In
atomic physicsAtomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and...
and
quantum chemistryQuantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. The description of the electronic behavior of atoms and molecules as pertaining to their reactivity is one of the applications of quantum...
,
electron configuration is the arrangement of
electronAn electron is a subatomic particle that carries a negative electric charge. It has no known substructure and is believed to be a point particle. An electron has a mass that is approximately 1836 times less than that of the proton. The intrinsic angular momentum of the electron is a half integer...
s of an
atomThe atom is a basic unit of matter consisting of a dense, central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
, a
moleculeA molecule is defined as an electrically neutral group of at least two atoms in a definite arrangement held together by very strong chemical bonds. Molecules are distinguished from polyatomic ions in this strict sense...
, or other physical structure. It concerns the way electrons can be distributed in the orbitals of the given system (
atomicAn atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons, in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. These functions...
or
molecularIn chemistry, a molecular orbital is a mathematical function that describes the wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The use of the term...
for instance).
Like other
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s, the electron is subject to the laws of
quantum mechanicsQuantum mechanics is a set of principles describing the physical reality at the atomic level of matter and the subatomic . These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation...
, and exhibits both particle-like and wave-like nature. Formally, the
quantum stateIn quantum physics, a quantum state is a mathematical object that fully describes a quantum system. One typically imagines some experimental apparatus and procedure which "prepares" this quantum state; the mathematical object then reflects the setup of the apparatus. Quantum states can be...
of a particular electron is defined by its wave function, a
complex-valuedA complex number, in mathematics, is a number comprising a real number and an imaginary number; it can be written in the form a + bi, where a and b are real numbers, and i is the standard imaginary unit, having the property that i
2 = −1...
function of space and time. According to the
Copenhagen interpretationThe Copenhagen interpretation is an interpretation of quantum mechanics. A key feature of quantum mechanics is that the state of every particle is described by a wavefunction, which is a mathematical representation used to calculate the probability for it to be found in a location or a state of...
of quantum mechanics, the position of a particular electron is not well defined until an act of measurement causes it to be detected. The probability that the act of measurement will detect the electron at a particular point in space is proportional to the square of the absolute value of the wavefunction at that point.
An energy is associated to each electron configuration and, upon certain conditions, electrons are able to move from one orbital to another by emission or absorption of a
quantumIn physics, a quantum is the minimum unit of any physical entity involved in an interaction. An example of an entity that is quantized is the energy transfer of elementary particles of matter and of photons and other bosons...
of energy, in the form of a
photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic field and the basic "unit" of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
.
Knowledge of the electron configuration of different atoms is useful in understanding the structure of the
periodic tableThe periodiс table of the chemical elements is a tabular display of the chemical elements...
of elements. The concept 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.
Shells and subshells
Electron configuration was first conceived of under the
Bohr modelIn atomic physics, the Bohr model, devised by Niels Bohr, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing...
of the atom, and it is still common to speak of shells and subshells despite the advances in understanding of the
quantum-mechanicalQuantum mechanics is a set of principles describing the physical reality at the atomic level of matter and the subatomic . These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation...
nature of electrons.
An electron shell is the set of
allowed statesIn quantum physics, a quantum state is a mathematical object that fully describes a quantum system. One typically imagines some experimental apparatus and procedure which "prepares" this quantum state; the mathematical object then reflects the setup of the apparatus. Quantum states can be...
electrons may occupy which share the same
principal quantum numberIn atomic physics, the principal quantum number symbolized as n is the firstof a set of quantum numbers of an atomic orbital.-Derivation:There are a set of quantum numbers associated with the energy states of the atom...
,
n (the number before the letter in the orbital label). An electron shell can accommodate 2
n2 electrons,
i.e. the first shell can accommodate 2 electrons, the second shell 8 electrons, the third shell 18 electrons,
etc. The factor of two arises because the allowed states are doubled due to
electron spinIn particle physics and quantum mechanics, spin is a fundamental characteristic property of elementary particles including the force carriers , composite particles , and atomic nuclei....
—each
atomic orbitalAn atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons, in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. These functions...
admits up to two otherwise identical electrons with opposite spin, one with a spin +1/2 (usually noted by an up-arrow) and one with a spin -1/2 (with a down-arrow).
A subshell is the set of states defined by a common
azimuthal quantum numberThe Azimuthal quantum number symbolized as ℓ is a quantum number for an atomic orbital that determines its orbital angular momentum...
,
l, within a shell. The values
l = 0, 1, 2, 3 correspond to the
s,
p,
d, and
f labels, respectively. The number of electrons which can be placed in a subshell is given by 2(2
l + 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 particular the Pauli exclusion principle, which states that no two electrons in the same atom can have the same values of the four
quantum numberQuantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
s.
