Electron configuration

In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals.[1] For example, the electron configuration of the neon atom is 1s2 2s2 2p6, using the notation explained below.

Electronic configurations describe each electron as moving independently in an orbital, in an average field created by all other orbitals. Mathematically, configurations are described by Slater determinants or configuration state functions.

According to the laws of quantum mechanics, for systems with only one electron, a level of energy is associated with each electron configuration and in certain conditions, electrons are able to move from one configuration to another by the emission or absorption of a quantum 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. This is also useful for describing the chemical bonds that hold atoms together. In bulk materials, this same idea helps explain the peculiar properties of lasers and semiconductors.

Shells and subshells

s (=0) p (=1)
m=0 m=0 m=±1
s pz px py
n=1 S1M0.png
n=2 S2M0.png Pz orbital.png Px orbital.png Py orbital.png

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 (the number before the letter in the orbital label), that electrons may occupy. An atom's nth electron shell can accommodate 2n2 electrons, e.g. the first shell can accommodate 2 electrons, the second shell 8 electrons, the third shell 18 electrons and so on. The factor of two arises because the allowed states are doubled due to electron spin—each atomic orbital admits up to two otherwise identical electrons with opposite spin, one with a spin +1/2 (usually denoted 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. For example, the 3d subshell has n = 3 and ℓ = 2. The maximum number of electrons that 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

Physicists and chemists use a standard notation to indicate the electron configurations of atoms and molecules. For atoms, the notation consists of a sequence of atomic subshell labels (e.g. for phosphorus the sequence 1s, 2s, 2p, 3s, 3p) with the number of electrons assigned to each subshell placed as a superscript. For example, hydrogen has one electron in the s-orbital of the first shell, so its configuration is written 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. 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 [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. 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" (or "fine"), 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.[4][5]

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 1s22s22p63s1, 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 of sodium 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 (1923) was the first to propose that the periodicity in the properties of the elements might be explained by the electronic structure of the atom.[6] 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.[7] 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):[8]

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 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),[9] see below) for the order in which atomic orbitals are filled with electrons.

Atoms: 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:[10]

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.
Klechkowski rule 2
The approximate order of filling of atomic orbitals, following the arrows from 1s to 7p. (After 7p the order includes orbitals outside the range of the diagram, starting with 8s.)

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,[9] and later given a theoretical justification by V.M. Klechkowski:[11]

  1. Orbitals are filled in the order of increasing n+l;
  2. 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, 7p, (8s, 5g, 6f, 7d, 8p, and 9s)

In this list the orbitals in parentheses are not occupied in the ground state of the heaviest atom now known (Og, Z = 118).

The Aufbau principle can be applied, in a modified form, to the protons and neutrons in the atomic nucleus, as in the shell model of nuclear physics and nuclear chemistry.

Periodic table

Periodic table blocks spdf (32 column)
Electron configuration 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. In general, the periodicity of the periodic table in terms of periodic table blocks is clearly due to the number of electrons (2, 6, 10, 14...) needed to fill s, p, d, and f subshells.

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 on more than a century before the idea of electron configuration.[12] It is not clear how far Madelung's rule explains (rather than simply describes) the periodic table,[13] 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; in both cases this is only approximately true. It considers atomic orbitals as "boxes" of fixed energy into which can be placed two electrons and no more. However, the energy of an electron "in" an atomic orbital depends on the energies of all the other electrons of the atom (or ion, or molecule, etc.). There are no "one-electron solutions" for systems of more than one electron, only a set of many-electron solutions that cannot be calculated exactly[14] (although there are mathematical approximations available, such as the Hartree–Fock method).

The fact that the Aufbau principle is based on an approximation can be seen from the fact that there is an almost-fixed filling order at all, that, within a given shell, the s-orbital is always filled before the p-orbitals. In a hydrogen-like atom, which only has one electron, the s-orbital and the p-orbitals of the same shell have exactly the same energy, to a very good approximation in the absence of external electromagnetic fields. (However, in a real hydrogen atom, the energy levels are slightly split by the magnetic field of the nucleus, and by the quantum electrodynamic effects of the Lamb shift.)

