In
atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...
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 ...
, 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
Neon is a chemical element with the symbol Ne and atomic number 10. It is a noble gas. Neon is a colorless, odorless, inert monatomic gas under standard conditions, with about two-thirds the density of air. It was discovered (along with krypton ...
atom is , meaning that the 1s, 2s and 2p subshells are occupied by 2, 2 and 6 electrons respectively.
Electronic configurations describe each electron as moving independently in an orbital, in an average field created by all other orbitals. Mathematically, configurations are described by
Slater determinants
In quantum mechanics, a Slater determinant is an expression that describes the wave function of a multi- fermionic system. It satisfies anti-symmetry requirements, and consequently the Pauli principle, by changing sign upon exchange of two elect ...
or
configuration state functions.
According to the laws of
quantum mechanics, for systems with only one electron, a level of energy is associated with each electron configuration and in certain conditions, electrons are able to move from one configuration to another by the emission or absorption of a
quantum
In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizati ...
of energy, in the form of a
photon.
Knowledge of the electron configuration of different atoms is useful in understanding the structure of the
periodic table
The periodic table, also known as the periodic table of the (chemical) elements, is a rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of ch ...
of elements. This is also useful for describing the chemical bonds that hold atoms together. In bulk materials, this same idea helps explain the peculiar properties of
lasers and
semiconductors
A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
.
Shells and subshells
Electron configuration was first conceived under the
Bohr model of the atom, and it is still common to speak of shells and subshells despite the advances in understanding of the
quantum-mechanical
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qua ...
nature of electrons.
An
electron shell is the set of
allowed states that share the same
principal quantum number, ''n'' (the number before the letter in the orbital label), that electrons may occupy. An atom's ''n''th electron shell can accommodate 2''n''
2 electrons, for example, the first shell can accommodate 2 electrons, the second shell 8 electrons, the third shell 18 electrons and so on. The factor of two arises because the allowed states are doubled due to
electron spin—each
atomic orbital admits up to two otherwise identical electrons with opposite spin, one with a spin + (usually denoted by an up-arrow) and one with a spin of − (with a down-arrow).
A
subshell is the set of states defined by a common
azimuthal quantum number, , within a shell. The value of is in the range from 0 to ''n'' − 1. The values = 0, 1, 2, 3 correspond to the s, p, d, and f labels, respectively. For example, the 3d subshell has ''n'' = 3 and = 2. The maximum number of electrons that can be placed in a subshell is given by 2(2 + 1). This gives two electrons in an s subshell, six electrons in a p subshell, ten electrons in a d subshell and fourteen electrons in an f subshell.
The numbers of electrons that can occupy each shell and each subshell arise from the equations of quantum mechanics,
[In formal terms, the ]quantum number
In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be kno ...
s ''n'', and ''m'' arise from the fact that the solutions to the time-independent Schrödinger equation for hydrogen-like atoms are based on spherical harmonics. in particular the
Pauli exclusion principle, which states that no two electrons in the same atom can have the same values of the four
quantum number
In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be kno ...
s.
Notation
Physicists and chemists use a standard notation to indicate the electron configurations of atoms and molecules. For atoms, the notation consists of a sequence of atomic subshell labels (e.g. for
phosphorus the sequence 1s, 2s, 2p, 3s, 3p) with the number of electrons assigned to each subshell placed as a superscript. For example,
hydrogen has one electron in the s-orbital of the first shell, so its configuration is written 1s
1.
Lithium has two electrons in the 1s-subshell and one in the (higher-energy) 2s-subshell, so its configuration is written 1s
2 2s
1 (pronounced "one-s-two, two-s-one").
Phosphorus (
atomic number 15) is as follows: 1s
2 2s
2 2p
6 3s
2 3p
3.