Notation
Physicists and chemists use a standard notation to describe the electron configurations of atoms and molecules. For atoms, the notation consists of a string of atomic orbital labels (eg, 1s, 2p, 3d, 4f) with the number of electrons assigned to each orbital (or set of orbitals sharing the same label) placed as a superscript. For example,
hydrogenHydrogen is the chemical element with atomic number 1. It is represented by the symbol H. At standard temperature and pressure, hydrogen is a colorless, odorless, nonmetallic, tasteless, highly flammable diatomic gas with the molecular formula H
2...
has one electron in the s-orbital of the first shell, so its configuration is written 1s
1.
LithiumLithium is a soft, silver-white metal that belongs to the alkali metal group of chemical elements. It is represented by the symbol Li, and it has the atomic number three. Under standard conditions it is the lightest metal and the least dense solid element. Like all alkali metals, lithium is highly...
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").
PhosphorusPhosphorus is the chemical element that has the symbol P and atomic number 15. A multivalent nonmetal of the nitrogen group, phosphorus is commonly found in inorganic phosphate rocks. Elemental phosphorus exists in two major forms - white phosphorus and red phosphorus...
(
atomic numberIn chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...
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, noting that the first few subshells are identical to those of one or another of the
noble gasThe noble gases are a group of chemical elements with very similar properties: under standard conditions, they are all odorless, colorless, monatomic gases, with a very low chemical reactivity...
es. Phosphorus, for instance, differs from
neonNeon is the chemical element that has the symbol Ne and atomic number 10. Although a very common element in the universe, it is rare on Earth. A colorless, inert noble gas under standard conditions, neon gives a distinct reddish-orange glow when used in discharge tubes and neon lamps...
(1s
2 2s
2 2p
6) only by the presence of a third shell. Thus, the electron configuration of neon is pulled out, and phosphorus is written as follows: [Ne] 3s
2 3p
3. This convention is useful as it is the electrons in the outermost shell which most determine the chemistry of the element.
The order of writing the orbitals is not completely fixed: some sources group all orbitals with the same value of
n together, while other sources (as here) follow the order given by Madelung's rule. Hence the electron configuration of iron can be written as [Ar] 3d
6 4s
2 (keeping the 3d-electrons with the 3s- and 3p-electrons which are implied by the configuration of argon) or as [Ar] 4s
2 3d
6 (following the Aufbau principle, see below).
The superscript 1 for a singly-occupied orbital is not compulsory. 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 ChemistryThe International Union of Pure and Applied Chemistry is a non-governmental organization established in 1919 as the successor of the International Congress of Applied Chemistry for the advancement of chemistry. Its members are national chemistry societies...
(IUPAC) recommends a normal typeface (as used here). The choice of letters originates from a now-obsolete system of categorizing spectral lines as "sharp", "principal", "diffuse" and "fine", based on their observed
fine structureIn atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to first order relativistic corrections.The gross structure of line spectra is the line spectra predicted by non-relativistic electrons with no spin. For a hydrogenic atom, the gross structure energy...
: their modern usage indicates orbitals with an
azimuthal quantum numberThe Azimuthal quantum number symbolized as ℓ is a quantum number for an atomic orbital that determines its orbital angular momentum...
,
l, of 0, 1, 2 or 3 respectively. After "f", the sequence continues alphabetically "g", "h", "i"... (
l = 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 orbitalIn chemistry, a molecular orbital is a mathematical function that describes the wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The use of the term...
labels are used instead of atomic orbital labels (see below).
Energy — Ground State - Excited state
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. Any other configuration is an excited state.
History
Niels BohrNiels Henrik David Bohr was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...
was the first to propose (1923) that the
periodicityPeriodicity is the quality of occurring at regular intervals or periods and can occur in different contexts:In timing devices:* A clock marks time at periodic intervals.* A metronome ticks at periodic intervals of time....
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 modelIn atomic physics, the Bohr model, devised by Niels Bohr, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing...
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:
sulfurSulfur or sulphur is the chemical element that has the atomic number 16. It is denoted with the symbol S. It is an abundant, multivalent non-metal. Sulfur, in its native form, is a yellow crystalline solid. In nature, it can be found as the pure element and as sulfide and sulfate minerals...
was given as 2.4.4.6 instead of 1s
2 2s
2 2p
6 3s
2 3p
4 (2.8.6).
The following year,
E. C. StonerEdmund Clifton Stoner was a British theoretical physicist. He is principally known for his work on the origin and nature of magnetism, including the collective electron theory of ferromagnetism and the Stoner criterion for ferromagnetism.-Biography:Stoner began to attend Cambridge in 1918,...
incorporated
Sommerfeld'sArnold Johannes Wilhelm Sommerfeld was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics...
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 spectraThe emission spectrum of an element or compound is the relative intensity of electromagnetic radiation of each frequency emitted by atoms or molecules of that element or compound when they are excited....
in a
magnetic fieldMagnetic fields surround magnetic materials and electric currents and are detected by the force they exert on other magnetic materials and moving electric charges...
(the
Zeeman effectThe Zeeman effect is the splitting of a spectral line into several components in the presence of a static magnetic field. It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field...
).
