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Hund's rule of maximum multiplicity is a rule based on observation of atomic spectra, which is used to predict the
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
of an atom or molecule with one or more open electronic shells. The rule states that for a given
electron configuration In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon ato ...
, the lowest energy
term Term may refer to: * Terminology, or term, a noun or compound word used in a specific context, in particular: **Technical term, part of the specialized vocabulary of a particular field, specifically: ***Scientific terminology, terms used by scient ...
is the one with the greatest value of spin multiplicity. This implies that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs. The rule, discovered by
Friedrich Hund Friedrich Hermann Hund (4 February 1896 – 31 March 1997) was a German physicist from Karlsruhe known for his work on atoms and molecules. Scientific career Hund worked at the Universities of Rostock, Leipzig, Jena, Frankfurt am Main, and GΓΆt ...
in 1925, is of important use in atomic chemistry,
spectroscopy Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter ...
, and
quantum chemistry Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions ...
, and is often abbreviated to Hund's rule, ignoring Hund's other two rules.


Atoms

The multiplicity of a state is defined as 2S + 1, where S is the total electronic spin. 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. 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
Pauli exclusion principle In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formula ...
. 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. However, quantum-mechanical calculations with accurate
wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
s since the 1970s have shown that the actual physical reason for the increased stability is a decrease in the
screening Screening may refer to: * Screening cultures, a type a medical test that is done to find an infection * Screening (economics), a strategy of combating adverse selection (includes sorting resumes to select employees) * Screening (environmental), ...
of electron-nuclear attractions, so that the unpaired electrons can approach the nucleus more closely and the electron-nuclear attraction is increased. As a result of Hund's rule, constraints are placed on the way atomic orbitals are filled in the ground state using the
Aufbau principle The aufbau principle , from the German ''Aufbauprinzip'' (building-up principle), also called the aufbau rule, states that in the ground state of an atom or ion, electrons fill subshells of the lowest available energy, then they fill subshells ...
. Before any two
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...
s occupy an orbital in a subshell, other orbitals in the same subshell 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. For example, in the oxygen atom, the 2p4 subshell arranges its electrons as ��↓ οΏ½οΏ½ οΏ½οΏ½rather than ��↓ οΏ½οΏ½ οΏ½οΏ½or ��↓ ��↓ ]. The manganese (Mn) atom has a 3d5 electron configuration with five unpaired electrons all of parallel spin, corresponding to a 6S ground state. The superscript 6 is the value of the Multiplicity (chemistry), multiplicity, corresponding to five unpaired electrons with parallel spin in accordance with Hund's rule. 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.


Molecules

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 pi
antibonding molecular orbital In chemical bonding theory, an antibonding orbital is a type of molecular orbital that weakens the chemical bond between two atoms and helps to raise the energy of the molecule relative to the separated atoms. Such an orbital has one or more no ...
s (Ο€*) occupied by only two electrons. In accordance with Hund's rule, the ground state is
triplet oxygen Triplet oxygen, 3O2, refers to the ''S'' = 1 electronic ground state of molecular oxygen (dioxygen). It is the most stable and common allotrope of oxygen. Molecules of triplet oxygen contain two unpaired electrons, making triplet oxygen an unus ...
with two unpaired electrons in singly occupied orbitals. The
singlet oxygen Singlet oxygen, systematically named dioxygen(singlet) and dioxidene, is a gaseous inorganic chemical with the formula O=O (also written as or ), which is in a quantum state where all electrons are spin paired. It is kinetically unstable at ambi ...
state with one doubly occupied and one empty Ο€* is an excited state with different chemical properties and greater reactivity than the ground state.


Exception

* In 2004, researchers reported the synthesis of 5-dehydro-''m''-xylylene (DMX), the first
organic Organic may refer to: * Organic, of or relating to an organism, a living entity * Organic, of or relating to an anatomical organ Chemistry * Organic matter, matter that has come from a once-living organism, is capable of decay or is the product ...
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
known to violate Hund's rule.


See also

*
Hund's rules 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 ...
(includes this plus 2 other rules) *
High spin Spin states when describing transition metal coordination complexes refers to the potential spin configurations of the central metal's d electrons. For several oxidation states, metals can adopt high-spin and low-spin configurations. The ambiguity o ...
metal complexes


References


External links


A glossary entry hosted on the web site of the Chemistry Department of Purdue University
{{DEFAULTSORT:Hund's Rule Of Maximum Multiplicity Quantum chemistry Rules