Hund's rule of maximum multiplicity

<h2 id="atoms">Atoms</h2>
<p>The <a href="/facts/Multiplicity_(chemistry)/SLUzvDWx">multiplicity</a> of a state is defined as 2S + 1, where S is the total electronic spin.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> A high multiplicity state is therefore the same as a high-spin state. The lowest-energy state with maximum multiplicity usually has unpaired electrons all with parallel spin. Since the spin of each electron is 1/2, the total spin is one-half the number of unpaired electrons, and the multiplicity is the number of unpaired electrons + 1. For example, the nitrogen atom ground state has three unpaired electrons of parallel spin, so that the total spin is 3/2 and the multiplicity is 4.
</p><p>The lower energy and increased stability of the atom arise because the high-spin state has  unpaired electrons of parallel spin, which must reside in different spatial orbitals according to the <a href="/facts/Pauli_exclusion_principle/lsBKGeHD">Pauli exclusion principle</a>. An early but incorrect explanation of the lower energy of high multiplicity states was that the different occupied spatial orbitals create a larger average distance between electrons, reducing electron-electron repulsion energy.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> However, quantum-mechanical calculations with accurate <a href="/facts/Wave_function/KgM5ykjY">wave functions</a> since the 1970s have shown that the actual physical reason for the increased stability is a decrease in the <a href="/facts/Shielding_effect/PoyU5vNr">screening</a> of electron-nuclear attractions, so that the unpaired electrons can approach the nucleus more closely and the electron-nuclear attraction is increased.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a>
</p><p>As a result of Hund's rule, constraints are placed on the way atomic orbitals are filled in the ground state using the <a href="/facts/Aufbau_principle/GLqThvnE">Aufbau principle</a>. Before any two <a href="/facts/Electron/L0KBo5cW">electrons</a> occupy an <a href="/facts/Electron_configuration/TQjRr22P">orbital</a> in a subshell, other orbitals in the same <a href="/facts/Electron_shell/QxI30eh9">subshell</a> must first each contain one electron. Also, the electrons filling a subshell will have parallel spin before the shell starts filling up with the opposite spin electrons (after the first orbital gains a second electron). As a result, when filling up atomic orbitals, the maximum number of unpaired electrons (and hence maximum total spin state) is assured.
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<p>For example, in the oxygen atom, the 2p4 subshell arranges its electrons as [↑↓] [↑] [↑] rather than [↑↓] [↑] [↓] or [↑↓] [↑↓][ ]. The manganese (Mn) atom has a 3d5 electron configuration with five unpaired electrons all of parallel spin, corresponding to a 6S ground state.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> The superscript 6 is the value of the <a href="/facts/Multiplicity_(chemistry)/SLUzvDWx">multiplicity</a>,  corresponding to five unpaired electrons with parallel spin in accordance with Hund's rule.
</p><p>An atom can have a ground state with two incompletely filled subshells which are close in energy. The lightest example is the chromium (Cr) atom with a 3d54s electron configuration. Here there are six unpaired electrons all of parallel spin for a 7S ground state.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a>
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<h2 id="molecules">Molecules</h2>
<p>Although most stable molecules have closed electron shells, a few have unpaired electrons for which Hund's rule is applicable. The most important example is the dioxygen molecule, O2, which has two degenerate <a href="/facts/Pi_bond/3Q6LAGYK">pi</a> <a href="/facts/Antibonding_molecular_orbital/9lhLNyt3">antibonding molecular orbitals</a> (π*) occupied by only two electrons. In accordance with Hund's rule, the ground state is <a href="/facts/Triplet_oxygen/uAE4t017">triplet oxygen</a> with two unpaired electrons in singly occupied orbitals. The <a href="/facts/Singlet_oxygen/db0PsrYh">singlet oxygen</a> state with one doubly occupied and one empty π* is an excited state with different chemical properties and greater reactivity than the ground state.
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<h2 id="exception">Exception</h2>
<ul><li>In 2004, researchers reported the synthesis of <a href="/facts/5-dehydro-m-xylylene/NY0cEycB">5-dehydro-<i>m</i>-xylylene</a> (DMX), the first <a href="/facts/Organic_compound/gqCNaN45">organic</a> <a href="/facts/Molecule/N9ljSfFq">molecule</a> known to violate Hund's rule.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a></li></ul>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Hund%27s_rules/pyyb3f6a">Hund's rules</a> (includes this plus 2 other rules)</li>
<li><a href="/facts/High_spin/QDMbT06M">High spin</a> metal complexes</li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="http://www.chem.purdue.edu/gchelp/gloss/hundsrule.html">A glossary entry hosted on the web site of the Chemistry Department of Purdue University</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>T. Engel and P. Reid, Physical Chemistry (Pearson Benjamin-Cummings, 2006) ISBN 080533842X, pp. 477–479 <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Engel and Reid p.473 <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Levine, I. N. (2013). Quantum Chemistry (7th ed.). Pearson. pp. 310–311. ISBN 978-0321803450. <a href="978-0321803450" target="_blank">978-0321803450</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Levine, I. N. (2013). Quantum Chemistry (7th ed.). Pearson. pp. 310–311. ISBN 978-0321803450. <a href="978-0321803450" target="_blank">978-0321803450</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>NIST Atomic Spectrum Database To read the manganese atom levels, type "Mn I" in the Spectrum box and click on Retrieve data. <a href="http://physics.nist.gov/PhysRefData/ASD/levels_form.html" target="_blank">http://physics.nist.gov/PhysRefData/ASD/levels_form.html</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>NIST Atomic Spectrum Database To read the chromium atom levels, type "Cr I" in the Spectrum box and click on Retrieve data. <a href="http://physics.nist.gov/PhysRefData/ASD/levels_form.html" target="_blank">http://physics.nist.gov/PhysRefData/ASD/levels_form.html</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>Slipchenko, L.; Munsch, T.; Wenthold, P.; Krylov, A. (2004). "5-Dehydro-1,3-quinodimethane: a hydrocarbon with an open-shell doublet ground state". Angewandte Chemie International Edition in English. 43 (6): 742–745. doi:10.1002/anie.200352990. PMID 14755709. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
</ol>

Hund's rule of maximum multiplicity open-in-new

Hund's rule of maximum multiplicity