Bohr was well aware of this shortcoming (and others), and had written to his friend
Wolfgang PauliWolfgang Ernst Pauli was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after being nominated by Albert Einstein, he received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or...
to ask for his help in saving quantum theory (the system now known as "
old quantum theoryThe old quantum theory was a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was a collection of heuristic prescriptions which are now understood to be the first quantum corrections to classical mechanics...
"). Pauli realized that the Zeeman effect must be due only to the outermost electrons of the atom, and 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 principleThe Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. It states that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement of this principle is that, for two identical fermions, the total wave function...
(1925):
It should be forbidden for more than one electron with the same value of the main quantum number n to have the same value for the other three quantum numbers k [l], j [ml] and m [ms].
The
Schrödinger equationIn physics, specifically quantum mechanics, the Schrödinger equation is an equation that describes how the quantum state of a physical system changes in time...
, 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 which 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.
Aufbau principle
The
Aufbau principleThe Aufbau principle is used to determine the electron configuration of an atom, molecule or ion. The principle postulates a hypothetical process in which an atom is "built up" by progressively adding electrons...
(from the
GermanGerman is a West Germanic language, thus related to and classified alongside English and Dutch. It is one of the world's major languages and the most widely spoken first language in the European Union. Around the world, German is spoken by approximately 105 million native speakers and also by...
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 orbitals are filled before electrons are placed in higher-energy orbitals.
The principle works very well (for the ground states of the atoms) for the first 18 elements, then increasingly less well for the following 100 elements. The modern form of the Aufbau principle describes an order of orbital energies given by Madelung's rule, first stated by
Erwin MadelungErwin Madelung was a German physicist. He was born in 1881 in Frankfurt/Main. His father was the surgeon Otto Wilhelm Madelung....
in 1936.
-
- Orbitals are filled in the order of increasing n+l;
- Where two orbitals have the same value of n+l, 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, and 7p
The Aufbau principle can be applied, in a modified form, to the
protonThe proton is a subatomic particle with an electric charge of +1 elementary charge. It is found in the nucleus of each atom but is also stable by itself and has a second identity as the hydrogen ion, H
+...
s and
neutronThe neutron is a subatomic particle with no net electric charge and a mass slightly larger than that of a proton.Neutron are usually found in atomic nuclei. The nuclei of most atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of protons in a...
s in the
atomic nucleusThe nucleus is the very dense region consisting of nucleons at the center of an atom. Almost all of the mass in an atom is made up from the protons and neutrons in the nucleus, with a very small contribution from the orbiting electrons....
, as in the
shell modelIn nuclear physics, the nuclear shell model is a model of the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels. The model was developed in 1949 following independent work by several physicists, most notably Eugene Paul...
of
nuclear physicsNuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei.The most commonly known applications of nuclear physics are nuclear power and nuclear weapons, but the research has provided wider applications, including those in medicine , materials...
.
The periodic table
The form of the
periodic tableThe periodiс table of the chemical elements is a tabular display of the chemical elements...
is closely related to the electron configuration of the atoms of the elements. For example, all the elements of
group 2The 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...
have an electron configuration of [E]
ns (where [E] is an inert gas configuration), and have notable similarities in their chemical properties. The outermost electron shell is often referred to as the "valence shell" and (to a first approximation) determines the chemical properties. It should be remembered that the similarities in the chemical properties were remarked more than a century before the idea of electron configuration, It is not clear how far Madelung's rule
explains (rather than simply describes) the periodic table, although some properties (such as the common +2
oxidation stateIn chemistry, the oxidation state is an indicator of the degree of oxidation of an atom in a chemical compound. The formal oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic. Oxidation states are typically represented by...
in the first row of the transition metals) would obviously be different with a different order of orbital filling.
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: neither of these is true (although they are approximately true enough for the principle to be useful). 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 which cannot be calculated exactly (although there are mathematical approximations available, such the
Hartree–Fock methodIn computational physics and chemistry, the Hartree–Fock method is an approximate method for the determination of the ground-state wave function and ground-state energy of a quantum many-body system....
).
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 atomA hydrogen-like atom is an atom with one electron and thus is isoelectronic with hydrogen. Except for the hydrogen atom itself these atoms carry the positive charge e, where Z is the atomic number of the atom. Examples of hydrogen-like ions are He+, Li2+, Be3+...
, 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 shiftIn physics, the Lamb shift, named after Willis Lamb , is a small difference in energy between two energy levels and of the hydrogen atom in quantum electrodynamics . According to Dirac, the and orbitals should have the same energies. However, the interaction between the electron and the vacuum...
).
Ionization of the transition metals
The naive application of the Aufbau principle leads to a well-known
paradoxA paradox is a statement or group of statements that leads to a contradiction or a situation which defies intuition. The term is also used for an apparent contradiction that actually expresses a non-dual truth...
(or apparent paradox) in the basic chemistry of the
transition metalThe term transition metal has two possible meanings:*In the past it referred to any element in the d-block of the periodic table, which includes groups 3 to 12 on the periodic table...
s.