For atoms with many electrons, this notation can become lengthy and so an abbreviated notation is used. The electron configuration can be visualized as the
core electrons, equivalent to the
noble gas of the preceding
period, and the
valence electrons: each element in a period differs only by the last few subshells. Phosphorus, for instance, is in the third period. It differs from the second-period
neon
Neon is a chemical element with the symbol Ne and atomic number 10. It is a noble gas. Neon is a colorless, odorless, inert monatomic gas under standard conditions, with about two-thirds the density of air. It was discovered (along with krypton ...
, whose configuration is 1s
2 2s
2 2p
6, only by the presence of a third shell. The portion of its configuration that is equivalent to neon is abbreviated as
e allowing the configuration of phosphorus to be written as
enbsp;3s
2 3p
3 rather than writing out the details of the configuration of neon explicitly. This convention is useful as it is the electrons in the outermost shell that most determine the chemistry of the element.
For a given configuration, the order of writing the orbitals is not completely fixed since only the orbital occupancies have physical significance. For example, the electron configuration of the
titanium ground state can be written as either
rnbsp;4s
2 3d
2 or
rnbsp;3d
2 4s
2. The first notation follows the order based on the
Madelung rule
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 Electron shell#Subshells, subshells of the lowest available energy, t ...
for the configurations of neutral atoms; 4s is filled before 3d in the sequence Ar, K, Ca, Sc, Ti. The second notation groups all orbitals with the same value of ''n'' together, corresponding to the "spectroscopic" order of orbital energies that is the reverse of the order in which electrons are removed from a given atom to form positive ions; 3d is filled before 4s in the sequence Ti
4+, Ti
3+, Ti
2+, Ti
+, Ti.
The superscript 1 for a singly occupied subshell is not compulsory; for example
aluminium may be written as either
enbsp;3s
2 3p
1 or
enbsp;3s
2 3p. In atoms where a subshell is unoccupied despite higher subshells being occupied (as is the case in some ions, as well as certain neutral atoms shown to deviate from the
Madelung rule
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 Electron shell#Subshells, subshells of the lowest available energy, t ...
), the empty subshell is either denoted with a superscript 0 or left out altogether. For example, neutral
palladium may be written as either or simply , and the
lanthanum(III) ion may be written as either or simply
e
It is quite common to see the letters of the orbital labels (s, p, d, f) written in an italic or slanting typeface, although the
International Union of Pure and Applied Chemistry (IUPAC) recommends a normal typeface (as used here). The choice of letters originates from a now-obsolete system of categorizing
spectral lines
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to ident ...
as "sharp", "principal", "diffuse" and "fundamental" (or "fine"), based on their observed
fine structure
In atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to electron spin and relativistic corrections to the non-relativistic Schrödinger equation. It was first measured precisely for the hydrogen atom ...
: their modern usage indicates orbitals with an
azimuthal quantum number, , of 0, 1, 2 or 3 respectively. After f, the sequence continues alphabetically g, h, i... ( = 4, 5, 6...), skipping j, although orbitals of these types are rarely required.
The electron configurations of molecules are written in a similar way, except that
molecular orbital labels are used instead of atomic orbital labels (see below).
Energy of ground state and excited states
The energy associated to an electron is that of its orbital. The energy of a configuration is often approximated as the sum of the energy of each electron, neglecting the electron-electron interactions. The configuration that corresponds to the lowest electronic energy is called 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. ...
. Any other configuration is an
excited state
In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). Excitation refers to a ...
.
As an example, the ground state configuration of the
sodium atom is 1s
2 2s
2 2p
6 3s
1, as deduced from the Aufbau principle (see below). The first excited state is obtained by promoting a 3s electron to the 3p orbital, to obtain the
1s
2 2s
2 2p
6 3p
1 configuration, abbreviated as the 3p level. Atoms can move from one configuration to another by absorbing or emitting energy. In a
sodium-vapor lamp for example, sodium atoms are excited to the 3p level by an electrical discharge, and return to the ground state by emitting yellow light of wavelength 589 nm.
