Electron configuration
In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals. For example, the electron configuration of the neon atom is, meaning that the 1s, 2s, and 2p subshells are occupied by two, two, and six electrons, respectively.
Electronic configurations describe each electron as moving independently in an orbital, in an average field created by the nuclei and all the other electrons. Mathematically, configurations are described by Slater determinants or configuration state functions.
According to the laws of quantum mechanics, a level of energy is associated with each electron configuration. In certain conditions, electrons are able to move from one configuration to another by the 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, for describing the chemical bonds that hold atoms together, and in understanding the chemical formulas of compounds and the geometries of molecules. In bulk materials, this same idea helps explain the peculiar properties of lasers and semiconductors.
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 nature of electrons.An electron shell is the set of allowed states that share the same principal quantum number, n, that electrons may occupy. In each term of an electron configuration, n is the positive integer that precedes each orbital letter. An atom's nth electron shell can accommodate 2n2 electrons. For example, the first shell can accommodate two electrons, the second shell eight electrons, the third shell eighteen, and so on. The factor of two arises because the number of allowed states doubles with each successive shell due to electron spin—each atomic orbital admits up to two otherwise identical electrons with opposite spin, one with a spin + and one with a spin of −.
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. This gives two electrons in an s subshell, six electrons in a p subshell, and ten electrons in a d 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 numbers.
Exhaustive technical details about the complete quantum mechanical theory of atomic spectra and structure can be found and studied in the basic book of Robert D. Cowan.
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 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 1s1. Lithium has two electrons in the 1s-subshell and one in the 2s-subshell, so its configuration is written 1s2 2s1. Phosphorus is as follows: 1s2 2s2 2p6 3s2 3p3.It is quite common to see the letters of the orbital labels written in an italic or slanting typeface, although the International Union of Pure and Applied Chemistry recommends a normal typeface. 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,, of 0, 1, 2 or 3 respectively. After f, the sequence continues alphabetically g, h, i..., 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.
Condensed
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, whose configuration is 1s2 2s2 2p6, only by the presence of a third shell. The portion of its configuration that is equivalent to neon is abbreviated as , allowing the configuration of phosphorus to be written as 3s2 3p3 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.Condensed symbols have the following meanings:
| Symbol | Meaning |
| [He] | |
| [Ne] | |
| [Ar] | |
| [Kr] | |
| [Xe] | |
| [Rn] | |
| [Og] |
Order
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 4s2 3d2 or 3d2 4s2. The first notation follows the order based on the Madelung rule 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 Ti4+, Ti3+, Ti2+, Ti+, Ti.Implied Values
The superscript 1 for a singly occupied subshell is not compulsory; for example, aluminium may be written as either 3s2 3p1 or 3s2 3p. In atoms where a subshell is unoccupied despite higher subshells being occupied, 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 ion may be written as either or simply .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. Any other configuration is an excited state.As an example, the ground state configuration of the sodium atom is 1s2 2s2 2p6 3s1, as deduced from the Aufbau principle. The first excited state is obtained by promoting a 3s electron to the 3p subshell, to obtain the
1s2 2s2 2p6 3p1 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 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 1s2 2s2 2p5 3s2 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
was the first to propose in his 1919 article "The Arrangement of Electrons in Atoms and Molecules" in which, building on Gilbert N. Lewis'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 and the Octet rule.Niels Bohr incorporated Langmuir's model that the periodicity 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 was given as 2.4.4.6 instead of 1s2 2s2 2p6 3s2 3p4. Bohr used 4 and 6 following Alfred Werner's 1893 paper. In fact, the chemists accepted the concept of 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.
Bohr was well aware of this shortcoming, and had written to his friend Wolfgang Pauli in 1923 to ask for his help in saving quantum theory. Pauli hypothesized successfully that the Zeeman effect can be explained as depending only on the response of the outermost 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 :
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. The examination of atomic spectra allowed the electron configurations of atoms to be determined experimentally, and led to an empirical rule for the order in which atomic orbitals are filled with electrons.