PotassiumPotassium is the chemical element with the symbol K , atomic number 19, and atomic mass 39.0983. Potassium was first isolated from potash...
and
calciumCalcium is the chemical element with the symbol Ca and atomic number 20. It has an atomic mass of 40.078 amu. Calcium is a soft grey alkaline earth metal, and is the fifth most abundant element by mass in the Earth's crust...
appear in the periodic table before the transition metals, and have electron configurations [Ar] 4s and [Ar] 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+
l = 4 (
n = 4,
l = 0) while the 3d-orbital has
n+
l = 5 (
n = 3,
l = 2). However,
chromiumChromium is a chemical element which has the symbol Cr and atomic number 24, first element in Group 6. It is a steely-gray, lustrous, hard metal that takes a high polish and has a high melting point. It is also odourless, tasteless, and malleable...
and
copperCopper is a chemical element with the symbol Cu and atomic number 29.It is a ductile metal with very high thermal and electrical conductivity. Pure copper is rather soft and malleable and a freshly-exposed surface has a pinkish or peachy color...
have electron configurations [Ar] 3d 4s and [Ar] 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".
The apparent paradox arises when electrons are
removed from the transition metal atoms to form
ionAn ion is an atom or molecule where the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge...
s. 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. The same is true when chemical compounds are formed. Chromium hexacarbonyl can be described as a chromium atom (not ion, it is in the
oxidation stateIn chemistry, the oxidation state is an indicator of the degree of oxidation of an atom in a chemical compound. The formal oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic. Oxidation states are typically represented by...
0) surrounded by six
carbon monoxideCarbon monoxide is a colorless, odorless and tasteless gas, yet very toxic to humans. It consists of one carbon atom and one oxygen atom, connected by a covalent double bond and a dative covalent bond...
ligandIn chemistry, a ligand is either an atom, ion, or molecule that binds to a central metal-atom to produce a coordination complex. The bonding between the metal and ligand generally involves formal donation of one or more of the ligand's electron pairs. The metal-ligand bonding ranges from covalent...
s: it is diamagnetic, and the electron configuration of the central chromium atom is described as 3d, i.e. the electron which was in the 4s-orbital in the free atom has passed into a 3d-orbital on forming the compound. This interchange of electrons between 4s and 3d is universal among the first series of the transition metals.
The phenomenon is only paradoxical if it is assumed that the energies of atomic orbitals are fixed and unaffected 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 doesn't. There is no special reason why the Fe ion should have the same electron configuration as the chromium atom, given that
ironIron is a metallic chemical element with the symbol Fe and atomic number 26. Iron is a group 8 and period 4 element and is therefore classified as a transition metal. Iron and iron alloys are by far the most common metals and the most common ferromagnetic materials in everyday use...
has two more protons in its nucleus than chromium and that the chemistry of the two species is very different. When care is taken to compare "like with like", the paradox disappears.
Other exceptions to Madelung's rule
There are several more exceptions to Madelung's rule among the heavier elements, and it is more and more difficult to resort to 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. For the heavier elements, it is also necessary to take account of the
effects of Special RelativityRelativistic quantum chemistry invokes quantum chemical and relativistic mechanical arguments to explain elemental properties and structure, especially for heavy elements of the periodic table....
on the energies of the atomic orbitals, as the inner-shell electrons are moving at speeds approaching the
speed of lightIn physics, the speed of light is a physical constant, the speed at which electromagnetic radiation, such as light, travels in free space . Its value is 299,792,458 metres per second...
. In general, these relativistic effects tend to decrease the energy of the s-orbitals in relation to the other atomic orbitals.
Electron shells filled in violation of Madelung's rule (red)
| Period 5 |
|
Period 6 |
|
Period 7 |
| Element |
Z |
Electron Configuration |
|
Element |
Z |
Electron Configuration |
|
Element |
Z |
Electron Configuration |
| |
|
LanthanumLanthanum is a chemical element with the symbol La and atomic number 57.Lanthanum is a silvery white metallic element that belongs to group 3 of the periodic table and is a lanthanoid. It is found in some rare-earth minerals, usually in combination with cerium and other rare earth elements...
|
57 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 5d1 |
|
Actinium Actinium is a radioactive chemical element with the symbol Ac and atomic number 89, which was discovered in 1899. It was the first non-primordial radioactive element to be isolated. Polonium, radium and radon were observed before actinium, but they were not isolated until 1902...
|
89 |
[RnRadon is a chemical element with symbol Rn and atomic number 86. It is a radioactive, colorless, odorless, tasteless noble gas, occurring naturally as the decay product of radium. It is one of the heaviest substances that remains a gas under normal conditions and is considered to be a health...