Usually, the excitation of
valence electrons (such as 3s for sodium) involves energies corresponding to
photons of visible or
ultraviolet light. The excitation of
core electrons is possible, but requires much higher energies, generally corresponding to
X-ray photons. This would be the case for example to excite a 2p electron of sodium to the 3s level and form the excited 1s
2 2s
2 2p
5 3s
2 configuration.
The remainder of this article deals only with the ground-state configuration, often referred to as "the" configuration of an atom or molecule.
History
Irving Langmuir
Irving Langmuir (; January 31, 1881 – August 16, 1957) was an American chemist, physicist, and engineer. He was awarded the Nobel Prize in Chemistry in 1932 for his work in surface chemistry.
Langmuir's most famous publication is the 1919 art ...
was the first to propose in his 1919 article "The Arrangement of Electrons in Atoms and Molecules" in which, building on
Gilbert N. Lewis
Gilbert Newton Lewis (October 23 or October 25, 1875 – March 23, 1946) was an American physical chemist and a Dean of the College of Chemistry at University of California, Berkeley. Lewis was best known for his discovery of the covalent bond a ...
's
cubical atom theory and
Walther Kossel's chemical bonding theory, he outlined his "concentric theory of atomic structure". Langmuir had developed his work on electron atomic structure from other chemists as is shown in the development of the
History of the periodic table
The periodic table is an arrangement of the chemical elements, structured by their atomic number, electron configuration and recurring chemical properties. In the basic form, elements are presented in order of increasing atomic number, in the r ...
and the
Octet rule.
Niels Bohr (1923) incorporated Langmuir’s model that the
periodicity
Periodicity or periodic may refer to:
Mathematics
* Bott periodicity theorem, addresses Bott periodicity: a modulo-8 recurrence relation in the homotopy groups of classical groups
* Periodic function, a function whose output contains values tha ...
in the properties of the elements might be explained by the electronic structure of the atom.
His proposals were based on the then current
Bohr model of the atom, in which the electron shells were orbits at a fixed distance from the nucleus. Bohr's original configurations would seem strange to a present-day chemist:
sulfur
Sulfur (or sulphur in British English) is a chemical element with the symbol S and atomic number 16. It is abundant, multivalent and nonmetallic. Under normal conditions, sulfur atoms form cyclic octatomic molecules with a chemical formula ...
was given as 2.4.4.6 instead of 1s
2 2s
2 2p
6 3s
2 3p
4 (2.8.6). Bohr used 4 and 6 following
Alfred Werner
Alfred Werner (12 December 1866 – 15 November 1919) was a Swiss chemist who was a student at ETH Zurich and a professor at the University of Zurich. He won the Nobel Prize in Chemistry in 1913 for proposing the octahedral configuration of ...
's 1893 paper. In fact, the chemists believed in atoms long before the physicists. Langmuir began his paper referenced above by saying,
«…The problem of the structure of atoms has been attacked mainly by physicists who have given little consideration to the chemical properties which must ultimately be explained by a theory of atomic structure. The vast store of knowledge of chemical properties and relationships, such as is summarized by the Periodic Table, should serve as a better foundation for a theory of atomic structure than the relatively meager experimental data along purely physical lines... These electrons arrange themselves in a series of concentric shells, the first shell containing two electrons, while all other shells tend to hold eight.…»
The valence electrons in the atom were described by
Richard Abegg in 1904.
In 1924,
E. C. Stoner incorporated
Sommerfeld's third quantum number into the description of electron shells, and correctly predicted the shell structure of sulfur to be 2.8.6. However neither Bohr's system nor Stoner's could correctly describe the changes in
atomic spectra in a
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
(the
Zeeman effect).
