Hunds RuleEdit
Hunds rule is a practical guideline in atomic physics and chemistry that helps predict how electrons arrange themselves in atoms when orbitals are degenerate (have the same energy). Formulated from early spectroscopic observations and the mathematics of electron exchange, it captures how the repulsion between electrons and the quantum requirement that electrons be antisymmetric under exchange combine to favor certain configurations. In everyday chemistry and spectroscopy, Hunds rule provides a surprisingly reliable road map for anticipating ground states and magnetic behavior, especially in lighter elements where relativistic effects are small and LS coupling is a good approximation.
The rule is most at home in the traditional, non-relativistic picture of atoms, where the emphasis is on the way electrons tend to maximize their overall spin before pairing up, and on how the total orbital motion of those spins interacts to set the lowest-energy arrangement. It is a cornerstone of how educators introduce electron configurations and term symbols, and it underpins explanations of paramagnetism, color in transition-metal complexes, and the ordering of spectral lines. Still, like many rules of thumb, its applicability has boundaries. In heavy elements where spin-orbit coupling becomes strong, or in systems where relativistic effects alter the simple LS coupling picture, Hunds rule can fail or require modification. See LS coupling and jj coupling for a sense of the framework in which these caveats arise.
Fundamentals
Hunds rule is usually presented as a trio of guiding principles for arranging electrons in degenerate orbitals within a subshell (for example, the p, d, or f subshells):
Rule 1 (maximum multiplicity): For a given electron configuration, the term with the maximum multiplicity (2S+1) lies lowest in energy. S is the total spin quantum number, so this rule favors the largest possible total spin and is a consequence of the exchange interaction, which lowers energy when electrons with parallel spins avoid each other in the same subshell. This makes high-spin states more stable in many cases. See Spin (physics), Multiplicity (physics), and Exchange interaction for the underlying physics.
Rule 2 (maximize unpaired spins in degenerate orbitals): Among configurations with the same multiplicity, electrons occupy different degenerate orbitals singly as far as possible before any pairing occurs. This maximizes the total spin and minimizes repulsion by keeping electrons apart in space. See Atomic orbital and Electron configuration for context.
Rule 3 (maximum L for terms of the same multiplicity under LS coupling): When several terms share the same multiplicity, the term with the largest total orbital angular momentum L is typically the lowest in energy under the LS coupling scheme. This reflects how the orbital motion of electrons contributes to the overall energy in this coupling picture. See Orbital angular momentum and LS coupling for details.
A useful way to see these ideas in action is to look at common light elements. For nitrogen, whose p^3 configuration yields a ground term of ^4S_{3/2}, the high multiplicity (S = 3/2) dominates and the orbital part (L = 0) is minimized in a way that places this state lowest. For carbon, with p^2, the ground term is ^3P, reflecting S = 1 and L = 1. For oxygen, the p^4 configuration gives a ground term of ^3P as well (S = 1, L = 1). These examples illustrate how electrons prefer to align their spins and, where applicable, arrange their orbital motion to minimize energy. See Carbon, Nitrogen, and Oxygen for these cases.
It is important to note that Hunds rule is a model-dependent guideline that works best when LS coupling is a good description of the atom. In heavier elements where spin-orbit coupling is stronger, or in situations where electron correlation plays a sizable role, the simple ordering predicted by Hunds rule can be modified. In such cases, other coupling schemes (e.g., jj coupling) or more sophisticated quantum-chemical calculations are employed to predict ground states and spectral patterns. See Relativistic quantum mechanics and Electron correlation for a broader view.
Applications and limitations
Hunds rule helps chemists and physicists interpret and predict a wide range of phenomena. In spectroscopy, it guides the assignment of term symbols to observed lines and explains why certain spin states are more populated than others. In inorganic chemistry, the rule informs the understanding of magnetic properties and color in transition-metal complexes, where the competition between exchange stabilization (favoring high-spin states) and pairing energy (favoring low-spin states) shapes reactivity and ligand behavior. See Spectroscopy and Transition metal for related topics.
In real-world systems, the rule has its limits. Electron correlations, the specifics of the subshell being filled, and relativistic effects in heavier elements can lead to deviations from the simplest Hunds-rule picture. When spin-orbit coupling is strong, the ground state may be better described by a different coupling scheme, and the neat separation into spin and orbital parts breaks down. Researchers routinely test Hunds-rule predictions against high-precision measurements and computational results to assess when the rule remains a good guide and when more complete theories are required. See Spin–orbit coupling and Electron correlation for context.
There are ongoing debates about how to teach and apply Hunds rule in modern environments. Advocates emphasize its enduring value as a compact, intuitive explanation for numerous spectroscopic patterns and magnetic phenomena. Critics alert that the rule is a simplification and that reliance on it without acknowledging its domain of validity can mislead in borderline cases—especially in heavy atoms, in compounds with unusual orbital mixing, or when relativistic effects are pronounced. Proponents of careful pedagogy argue for presenting Hunds rule as a principled guide with explicit conditions, rather than as an absolute law. See Educational pedagogy in science education and Atomic term symbol for related framing.
The broader scientific context recognizes that rules like Hunds rule emerge from deeper quantum mechanics—the interplay of antisymmetry, exchange energy, and the structure of electron-electron interactions. In that sense, Hunds rule is part of a spectrum of tools scientists use to connect complex many-body problems to workable, predictive models. See Quantum mechanics and Atomic physics for foundational perspectives.