] 7s2 6d1 |
| |
|
Cerium Cerium is a chemical element with the symbol Ce and atomic number 58. It is a soft, silvery, ductile metal which easily oxidizes in air. Cerium was named after the dwarf planet . Cerium is the most abundant of the rare earth elements, making up about 0.0046% of the Earth's crust by weight. It is...
|
58 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f1 5d1 |
|
ThoriumThorium is a chemical element with the symbol Th and atomic number 90. It is a naturally occurring, slightly radioactive metal. Thorium is estimated to be about three to four times more abundant than uranium in the earth's crust...
|
90 |
[RnRadon is a chemical element with symbol Rn and atomic number 86. It is a radioactive, colorless, odorless, tasteless noble gas, occurring naturally as the decay product of radium. It is one of the heaviest substances that remains a gas under normal conditions and is considered to be a health...
] 7s2 6d2 |
| |
|
Praseodymium Praseodymium is a chemical element that has the symbol Pr and atomic number 59.-Physical:Praseodymium is a soft, silvery, malleable and ductile metal in the lanthanoid group...
|
59 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f3 |
|
Protactinium Protactinium is a chemical element with the symbol Pa and atomic number 91. Its longest-lived and most abundant naturally-occurring isotope by far, Pa-231, is a decay product of uranium-235 , and it has a half-life of 32,760 years...
|
91 |
[RnRadon is a chemical element with symbol Rn and atomic number 86. It is a radioactive, colorless, odorless, tasteless noble gas, occurring naturally as the decay product of radium. It is one of the heaviest substances that remains a gas under normal conditions and is considered to be a health...
] 7s2 5f2 6d1 |
| |
|
NeodymiumNeodymium is a chemical element with the symbol Nd and atomic number 60. It is a soft silvery metal which tarnishes in air. Neodymium was discovered in 1885. Its various compounds are present in trace amounts in minerals monazite and bastnäsite. Pure neodymium is not found naturally and it is...
|
60 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f4 |
|
UraniumUranium is a silvery-white metallic chemical element in the actinide series of the periodic table that has the symbol U and atomic number 92. Besides its 92 protons, a uranium nucleus can have between 141 and 146 neutrons. The most common uranium isotopes are U-238 and U-235 . A uranium atom has...
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92 |
[RnRadon is a chemical element with symbol Rn and atomic number 86. It is a radioactive, colorless, odorless, tasteless noble gas, occurring naturally as the decay product of radium. It is one of the heaviest substances that remains a gas under normal conditions and is considered to be a health...
] 7s2 5f3 6d1 |
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Promethium Promethium is a chemical element with the symbol Pm and atomic number 61. It is notable for being the only other exclusively radioactive element besides technetium which is followed by chemical elements that have stable isotopes.-Physical:...
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61 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f5 |
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Neptunium Neptunium is a chemical element with the symbol Np and atomic number 93. A radioactive metallic element, neptunium is the first transuranic element and belongs to the actinide series. Its most stable isotope, 237Np, is a by-product of nuclear reactors and plutonium production and it...
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93 |
[RnRadon is a chemical element with symbol Rn and atomic number 86. It is a radioactive, colorless, odorless, tasteless noble gas, occurring naturally as the decay product of radium. It is one of the heaviest substances that remains a gas under normal conditions and is considered to be a health...
] 7s2 5f4 6d1 |
| |
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Samarium Samarium is a chemical element with the symbol Sm and atomic number 62.-Physical:Samarium is a rare earth metal, with a bright silver luster. Three crystal modifications of the metal also exist, with transformations at 734 and 922 °C, making it polymorphic...
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62 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f6 |
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PlutoniumPlutonium is a rare transuranic radioactive element. It is an actinide metal of silvery-white appearance that tarnishes when exposed to air, forming a dull coating when oxidized. The element normally exhibits six allotropes and four oxidation states. It reacts with carbon, halogens, nitrogen and...
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94 |
[RnRadon is a chemical element with symbol Rn and atomic number 86. It is a radioactive, colorless, odorless, tasteless noble gas, occurring naturally as the decay product of radium. It is one of the heaviest substances that remains a gas under normal conditions and is considered to be a health...
] 7s2 5f6 |
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EuropiumEuropium is a chemical element with the symbol Eu and atomic number 63. It was named after the continent of Europe.-Physical:Europium is about as hard as lead and quite ductile...
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63 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f7 |
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AmericiumAmericium is a synthetic element that has the symbol Am and atomic number 95. A radioactive metallic element, americium is an actinide that was obtained in 1944 by Glenn T. Seaborg who was bombarding plutonium with neutrons and was the fourth transuranic element to be discovered. It was named for...
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95 |
[RnRadon is a chemical element with symbol Rn and atomic number 86. It is a radioactive, colorless, odorless, tasteless noble gas, occurring naturally as the decay product of radium. It is one of the heaviest substances that remains a gas under normal conditions and is considered to be a health...