Bohr was well aware of this shortcoming (and others), and had written to his friend
Wolfgang Pauli in 1923 to ask for his help in saving quantum theory (the system now known as "
old quantum theory"). Pauli hypothesized successfully that the Zeeman effect can be explained as depending only on the response of the outermost (i.e., valence) electrons of the atom. Pauli was able to reproduce Stoner's shell structure, but with the correct structure of subshells, by his inclusion of a fourth quantum number and his
exclusion principle (1925):
The
Schrödinger equation, published in 1926, gave three of the four quantum numbers as a direct consequence of its solution for the hydrogen atom:
this solution yields the atomic orbitals that are shown today in textbooks of chemistry (and above). The examination of atomic spectra allowed the electron configurations of atoms to be determined experimentally, and led to an empirical rule (known as Madelung's rule (1936),
see below) for the order in which atomic orbitals are filled with electrons.
Atoms: Aufbau principle and Madelung rule
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 o ...
(from the
German
German(s) may refer to:
* Germany (of or related to)
**Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ger ...
''Aufbau'', "building up, construction") was an important part of Bohr's original concept of electron configuration. It may be stated as:
:''a maximum of two electrons are put into orbitals in the order of increasing orbital energy: the lowest-energy subshells are filled before electrons are placed in higher-energy orbitals.''
The principle works very well (for the ground states of the atoms) for the known 118 elements, although it is sometimes slightly wrong. The modern form of the aufbau principle describes an order of orbital energies given by Madelung's rule (or Klechkowski's rule). This rule was first stated by
Charles Janet in 1929, rediscovered by
Erwin Madelung in 1936,
and later given a theoretical justification by
V. M. Klechkowski
Vsevolod Mavrikievich Klechkovsky (russian: Все́волод Маври́киевич Клечко́вский; also transliterated as Klechkovskii and Klechkowski; November 28, 1900 – May 2, 1972) was a Soviet and Russian Agriculture, agricult ...
:
#Subshells are filled in the order of increasing ''n'' + .
#Where two subshells have the same value of ''n'' + , they are filled in order of increasing ''n''.
This gives the following order for filling the orbitals:
:1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, (8s, , 6f, 7d, 8p, and 9s)
In this list the subshells in parentheses are not occupied in the ground state of the heaviest atom now known (
Og, ''Z'' = 118).
The aufbau principle can be applied, in a modified form, to the
proton
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s and
neutrons in the
atomic nucleus, as in the
shell model of
nuclear physics and
nuclear chemistry.
Periodic table
The form of the
periodic table
The periodic table, also known as the periodic table of the (chemical) elements, is a rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of ch ...
is closely related to the atomic electron configuration for each element. For example, all the elements of
group 2 The term Group 2 may refer to:
* Alkaline earth metal, a chemical element classification
* Astronaut Group 2, also known as The New Nine, the second group of astronauts selected by NASA in 1962
* Group 2 (racing), an FIA classification for cars in a ...
(the table's second column) have an electron configuration of
nbsp;''n''s (where
is a
noble gas configuration), and have notable similarities in their chemical properties. The periodicity of the periodic table in terms of
periodic table block
A block of the periodic table is a set of elements unified by the atomic orbitals their valence electrons or vacancies lie in. The term appears to have been first used by Charles Janet. Each block is named after its characteristic orbital: s-bloc ...
s is due to the number of electrons (2, 6, 10, and 14) needed to fill s, p, d, and f subshells. These blocks appear as the rectangular sections of the periodic table. The exception is
helium, which despite being an s-block atom is conventionally placed with the other
noble gasses in the p-block due to its chemical inertness, a consequence of its full outer shell.
The electrons in the valence (outermost) shell largely determine each element's chemical properties. The similarities in the chemical properties were remarked on more than a century before the idea of electron configuration.
Shortcomings of the aufbau principle
The aufbau principle rests on a fundamental postulate that the order of orbital energies is fixed, both for a given element and between different elements; in both cases this is only approximately true. It considers atomic orbitals as "boxes" of fixed energy into which can be placed two electrons and no more. However, the energy of an electron "in" an atomic orbital depends on the energies of all the other electrons of the atom (or ion, or molecule, etc.). There are no "one-electron solutions" for systems of more than one electron, only a set of many-electron solutions that cannot be calculated exactly (although there are mathematical approximations available, such as the
Hartree–Fock method).
