Electron atomic and molecular orbitals
Electron configuration table
Electron configuration
From Wikipedia, the free encyclopedia
In atomic physics and quantum chemistry, electron configuration is the
arrangement of electrons of an atom, a molecule, or other physical structure.[1] It
concerns the way electrons can be distributed in the orbitals of the given system
(atomic or molecular for instance).
Like other elementary particles, the electron is subject to the laws of quantum
mechanics, and exhibits both particle-like and wave-like nature. Formally, the
quantum state of a particular electron is defined by its wave function, a complex-
valued function of space and time. According to the Copenhagen interpretation 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 with each electron configuration and, upon certain conditions, electrons are able to move from one orbital to
another by emission or absorption of a quantum 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 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.
Contents
1 Shells and subshells
2 Notation
3 Energy — ground state and excited states
4 History
5 Aufbau principle and Madelung rule
5.1 The periodic table
5.2 Shortcomings of the Aufbau principle
5.3 Ionization of the transition metals
5.4 Other exceptions to Madelung's rule
6 Electron configuration in molecules
6.1 Electron configuration in solids
7 Applications
8 See also
9 Notes
10 References
11 External links
Shells and subshells
See also: Electron shell
Electron configuration was first conceived of 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
nature of electrons.
An electron shell is the set of allowed states electrons may occupy which share the same principal
quantum number, n (the number before the letter in the orbital label). An atom's nth electron shell
can accommodate 2n2 electrons, e.g. the first shell can accommodate 2 electrons, the second shell
8 electrons, and the third shell 18 electrons. 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 +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 number, l, within a shell. The values l = 0, 1, 2, 3 correspond to
the s, p, d, and f labels, respectively. The maximum number of electrons which can be placed in a subshell is given by 2(2l + 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,[2] 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
numbers.[3]
Notation
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See also: Atomic orbital
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 orbital labels (e.g. for phosphorus the sequence 1s, 2s, 2p, 3s, 3p) with the number of electrons
assigned to each orbital (or set of orbitals sharing the same label) placed as a superscript. For example, hydrogen has one electron in
the s-orbital of the first shell, so its configuration is written 1s1. Lithium has two electrons in the 1s-subshell and one in the (higher-
energy) 2s-subshell, so its configuration is written 1s2 2s1 (pronounced "one-s-two, two-s-one"). Phosphorus (atomic number 15), is as
follows: 1s2 2s2 2p6 3s2 3p3.
For atoms with many electrons, this notation can become lengthy and so an abbreviated notation is used, since all but the last few
subshells are identical to those of one or another of the noble gases. Phosphorus, for instance, differs from neon (1s2 2s2 2p6) only by
the presence of a third shell. Thus, the electron configuration of neon is pulled out, and phosphorus is written as follows: [Ne] 3s2 3p3.
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] 3d6 4s2
(keeping the 3d-electrons with the 3s- and 3p-electrons which are implied by the configuration of argon) or as [Ar] 4s2 3d6 (following the
Aufbau principle, see below).
The superscript 1 for a singly-occupied orbital is not compulsory.[4] 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 as "sharp", "principal",
"diffuse" and "fundamental", based on their observed fine structure: their modern usage indicates orbitals with an azimuthal quantum
number, 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 orbital labels are used instead of atomic
orbital labels (see below).
Energy — 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. Any other configuration is an excited state.
As an example, the ground state configuration of the sodium atom is 1s22s22p63s, 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 1s22s22p63p 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 to the 3s level and form the excited 1s22s22p53s2 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
Niels Bohr was the first to propose (1923) that the periodicity in the properties of the elements might be explained by the electronic
structure of the atom.[5] 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 was given as
2.4.4.6 instead of 1s2 2s2 2p6 3s2 3p4 (2.8.6).
The following year, 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.[6] However neither Bohr's system nor Stoner's could correctly describe the changes in
atomic spectra in a magnetic field (the Zeeman effect).
Bohr was well aware of this shortcoming (and others), and had written to his friend Wolfgang Pauli to ask for his help in saving quantum
theory (the system now known as "old quantum theory"). 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 principle (1925):[7]
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 equation, published in 1926, gave three of the four quantum numbers as a direct consequence of its solution for the
hydrogen atom:[2] 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),[8] see below) for the order in which atomic orbitals are filled with electrons.
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The approximate order of filling of atomic
orbitals, following the arrows.
Aufbau principle and Madelung rule
The Aufbau principle (from the German Aufbau, "building up, construction") was an important part of Bohr's original concept of electron
configuration. It may be stated as:[9]
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 decreasingly well for the following 100 elements. 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,[8]and later given a theoretical justification by V.M. Klechkowski[10]
Orbitals are filled in the order of increasing n+l;1.