] 7s2 5f7 |
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Gadolinium Gadolinium is a chemical element that has the symbol Gd and atomic number 64. It is a silvery-white, malleable and ductile rare-earth metal. Gadolinium has exceptionally high absorption of neutrons and therefore is used for shielding in neutron radiography and in nuclear reactors...
|
64 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f7 5d1 |
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CuriumCurium is a synthetic chemical element with the symbol Cm and atomic number 96. A radioactive metallic transuranic element of the actinide series, curium is produced by bombarding plutonium with alpha particles and was named for Marie Curie and her husband Pierre.- Characteristics :The isotope...
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96 |
[RnRadon is a chemical element with symbol Rn and atomic number 86. It is a radioactive, colorless, odorless, tasteless noble gas, occurring naturally as the decay product of radium. It is one of the heaviest substances that remains a gas under normal conditions and is considered to be a health...
] 7s2 5f7 6d1 |
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TerbiumTerbium is a chemical element with the symbol Tb and atomic number 65. It is a silvery-white rare earth metal that is malleable, ductile and soft enough to be cut with a knife...
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65 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f9 |
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Berkelium Berkelium is a synthetic element with the symbol Bk and atomic number 97. A radioactive metallic element in the actinide series, berkelium was first synthesized by bombarding americium with alpha particles and was named after the University of California, Berkeley...
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97 |
[RnRadon is a chemical element with symbol Rn and atomic number 86. It is a radioactive, colorless, odorless, tasteless noble gas, occurring naturally as the decay product of radium. It is one of the heaviest substances that remains a gas under normal conditions and is considered to be a health...
] 7s2 5f9 |
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YttriumYttrium is a chemical element with symbol Y and atomic number 39. It is a silvery-metallic transition metal chemically similar to the lanthanoids and has historically been classified as a rare earth element. Yttrium is almost always found combined with the lanthanoids in rare earth minerals and is...
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39 |
[KrKrypton is a chemical element with the symbol Kr and atomic number 36. It is a member of Group 18 and Period 4 elements. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere, is isolated by fractionally distilling liquified air, and is often used with other...
] 5s2 4d1 |
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LutetiumLutetium is a chemical element with the symbol Lu and atomic number 71. It is in the d-block of the periodic table, not the f-block, but the IUPAC classifies it as a lanthanide. It is one of the elements that traditionally was included in the classification, "rare earths"...
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71 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f14 5d1 |
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Lawrencium Lawrencium is a radioactive synthetic element with the symbol Lr and atomic number 103.Its most stable known isotope is 262Lr, with a half-life of approximately 3.6 hours...
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103 |
[RnRadon is a chemical element with symbol Rn and atomic number 86. It is a radioactive, colorless, odorless, tasteless noble gas, occurring naturally as the decay product of radium. It is one of the heaviest substances that remains a gas under normal conditions and is considered to be a health...
] 7s2 5f14 7p1 |
ZirconiumZirconium is a chemical element with the symbol Zr and atomic number 40. It is a lustrous, gray-white, strong transition metal that resembles titanium. Zirconium is used as an alloying agent due to its high resistance to corrosion. It is never found as a native metal; it is obtained mainly from...
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40 |
[KrKrypton is a chemical element with the symbol Kr and atomic number 36. It is a member of Group 18 and Period 4 elements. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere, is isolated by fractionally distilling liquified air, and is often used with other...
] 5s2 4d2 |
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HafniumHafnium is a chemical element with the symbol Hf and atomic number 72. A lustrous, silvery gray, tetravalent transition metal, hafnium chemically resembles zirconium and is found in zirconium minerals. Its existence was predicted by Dmitri Mendeleev in 1869. Hafnium was the penultimate stable...
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72 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f14 5d2 |
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RutherfordiumRutherfordium is a chemical element with the symbol Rf and atomic number 104.This is a radioactive synthetic element whose most stable known isotope is 267Rf with a half-life of approximately 1.3 hours...
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104 |
(unknown) |
NiobiumNiobium , or columbium , is the chemical element with the symbol Nb and the atomic number 41...
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41 |
[KrKrypton is a chemical element with the symbol Kr and atomic number 36. It is a member of Group 18 and Period 4 elements. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere, is isolated by fractionally distilling liquified air, and is often used with other...
] 5s1 4d4 |
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Tantalium |
73 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f14 5d3 |
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MolybdenumMolybdenum , is a Group 6 chemical element with the symbol Mo and atomic number 42. The free element, which is a silvery metal, has the sixth-highest melting point of any element. It readily forms hard, stable carbides, and for this reason it is often used in high-strength steel alloys...
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42 |
[KrKrypton is a chemical element with the symbol Kr and atomic number 36. It is a member of Group 18 and Period 4 elements. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere, is isolated by fractionally distilling liquified air, and is often used with other...
] 5s1 4d5 |
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TungstenTungsten , also known as wolfram , is a chemical element with the chemical symbol W and atomic number 74.A steel-gray metal, tungsten is found in several ores, including wolframite and scheelite...
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74 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f14 5d4 |
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| Technetium Technetium is the lightest chemical element with no stable isotope, and is therefore the lightest radioactive element. It has atomic number 43 and symbol Tc. Technetium occurs in nature only in minute amounts; as a spontaneous fission product in uranium ore or by neutron capture in molybdenum...