The fact that the aufbau principle is based on an approximation can be seen from the fact that there is an almost-fixed filling order at all, that, within a given shell, the s-orbital is always filled before the p-orbitals. In a
hydrogen-like atom, which only has one electron, the s-orbital and the p-orbitals of the same shell have exactly the same energy, to a very good approximation in the absence of external electromagnetic fields. (However, in a real hydrogen atom, the
energy levels are slightly split by the magnetic field of the nucleus, and by the
quantum electrodynamic effects of the
Lamb shift.)
Ionization of the transition metals
The naïve application of the aufbau principle leads to a well-known
paradox (or apparent paradox) in the basic chemistry of the
transition metals.
Potassium and
calcium appear in the periodic table before the transition metals, and have electron configurations
rnbsp;4s and
rnbsp;4s respectively, i.e. the 4s-orbital is filled before the 3d-orbital. This is in line with Madelung's rule, as the 4s-orbital has ''n'' + = 4 (''n'' = 4, = 0) while the 3d-orbital has ''n'' + = 5 (''n'' = 3, = 2). After calcium, most neutral atoms in the first series of transition metals (
scandium through
zinc) have configurations with two 4s electrons, but there are two exceptions.
Chromium
Chromium is a chemical element with the symbol Cr and atomic number 24. It is the first element in group 6. It is a steely-grey, lustrous, hard, and brittle transition metal.
Chromium metal is valued for its high corrosion resistance and hardne ...
and
copper have electron configurations
rnbsp;3d 4s and
rnbsp;3d 4s respectively, i.e. one electron has passed from the 4s-orbital to a 3d-orbital to generate a half-filled or filled subshell. In this case, the usual explanation is that "half-filled or completely filled subshells are particularly stable arrangements of electrons". However this is not supported by the facts, as
tungsten (W) has a Madelung-following d s configuration and not d s, and
niobium
Niobium is a chemical element with chemical symbol Nb (formerly columbium, Cb) and atomic number 41. It is a light grey, crystalline, and ductile transition metal. Pure niobium has a Mohs hardness rating similar to pure titanium, and it has sim ...
(Nb) has an anomalous d s configuration that does not give it a half-filled or completely filled subshell.
The apparent paradox arises when electrons are ''removed'' from the transition metal atoms to form
ions. The first electrons to be ionized come not from the 3d-orbital, as one would expect if it were "higher in energy", but from the 4s-orbital. This interchange of electrons between 4s and 3d is found for all atoms of the first series of transition metals. The configurations of the neutral atoms (K, Ca, Sc, Ti, V, Cr, ...) usually follow the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, ...; however the successive stages of ionization of a given atom (such as Fe
4+, Fe
3+, Fe
2+, Fe
+, Fe) usually follow the order 1s, 2s, 2p, 3s, 3p, 3d, 4s, ...
This phenomenon is only paradoxical if it is assumed that the energy order of atomic orbitals is fixed and unaffected by the nuclear charge or by the presence of electrons in other orbitals. If that were the case, the 3d-orbital would have the same energy as the 3p-orbital, as it does in hydrogen, yet it clearly does not. There is no special reason why the Fe ion should have the same electron configuration as the chromium atom, given that
iron has two more protons in its nucleus than chromium, and that the chemistry of the two species is very different. Melrose and
Eric Scerri have analyzed the changes of orbital energy with orbital occupations in terms of the two-electron repulsion integrals of the
Hartree–Fock method of atomic structure calculation. More recently Scerri has argued that contrary to what is stated in the vast majority of sources including the title of his previous article on the subject, 3d orbitals rather than 4s are in fact preferentially occupied.
