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In atomic physics and quantum chemistry, the electron configuration is the distribution of of an atom or molecule (or other physical structure) in Atomic orbital 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 Atomic orbital, in an average field created by the Atomic nucleus and all the other electrons. Mathematically, configurations are described by Slater determinants or configuration state functions.
According to the laws of quantum mechanics, a Energy level 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, for describing the that hold atoms together, and in understanding the of compounds and the geometries of molecules. In bulk materials, this same idea helps explain the peculiar properties of lasers and semiconductors.
Electron configuration was first conceived under the Bohr model of the atom, and it is still common to speak of Electron shell despite the advances in understanding of the quantum-mechanical nature of Electron.
An electron shell is the set of Quantum state that share the same principal quantum number, n, that electrons may occupy. In each term of an electron configuration, n is the Natural number that precedes each orbital letter (e.g. helium's electron configuration is 1s2, therefore n = 1, and the orbital contains two electrons). An atom's nth electron shell can accommodate 2 n2 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 + (usually denoted by an up-arrow) and one with a spin of − (with a down-arrow).
A subshell is the set of states defined by a common azimuthal quantum number, , within a shell. The value of is in the range from 0 to n − 1. The values = 0, 1, 2, 3 correspond to the s, p, d, and f labels, respectively. For example, the 3d subshell has n = 3 and = 2. The maximum number of electrons that can be placed in a subshell is given by 2(2 + 1). This gives two electrons in an s subshell, six electrons in a p subshell, ten electrons in a d subshell and fourteen electrons in an f subshell.
The numbers of electrons that can occupy each shell and each subshell arise from the equations of quantum mechanics, in particular the Pauli exclusion principle, which states that no two electrons in the same atom can have the same values of the four .
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.
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 , equivalent to the noble gas of the preceding period, and the : 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 Ne, allowing the configuration of phosphorus to be written as Ne 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.
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 Ar 4s2 3d2 or Ar 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.
The superscript 1 for a singly occupied subshell is not compulsory; for example aluminium may be written as either Ne 3s2 3p1 or Ne 3s2 3p. In atoms where a subshell is unoccupied despite higher subshells being occupied (as is the case in some ions, as well as certain neutral atoms shown to deviate from the Madelung rule), the 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 Xe. (2025). 9781319154110, Macmillan Education. ISBN 9781319154110
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 series", " principal", "Diffuse series" and " fundamental" (or " fine"), 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... ( = 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).
As an example, the ground state configuration of the sodium atom is 1s2 2s2 2p6 3s1, as deduced from the Aufbau principle (see below). 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 (such as 3s for sodium) involves energies corresponding to of visible or ultraviolet light. The excitation of 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.
«…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 Octet rule.…»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 (the Zeeman effect).
Bohr was well aware of this shortcoming (and others), and had written to his friend Wolfgang Pauli in 1923 to ask for his help in saving quantum theory (the system now known as "old quantum theory"). Pauli hypothesized successfully that the Zeeman effect can be explained as depending only on the response of the outermost (i.e., valence) electrons of the atom. Pauli was able to reproduce Stoner's shell structure, but with the correct structure of subshells, by his inclusion of a fourth quantum number and his exclusion principle (1925): English translation from
The Schrödinger equation, published in 1926, gave three of the four quantum numbers as a direct consequence of its solution for the hydrogen atom: this solution yields the atomic orbitals that are shown today in textbooks of chemistry (and above). The examination of atomic spectra allowed the electron configurations of atoms to be determined experimentally, and led to an empirical rule (known as Madelung's rule (1936), see below) for the order in which atomic orbitals are filled with electrons.
principle works very well (for the ground states of the atoms) for the known 118 elements, although it is sometimes slightly wrong. The modern form of the aufbau principle describes an order of orbital energies given by Madelung's rule (or Klechkowski's rule). This rule was first stated by Charles Janet in 1929, rediscovered by Erwin Madelung in 1936, and later given a theoretical justification by V. M. Klechkowski:
In this list the subshells in parentheses are not occupied in the ground state of the heaviest atom now known (Oganesson, Z = 118).
The aufbau principle can be applied, in a modified form, to the and in the atomic nucleus, as in the shell model of nuclear physics and nuclear chemistry.
The electrons in the Valence electron largely determine each element's chemical properties. The similarities in the chemical properties were remarked on more than a century before the idea of electron configuration.
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 are slightly split by the magnetic field of the nucleus, and by the quantum electrodynamic effects of the Lamb shift.)