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43 |
[KrKrypton is a chemical element with the symbol Kr and atomic number 36. It is a member of Group 18 and Period 4 elements. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere, is isolated by fractionally distilling liquified air, and is often used with other...
] 5s2 4d5 |
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RheniumRhenium is a chemical element with the symbol Re and atomic number 75. It is a silvery-white, heavy, third-row transition metal in group 7 of the periodic table. With an average concentration of 1 part per billion , rhenium is one of the rarest elements in the Earth's crust...
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75 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f14 5d5 |
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RutheniumRuthenium is a chemical element that has the symbol Ru and atomic number 44. A rare transition metal of the platinum group of the periodic table, ruthenium is found associated with platinum ores and used as a catalyst in some platinum alloys....
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44 |
[KrKrypton is a chemical element with the symbol Kr and atomic number 36. It is a member of Group 18 and Period 4 elements. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere, is isolated by fractionally distilling liquified air, and is often used with other...
] 5s1 4d7 |
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OsmiumOsmium is a chemical element that has the symbol Os and atomic number 76. Osmium is a hard, brittle, blue-gray or blue-black transition metal in the platinum family, and is the densest natural element. The density of osmium is , slightly greater than that of iridium, the second densest element....
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76 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f14 5d6 |
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RhodiumRhodium is a chemical element that is a rare, silvery-white, hard transition metal and a member of the platinum group. Rhodium is found in platinum ores and is used in alloys with platinum and as a catalyst. It is abbreviated to Rh and has atomic number 45...
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45 |
[KrKrypton is a chemical element with the symbol Kr and atomic number 36. It is a member of Group 18 and Period 4 elements. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere, is isolated by fractionally distilling liquified air, and is often used with other...
] 5s1 4d8 |
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IridiumIridium is the chemical element with atomic number 77, and is represented by the symbol Ir. A very hard, brittle, silvery-white transition metal of the platinum family, iridium is the second densest element and is the most corrosion-resistant metal, even at temperatures as high as 2000 °C...
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77 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f14 5d7 |
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PalladiumPalladium is a chemical element with the chemical symbol Pd and an atomic number of 46. Palladium is a rare and lustrous silvery-white metal that was discovered in 1803 by William Hyde Wollaston, who named it after the asteroid Pallas, which in turn, was named after the epithet of the Greek...
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46 |
[KrKrypton is a chemical element with the symbol Kr and atomic number 36. It is a member of Group 18 and Period 4 elements. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere, is isolated by fractionally distilling liquified air, and is often used with other...
] 4d10 |
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PlatinumPlatinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is in Group 10 of the periodic table of elements...
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78 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s1 4f14 5d9 |
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SilverSilver is a chemical element with the chemical symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal...
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47 |
[KrKrypton is a chemical element with the symbol Kr and atomic number 36. It is a member of Group 18 and Period 4 elements. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere, is isolated by fractionally distilling liquified air, and is often used with other...
] 5s1 4d10 |
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Gold Gold is a chemical element with the symbol Au and an atomic number of 79. It has been a highly sought-after precious metal for coinage, jewelry, and other arts since the beginning of recorded history. The metal occurs as nuggets or grains in rocks, in veins and in alluvial deposits. Gold is...
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79 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s1 4f14 5d10 |
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CadmiumCadmium is a chemical element with the symbol Cd and atomic number 48. The soft, bluish-white transition metal is chemically similar to the two other metals in group 12, zinc and mercury. Similar to zinc it prefers oxidation state +2 in most of its compounds and similar to mercury it shows a low...
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48 |
[KrKrypton is a chemical element with the symbol Kr and atomic number 36. It is a member of Group 18 and Period 4 elements. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere, is isolated by fractionally distilling liquified air, and is often used with other...
] 5s2 4d10 |
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MercuryMercury , also called quicksilver or hydrargyrum , is a chemical element with the symbol Hg and atomic number 80...
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80 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f14 5d10 |
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IndiumIndium is a chemical element with chemical symbol In and atomic number 49. This rare, soft, malleable and easily fusible post-transition metal is chemically similar to aluminium or gallium but more closely resembles zinc .Indium's current primary application is to form transparent electrodes from...
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49 |
[KrKrypton is a chemical element with the symbol Kr and atomic number 36. It is a member of Group 18 and Period 4 elements. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere, is isolated by fractionally distilling liquified air, and is often used with other...
] 5s2 4d10 5p1 |
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ThalliumThallium is a chemical element with the symbol Tl and atomic number 81. This soft gray malleable poor metal resembles tin but discolors when exposed to air. Approximately 60-70% of thallium production is used in the electronics industry, and the rest is used in the pharmaceutical industry and in...
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81 |
[XeXenon is a chemical element represented by the symbol Xe. Its atomic number is 54. A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...