In chemical environments, configurations can change even more: Th
3+ as a bare ion has a configuration of
nnbsp;5f
1, yet in most Th
III compounds the thorium atom has a 6d
1 configuration instead. Mostly, what is present is rather a superposition of various configurations.
For instance, copper metal is poorly described by either an
rnbsp;3d 4s or an
rnbsp;3d 4s configuration, but is rather well described as a 90% contribution of the first and a 10% contribution of the second. Indeed, visible light is already enough to excite electrons in most transition metals, and they often continuously "flow" through different configurations when that happens (copper and its group are an exception).
Similar ion-like 3d 4s configurations occur in
transition metal complexes as described by the simple
crystal field theory Crystal field theory (CFT) describes the breaking of degeneracies of electron orbital states, usually ''d'' or ''f'' orbitals, due to a static electric field produced by a surrounding charge distribution (anion neighbors). This theory has been used ...
, even if the metal has
oxidation state 0. For example,
chromium hexacarbonyl
Chromium carbonyl, also known as chromium hexacarbonyl, is the chemical compound with the formula Cr( CO)6. At room temperature the solid is stable to air, although it does have a high vapor pressure and sublimes readily. Cr(CO)6 is zerovalent ...
can be described as a chromium atom (not ion) surrounded by six
carbon monoxide ligands. The electron configuration of the central chromium atom is described as 3d with the six electrons filling the three lower-energy d orbitals between the ligands. The other two d orbitals are at higher energy due to the crystal field of the ligands. This picture is consistent with the experimental fact that the complex is
diamagnetic, meaning that it has no unpaired electrons. However, in a more accurate description using
molecular orbital theory, the d-like orbitals occupied by the six electrons are no longer identical with the d orbitals of the free atom.
Other exceptions to Madelung's rule
There are several more exceptions to
Madelung's rule among the heavier elements, and as atomic number increases it becomes more and more difficult to find simple explanations such as the stability of half-filled subshells. It is possible to predict most of the exceptions by Hartree–Fock calculations, which are an approximate method for taking account of the effect of the other electrons on orbital energies. Qualitatively, for example, we can see that the 4d elements have the greatest concentration of Madelung anomalies, because the 4d–5s gap is larger than the 3d–4s and 5d–6s gaps.
For the heavier elements, it is also necessary to take account of the
effects of special relativity on the energies of the atomic orbitals, as the inner-shell electrons are moving at speeds approaching the
speed of light. In general, these relativistic effects tend to decrease the energy of the s-orbitals in relation to the other atomic orbitals. This is the reason why the 6d elements are predicted to have no Madelung anomalies apart from lawrencium (for which relativistic effects stabilise the p
1/2 orbital as well and cause its occupancy in the ground state), as relativity intervenes to make the 7s orbitals lower in energy than the 6d ones.
The table below shows the configurations of the f-block (green) and d-block (blue) atoms. It shows the ground state configuration in terms of orbital occupancy, but it does not show the ground state in terms of the sequence of orbital energies as determined spectroscopically. For example, in the transition metals, the 4s orbital is of a higher energy than the 3d orbitals; and in the lanthanides, the 6s is higher than the 4f and 5d. The ground states can be seen in the
Electron configurations of the elements (data page)
This page shows the electron configurations of the neutral gaseous atoms in their ground states. For each atom the subshells are given first in concise form, then with all subshells written out, followed by the number of electrons per shell. Elect ...
. However this also depends on the charge: a
calcium atom has 4s lower in energy than 3d, but a Ca
2+ cation has 3d lower in energy than 4s. In practice the configurations predicted by the Madelung rule are at least close to the ground state even in these anomalous cases. The empty f orbitals in lanthanum, actinium, and thorium contribute to chemical bonding,
as do the empty p orbitals in transition metals.