The apparent paradox arises when electrons are removed from the transition metal atoms to form . The first electrons to be ionized come not from the 3d-orbital, as one would expect if it were "higher in energy", but from the 4s-orbital. This interchange of electrons between 4s and 3d is found for all atoms of the first series of transition metals. The configurations of the neutral atoms (K, Ca, Sc, Ti, V, Cr, ...) usually follow the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, ...; however the successive stages of ionization of a given atom (such as Fe4+, Fe3+, Fe2+, Fe+, Fe) usually follow the order 1s, 2s, 2p, 3s, 3p, 3d, 4s, ...
This phenomenon is only paradoxical if it is assumed that the energy order of atomic orbitals is fixed and unaffected by the nuclear charge or by the presence of electrons in other orbitals. If that were the case, the 3d-orbital would have the same energy as the 3p-orbital, as it does in hydrogen, yet it clearly does not. There is no special reason why the Fe ion should have the same electron configuration as the chromium atom, given that iron has two more protons in its nucleus than chromium, and that the chemistry of the two species is very different. Melrose and Eric Scerri have analyzed the changes of orbital energy with orbital occupations in terms of the two-electron repulsion integrals of the Hartree–Fock method of atomic structure calculation. More recently Scerri has argued that contrary to what is stated in the vast majority of sources including the title of his previous article on the subject, 3d orbitals rather than 4s are in fact preferentially occupied.
In chemical environments, configurations can change even more: Th3+ as a bare ion has a configuration of Rn 5f1, yet in most ThIII compounds the thorium atom has a 6d1 configuration instead. Mostly, what is present is rather a superposition of various configurations. For instance, copper metal is poorly described by either an Ar 3d 4s or an Ar 3d 4s configuration, but is rather well described as a 90% contribution of the first and a 10% contribution of the second. Indeed, visible light is already enough to excite electrons in most transition metals, and they often continuously "flow" through different configurations when that happens (copper and its group are an exception).
Similar ion-like 3d 4s configurations occur in transition metal complexes as described by the simple crystal field theory, even if the metal has oxidation state 0. For example, chromium hexacarbonyl can be described as a chromium atom (not ion) surrounded by six carbon monoxide . The electron configuration of the central chromium atom is described as 3d with the six electrons filling the three lower-energy d orbitals between the ligands. The other two d orbitals are at higher energy due to the crystal field of the ligands. This picture is consistent with the experimental fact that the complex is diamagnetic, meaning that it has no unpaired electrons. However, in a more accurate description using molecular orbital theory, the d-like orbitals occupied by the six electrons are no longer identical with the d orbitals of the free atom.
For the heavier elements, it is also necessary to take account of the effects of special relativity on the energies of the atomic orbitals, as the inner-shell electrons are moving at speeds approaching the speed of light. In general, these relativistic effects tend to decrease the energy of the s-orbitals in relation to the other atomic orbitals. This is the reason why the 6d elements are predicted to have no Madelung anomalies apart from lawrencium (for which relativistic effects stabilise the p1/2 orbital as well and cause its occupancy in the ground state), as relativity intervenes to make the 7s orbitals lower in energy than the 6d ones.
The table below shows the configurations of the f-block (green) and d-block (blue) atoms. It shows the ground state configuration in terms of orbital occupancy, but it does not show the ground state in terms of the sequence of orbital energies as determined spectroscopically. For example, in the transition metals, the 4s orbital is of a higher energy than the 3d orbitals; and in the lanthanides, the 6s is higher than the 4f and 5d. The ground states can be seen in the Electron configurations of the elements (data page). However this also depends on the charge: a calcium atom has 4s lower in energy than 3d, but a Ca2+ cation has 3d lower in energy than 4s. In practice the configurations predicted by the Madelung rule are at least close to the ground state even in these anomalous cases.See the NIST tables The empty f orbitals in lanthanum, actinium, and thorium contribute to chemical bonding, as do the empty p orbitals in transition metals. Example for platinum
Vacant s, d, and f orbitals have been shown explicitly, as is occasionally done,See for example this Russian periodic table poster by A. V. Kulsha and T. A. Kolevich to emphasise the filling order and to clarify that even orbitals unoccupied in the ground state (e.g. lanthanum 4f or palladium 5s) may be occupied and bonding in chemical compounds. (The same is also true for the p-orbitals, which are not explicitly shown because they are only actually occupied for lawrencium in gas-phase ground states.)