] 6s2 4f14 5d10 6p1 |
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By the Madelung rule,
103 LawrenciumLawrencium is a radioactive synthetic element with the symbol Lr and atomic number 103.Its most stable known isotope is 262Lr, with a half-life of approximately 3.6 hours...
would be an expected *[Rn] 7s
2 5f
14 6d
1. The electron-shell configuration of heavier elements is not yet known.
Electron configuration in molecules
In
moleculeA molecule is defined as an electrically neutral group of at least two atoms in a definite arrangement held together by very strong chemical bonds. Molecules are distinguished from polyatomic ions in this strict sense...
s, the situation becomes more complex, as each molecule has a different orbital structure. The
molecular orbitalIn chemistry, a molecular orbital is a mathematical function that describes the wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The use of the term...
s are labelled according to their
symmetryMolecular symmetry in chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can predict or explain many of a molecule's chemical properties, such as its dipole moment...
, rather than the
atomic orbitalAn atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons, in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. These functions...
labels used for atoms and monoatomic ions: hence, the electron configuration of the dioxygen molecule, O, is 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, these electrons have parallel spins in the ground state, and so dioxygen has a net
magnetic momentThe magnetic moment of a system is a measure of the strength and the direction of its magnetism. More technically , the term magnetic moment of a system usually refers to its magnetic dipole moment, and quantifies the contribution...
(it is paramagnetic). The explanation of the paramagnetism of dioxygen was a major success for
molecular orbital theoryIn chemistry, molecular orbital theory is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule...
.
Electron configuration in solids
In a
solidMatter is generally found in three different forms: solid, liquid, and gas . The solid state of matter is characterized by a distinct structural rigidity and resistance to deformation . Most solids have high values both of Young's modulus and of the shear modulus of elasticity...
, the electron states become very numerous. They cease to be discrete, and effectively blend together into continuous ranges of possible states (an electron band). The notion of electron configuration ceases to be relevant, and yields to band theory.
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 theoryIn chemistry, molecular orbital theory is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule...
, have become the modern equivalent of the
valenceIn chemistry, valence, also known as valency or valency number, is a measure of the number of chemical bonds formed by the atoms of a given element...
concept, describing the number and type of chemical bonds that an atom can be expected to form.
This approach is taken further in
computational chemistryComputational chemistry is a branch of chemistry that uses computers to assist in solving chemical problems. It uses the results of theoretical chemistry, incorporated into efficient computer programs, to calculate the structures and properties of molecules and solids...
, 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 setA basis set in chemistry is a set of functions used to create the molecular orbitals, which are expanded as a linear combination of such functions with the weights or coefficients to be determined...
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 theoryDensity functional theory is a quantum mechanical theory used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by using...
(DFT) is an important example of a method which discards the model.
A fundamental application of electron configurations is in the interpretation of
atomic spectraThe emission spectrum of an element or compound is the relative intensity of electromagnetic radiation of each frequency emitted by atoms or molecules of that element or compound when they are excited....
. In this case, it is necessary to convert the electron configuration into one or more
term symbolIn quantum mechanics, the Russell-Saunders term symbol is an abbreviated description of the angular momentum quantum numbers in a multi-electron atom. It is related with the energy level of a given electron configuration. LS coupling is assumed...
s, 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
- Atomic electron configuration table
This is a table of electron configurations of atoms.In the chart below, when drawing electrons in shells, the number at the beginning is the ring closest to the nucleus and the others are in order going out....
- Periodic table (electron configurations)
* Configurations of elements with light gray background are uncertain or not available.* Grayed out electron numbers indicate subshells that are filled to their maximum....
- Atomic orbital
An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons, in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. These functions...
- Energy level
A quantum mechanical system or particle that is bound, confined spatially, can only take on certain discrete values of energy, as opposed to classical particles, which can have any energy. These values are called energy levels. The term is most commonly used for the energy levels of electrons in...
- Molecular term symbol
In molecular physics, the molecular term symbol is a shorthand expression of the group representation and angular momenta that characterize the state of a molecule, i.e. its electronic quantum state which is an eigenstate of the electronic molecular Hamiltonian. It is the equivalent of the term...
- HOMO/LUMO
HOMO and LUMO are acronyms for highest occupied molecular orbital and lowest unoccupied molecular orbital, respectively. The difference of the energies of the HOMO and LUMO, termed the band gap, can sometimes serve as a measure of the excitability of the molecule: the smaller the energy, the more...
- Pwpaw
PWPAW A Projector Augmented Wave code for electronic structure calculation. It is a free software package, distributed under the copyleft GNU General Public License. It is a plane wave implementation of the Projector Augmented Wave method developed by Peter E Blochl for electronic structure...
Software package for electron configuration calculations
- Periodic Table Group
- d electron count
The d electron count is a chemistry formalism used to describe the electron configuration of the valence electrons of a transition metal center in a coordination complexes. The d electron count is an effective way to understand the geometry and reactivity of transition metal complexes...
- Extension of the periodic table beyond the seventh period Discusses the limits of the periodic table
External links