 1. Maximise S (within Pauli) 2. Maximise L (within Pauli) 3. Min J (for...
  9. T

    Possible partial waves for photoelectron of nitrogen

    Homework Statement (a) The nitrogen atom has seven electrons. Write down the electronic configuration in the ground state, and the values of parity (Π), spin (S), orbital angular momentum (L), and total angular momentum (J) of the atom. (b) If an extra electron is attached to form the N–...
  10. R

    Using Hund's rules to calculate ground state of erbium

    Homework Statement Calculate ground state of erbium [Xe] 4f^12 6s^2 The Attempt at a Solution so i know that the f orbital can hold 14 electrons and has 7 types of orbitals that is -3,-2,-1,0,1,2,3 So i constructed a table with axes of m_l (-3 to +3 above) and m_s. Then hunds rules...
  11. D

    Solve N Ground State in (2s+1)(L)(J) Format

    Homework Statement Find the ground state of nitrogen in the form (2s+1)(L)(J), where s represents the total spin, L represents the total orbital angular momentum (s,p,d,f), and J represents the total angular momentum. Attempt at solution Well, the electron configuration is [He](2s)^2...
  12. S

    Questions about Hund's Rules and L-S Coupling

    I would like to ask two questions about Hund's rules and L-S coupling: 1. Some textbooks state that when doing L-S coupling and applying Hund's rules, "The maximum values of S and L are subject to the condition that no two electrons may have the same pair of values for m(sub s) and m(sub l)...
  13. S

    Hund's Rules and L-S Coupling: Understanding Limitations and Confusions"

    I would like to ask two questions about Hund's rules and L-S coupling: 1. Some textbooks state that when doing L-S coupling and applying Hund's rules, "The maximum values of S and L are subject to the condition that no two electrons may have the same pair of values for m(sub s) and m(sub l)...