Where two orbitals have the same value of n+l, they are filled in order of
increasing n.
2.
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 protons and neutrons in the atomic nucleus, as in the shell model of
nuclear physics and nuclear chemistry.
The periodic table
The form of the periodic table is closely related to the electron configuration of the atoms of the elements. For example, all the elements
of group 2 have an electron configuration of [E] ns2 (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,[11] It is not clear how far Madelung's rule explains (rather than simply describes) the periodic table,[12]
although some properties (such as the common +2 oxidation state 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[13] (although there are
mathematical approximations available, such 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 naive 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 [Ar] 4s1 and
[Ar] 4s2 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, chromium and copper have electron configurations [Ar] 3d5 4s1 and
[Ar] 3d10 4s1 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 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. 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 state 0) surrounded
by six carbon monoxide ligands: it is diamagnetic, and the electron configuration of the central chromium atom is described as 3d6, 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.[14]
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 Fe2+ 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. When care is
taken to compare "like with like", the paradox disappears.[15]
Other exceptions to Madelung's rule
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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,[16]
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 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[17] tend to decrease the energy of the s-orbitals in
relation to the other atomic orbitals.[18]
Electron shells filled in violation of Madelung's rule (red)
Period 5 Period 6 Period 7
Element Z ElectronConfiguration Element Z
Electron
Configuration Element Z
Electron
Configuration
Lanthanum 57 [Xe] 6s2 5d1 Actinium 89 [Rn] 7s2 6d1
Cerium 58 [Xe] 6s2 4f1 5d1 Thorium 90 [Rn] 7s2 6d2
Praseodymium 59 [Xe] 6s2 4f3 Protactinium 91 [Rn] 7s2 5f2 6d1
Neodymium 60 [Xe] 6s2 4f4 Uranium 92 [Rn] 7s2 5f3 6d1
Promethium 61 [Xe] 6s2 4f5 Neptunium 93 [Rn] 7s2 5f4 6d1
Samarium 62 [Xe] 6s2 4f6 Plutonium 94 [Rn] 7s2 5f6
Europium 63 [Xe] 6s2 4f7 Americium 95 [Rn] 7s2 5f7
Gadolinium 64 [Xe] 6s2 4f7 5d1 Curium 96 [Rn] 7s2 5f7 6d1
Terbium 65 [Xe] 6s2 4f9 Berkelium 97 [Rn] 7s2 5f9
Yttrium 39 [Kr] 5s2 4d1 Lutetium 71 [Xe] 6s2 4f14 5d1 Lawrencium 103 [Rn] 7s2 5f14 7p1
Zirconium 40 [Kr] 5s2 4d2 Hafnium 72 [Xe] 6s2 4f14 5d2 Rutherfordium 104 (unknown)
Niobium 41 [Kr] 5s1 4d4 Tantalium 73 [Xe] 6s2 4f14 5d3
Molybdenum 42 [Kr] 5s1 4d5 Tungsten 74 [Xe] 6s2 4f14 5d4
Technetium 43 [Kr] 5s2 4d5 Rhenium 75 [Xe] 6s2 4f14 5d5
Ruthenium 44 [Kr] 5s1 4d7 Osmium 76 [Xe] 6s2 4f14 5d6
Rhodium 45 [Kr] 5s1 4d8 Iridium 77 [Xe] 6s2 4f14 5d7
Palladium 46 [Kr] 4d10 Platinum 78 [Xe] 6s1 4f14 5d9
Silver 47 [Kr] 5s1 4d10 Gold 79 [Xe] 6s1 4f14 5d10
Cadmium 48 [Kr] 5s2 4d10 Mercury 80 [Xe] 6s2 4f14 5d10
Indium 49 [Kr] 5s2 4d10 5p1 Thallium 81 [Xe] 6s2 4f14 5d10 6p1
By the Madelung rule, 103 Lawrencium would be an expected *[Rn] 7s2 5f14 6d1. The electron-shell configuration of heavier elements is
not yet known.
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,[19] rather than the atomic orbital labels used for atoms and monoatomic ions: hence, the electron
configuration of the dioxygen molecule, O2, is 1σg2 1σu2 2σg2 2σu2 1πu4 3σg2 1πg2.[1] The term 1πg2 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 moment (it is paramagnetic). The explanation of the paramagnetism of dioxygen was a major success for molecular
orbital theory.
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.
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 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, which typically attempts to make quantitative estimates of chemical properties.
For many years, most such calculations relied upon the "linear combination of atomic orbitals" (