Vacant s, d, and f orbitals have been shown explicitly, as is occasionally done, to emphasise the filling order and to clarify that even orbitals unoccupied in the ground state (e.g.
lanthanum 4f or
palladium 5s) may be occupied and bonding in chemical compounds. (The same is also true for the p-orbitals, which are not explicitly shown because they are only actually occupied for lawrencium in gas-phase ground states.)
The various anomalies describe the free atoms and do not necessarily predict chemical behavior. Thus for example neodymium typically forms the +3 oxidation state, despite its configuration that if interpreted naïvely would suggest a more stable +2 oxidation state corresponding to losing only the 6s electrons. Contrariwise, uranium as is not very stable in the +3 oxidation state either, preferring +4 and +6.
The electron-shell configuration of elements beyond
hassium has not yet been empirically verified, but they are expected to follow Madelung's rule without exceptions until
element 120.
Element 121 should have the anomalous configuration , having a p rather than a g electron. Electron configurations beyond this are tentative and predictions differ between models, but Madelung's rule is expected to break down due to the closeness in energy of the , 6f, 7d, and 8p
1/2 orbitals.
That said, the filling sequence 8s, , 6f, 7d, 8p is predicted to hold approximately, with perturbations due to the huge spin-orbit splitting of the 8p and 9p shells, and the huge relativistic stabilisation of the 9s shell.
Open and closed shells
In the context of
atomic orbitals, an open shell is a
valence shell which is not completely filled with
electrons or that has not given all of its valence electrons through
chemical bonds with other
atoms or
molecules during a chemical reaction. Conversely a closed shell is obtained with a completely filled valence shell. This configuration is very stable.
For molecules, "open shell" signifies that there are unpaired electrons. In
molecular orbital theory, this leads to molecular orbitals that are singly occupied. In
computational chemistry
Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into computer programs, to calculate the structures and properties of m ...
implementations of molecular orbital theory, open-shell molecules have to be handled by either the
restricted open-shell Hartree–Fock method or the
unrestricted Hartree–Fock method. Conversely a closed-shell configuration corresponds to a state where all
molecular orbitals are either doubly occupied or empty (a
singlet state). Open shell molecules are more difficult to study computationally
Noble gas configuration
Noble gas configuration is the electron configuration of noble gases. The basis of all
chemical reactions is the tendency of
chemical elements
A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler sub ...
to acquire stability.
Main-group atoms generally obey the
octet rule, while
transition metals generally obey the
18-electron rule. The
noble gases (
He,
Ne,
Ar,
Kr,
Xe,
Rn) are less reactive than other elements because they already have a noble gas configuration.
Oganesson is predicted to be more reactive due to relativistic effects for heavy atoms.
:
Every system has the tendency to acquire the state of stability or a state of minimum energy, and so
chemical elements
A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler sub ...
take part in
chemical reactions to acquire a stable electronic configuration similar to that of its nearest
noble gas. An example of this tendency is two
hydrogen (H) atoms reacting with one
oxygen (O) atom to form water (H
2O). Neutral atomic
hydrogen has 1 electron in the valence shell, and on formation of water it acquires a share of a second electron coming from oxygen, so that its configuration is similar to that of its nearest
noble gas helium with 2 electrons in the valence shell. Similarly, neutral atomic oxygen has 6 electrons in the valence shell, and acquires a share of two electrons from the two hydrogen atoms, so that its configuration is similar to that of its nearest noble gas
neon
Neon is a chemical element with the symbol Ne and atomic number 10. It is a noble gas. Neon is a colorless, odorless, inert monatomic gas under standard conditions, with about two-thirds the density of air. It was discovered (along with krypton ...
with 8 electrons in the valence shell.
Electron configuration in molecules
In
molecules, the situation becomes more complex, as each molecule has a different orbital structure. The
molecular orbitals are labelled according to their
symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...
, rather than the
atomic orbital labels used for atoms and monatomic ions: hence, the electron configuration of the
dioxygen molecule, O, is written 1σ 1σ 2σ 2σ 3σ 1π 1π,
[Miessler G.L. and Tarr D.A. ''Inorganic Chemistry'' (2nd ed., Prentice Hall 1999) p.118 ] or equivalently 1σ 1σ 2σ 2σ 1π 3σ 1π.