| +Electron shells filled in violation of Madelung's rule (red) Predictions for elements 109–112 | ||
| [radon] 7s2 5f0 6d1 | ||
| [radon] 7s2 5f0 6d2 | ||
| [radon] 7s2 5f2 6d1 | ||
| [radon] 7s2 5f3 6d1 | ||
| [radon] 7s2 5f4 6d1 | ||
| [radon] 7s2 5f6 6d0 | ||
| [radon] 7s2 5f7 6d0 | ||
| [radon] 7s2 5f7 6d1 | ||
| [radon] 7s2 5f9 6d0 | ||
| [radon] 7s2 5f10 6d0 | ||
| [radon] 7s2 5f11 6d0 | ||
| [radon] 7s2 5f12 6d0 | ||
| [radon] 7s2 5f13 6d0 | ||
| [radon] 7s2 5f14 6d0 | ||
| [Radon] 7s2 5f14 6d0 7p1 | ||
| [Radon] 7s2 5f14 6d2 | ||
| [Radon] 7s2 5f14 6d3 | ||
| [Radon] 7s2 5f14 6d4 | ||
| [Radon] 7s2 5f14 6d5 | ||
| [Radon] 7s2 5f14 6d6 | ||
| 77 | [xenon] 6s2 4f14 5d7|| || Meitnerium | 109 | [Radon] 7s2 5f14 6d7 |
| 110 | [Radon] 7s2 5f14 6d8 | |
| [Radon] 7s2 5f14 6d9 | ||
| [Radon] 7s2 5f14 6d10 |
The various anomalies describe the free atoms and do not necessarily predict chemical behavior. Thus for example neodymium typically forms the +3 oxidation state, despite its configuration that if interpreted naïvely would suggest a more stable +2 oxidation state corresponding to losing only the 6s electrons. Contrariwise, uranium as is not very stable in the +3 oxidation state either, preferring +4 and +6.
The electron-shell configuration of elements beyond hassium has not yet been empirically verified, but they are expected to follow Madelung's rule without exceptions until unbinilium. Unbiunium should have the anomalous configuration , having a p rather than a g electron. Electron configurations beyond this are tentative and predictions differ between models, but Madelung's rule is expected to break down due to the closeness in energy of the , 6f, 7d, and 8p1/2 orbitals. (2025). 9781402035555, Springer Science+Business Media. ISBN 9781402035555 That said, the filling sequence 8s, , 6f, 7d, 8p is predicted to hold approximately, with perturbations due to the huge spin-orbit splitting of the 8p and 9p shells, and the huge relativistic stabilisation of the 9s shell.
For molecules, "open shell" signifies that there are unpaired electrons. In molecular orbital theory, this leads to molecular orbitals that are singly occupied. In computational chemistry implementations of molecular orbital theory, open-shell molecules have to be handled by either the restricted open-shell Hartree–Fock method or the unrestricted Hartree–Fock method. Conversely a closed-shell configuration corresponds to a state where all molecular orbitals are either doubly occupied or empty (a diradical). Open shell molecules are more difficult to study computationally.
| ! Period ! Element ! colspan="7" Configuration |
| 7s2 5f14 6d10 7p6 |
Every system has the tendency to acquire the state of stability or a state of minimum energy, and so chemical elements take part in chemical reactions to acquire a stable electronic configuration similar to that of its nearest noble gas. An example of this tendency is two hydrogen (H) atoms reacting with one oxygen (O) atom to form water (H2O). Neutral atomic hydrogen has one electron in its Valence electron, and on formation of water it acquires a share of a second electron coming from oxygen, so that its configuration is similar to that of its nearest noble gas helium (He) with two electrons in its valence shell. Similarly, neutral atomic oxygen has six electrons in its valence shell, and acquires a share of two electrons from the two hydrogen atoms, so that its configuration is similar to that of its nearest noble gas neon with eight electrons in its valence shell.
The electronic configuration of polyatomic molecules can change without absorption or emission of a photon through vibronic couplings.
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" (LCAO) approximation, using an ever-larger and more complex basis set of Atomic orbital 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 computational chemistry rely on electron configuration: density functional theory (DFT) is an important example of a method that discards the model.
For Atom or Molecule with more than one electron, the motion of electrons are correlated and such a picture is no longer exact. A very large number of electronic configurations are needed to exactly describe any multi-electron system, and precisely associating a certain energy level with any single configuration is not possible. However, the electronic wave function is usually dominated by a very small number of configurations and therefore the notion of electronic configuration remains essential for multi-electron systems.
A fundamental application of electron configurations is in the interpretation of atomic spectra. In this case, it is necessary to supplement the electron configuration with one or more , which describe the different Energy level 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.
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