The term 1π represents the two electrons in the two degenerate π*-orbitals (antibonding). From
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 e ...
, these electrons have parallel spins in 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. ...
, and so dioxygen has a net
magnetic moment (it is
paramagnetic). The explanation of the paramagnetism of dioxygen was a major success for
molecular orbital theory.
The electronic configuration of polyatomic molecules can change without absorption or emission of a photon through
vibronic couplings.
Electron configuration in solids
In a
solid, the electron states become very numerous. They cease to be discrete, and effectively blend into continuous ranges of possible states (an
electron band). The notion of electron configuration ceases to be relevant, and yields to
band theory
In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called ''band gaps'' or '' ...
.
Applications
The most widespread application of electron configurations is in the rationalization of chemical properties, in both inorganic and organic chemistry. In effect, electron configurations, along with some simplified form of
molecular orbital theory, have become the modern equivalent of the
valence
Valence or valency may refer to:
Science
* Valence (chemistry), a measure of an element's combining power with other atoms
* Degree (graph theory), also called the valency of a vertex in graph theory
* Valency (linguistics), aspect of verbs rel ...
concept, describing the number and type of chemical bonds that an atom can be expected to form.
This approach is taken further in
computational chemistry
Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into computer programs, to calculate the structures and properties of m ...
, which typically attempts to make quantitative estimates of chemical properties. For many years, most such calculations relied upon the "
linear combination of atomic orbitals" (LCAO) approximation, using an ever-larger and more complex
basis set of atomic orbitals as the starting point. The last step in such a calculation is the assignment of electrons among the molecular orbitals according to the Aufbau principle. Not all methods in calculational chemistry rely on electron configuration:
density functional theory (DFT) is an important example of a method that discards the model.
For atoms or molecules with more than one electron, the motion of electrons are
correlated and such a picture is no longer exact. A very large number of electronic configurations are needed to exactly describe any multi-electron system, and no energy can be associated with one single configuration. However, the electronic wave function is usually dominated by a very small number of configurations and therefore the notion of electronic configuration remains essential for multi-electron systems.
A fundamental application of electron configurations is in the interpretation of
atomic spectra. In this case, it is necessary to supplement the electron configuration with one or more
term symbols, which describe the different energy levels available to an atom. Term symbols can be calculated for any electron configuration, not just the ground-state configuration listed in tables, although not all the energy levels are observed in practice. It is through the analysis of atomic spectra that the ground-state electron configurations of the elements were experimentally determined.
See also
*
Born–Oppenheimer approximation
*
Electron configurations of the elements (data page)
This page shows the electron configurations of the neutral gaseous atoms in their ground states. For each atom the subshells are given first in concise form, then with all subshells written out, followed by the number of electrons per shell. Elect ...
*
Periodic table (electron configurations)
* Configurations of elements 109 and above are not available. Predictions from reliable sources have been used for these elements.
* electron numbers indicate subshells that are filled to their maximum.
* The bracketed noble gas symbols on the lef ...
*
Molecular term symbol
*
HOMO/LUMO
In chemistry, HOMO and LUMO are types of molecular orbitals. The acronyms stand for ''highest occupied molecular orbital'' and ''lowest unoccupied molecular orbital'', respectively. HOMO and LUMO are sometimes collectively called the ''frontie ...
*
Group (periodic table)
*
d electron count
*
Extended periodic table – discusses the limits of the periodic table
*
Spherical harmonics
*
Unpaired electron
*
Octet rule
*
Valence shell
Notes
External links
What does an atom look like? Configuration in 3D
{{Use dmy dates, date=April 2017
Atomic physics
Chemical properties
Electron states
Molecular physics
Quantum chemistry
Theoretical chemistry