Ionization of the transition metals

The naïve application of the Aufbau principle leads to a well-known paradox (or apparent paradox) in the basic chemistry of the transition metals. Potassium and calcium appear in the periodic table before the transition metals, and have electron configurations [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). After calcium, most neutral atoms in the first series of transition metals (Sc-Zn) have configurations with two 4s electrons, but there are two exceptions. 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. This interchange of electrons between 4s and 3d is found for all atoms of the first series of transition metals.[15] 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 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. 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.[16] 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.[17]

Similar ion-like 3dx4s0 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 ligands. The electron configuration of the central chromium atom is described as 3d6 with the six electrons filling the three lower-energy d orbitals between the ligands. The other two d orbitals are at higher energy due to the crystal field of the ligands. This picture is consistent with the experimental fact that the complex is diamagnetic, meaning that it has no unpaired electrons. However, in a more accurate description using molecular orbital theory, the d-like orbitals occupied by the six electrons are no longer identical with the d orbitals of the free atom.

Other exceptions to Madelung's rule

There are several more exceptions to Madelung's rule among the heavier elements, and as atomic number increases it becomes more and more difficult to find simple explanations such as the stability of half-filled subshells. It is possible to predict most of the exceptions by Hartree–Fock calculations,[18] 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[19] tend to decrease the energy of the s-orbitals in relation to the other atomic orbitals.[20] The table below 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).

Electron shells filled in violation of Madelung's rule[21] (red)
Period 4   Period 5   Period 6   Period 7
Element Z Electron Configuration   Element Z Electron Configuration   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
             
Scandium 21 [Ar] 4s2 3d1   Yttrium 39 [Kr] 5s2 4d1   Lutetium 71 [Xe] 6s2 4f14 5d1   Lawrencium 103 [Rn] 7s2 5f14 7p1
Titanium 22 [Ar] 4s2 3d2   Zirconium 40 [Kr] 5s2 4d2   Hafnium 72 [Xe] 6s2 4f14 5d2   Rutherfordium 104 [Rn] 7s2 5f14 6d2
Vanadium 23 [Ar] 4s2 3d3   Niobium 41 [Kr] 5s1 4d4   Tantalum 73 [Xe] 6s2 4f14 5d3   Dubnium 105 [Rn] 7s2 5f14 6d3
Chromium 24 [Ar] 4s1 3d5   Molybdenum 42 [Kr] 5s1 4d5   Tungsten 74 [Xe] 6s2 4f14 5d4   Seaborgium 106 [Rn] 7s2 5f14 6d4
Manganese 25 [Ar] 4s2 3d5   Technetium 43 [Kr] 5s2 4d5   Rhenium 75 [Xe] 6s2 4f14 5d5   Bohrium 107 [Rn] 7s2 5f14 6d5
Iron 26 [Ar] 4s2 3d6   Ruthenium 44 [Kr] 5s1 4d7   Osmium 76 [Xe] 6s2 4f14 5d6   Hassium 108 [Rn] 7s2 5f14 6d6
Cobalt 27 [Ar] 4s2 3d7   Rhodium 45 [Kr] 5s1 4d8   Iridium 77 [Xe] 6s2 4f14 5d7    
Nickel 28 [Ar] 4s2 3d8 or
[Ar] 4s1 3d9 (disputed)[22]
  Palladium 46 [Kr] 4d10   Platinum 78 [Xe] 6s1 4f14 5d9    
Copper 29 [Ar] 4s1 3d10   Silver 47 [Kr] 5s1 4d10   Gold 79 [Xe] 6s1 4f14 5d10    
Zinc 30 [Ar] 4s2 3d10   Cadmium 48 [Kr] 5s2 4d10   Mercury 80 [Xe] 6s2 4f14 5d10    

The electron-shell configuration of elements beyond hassium has not yet been empirically verified, but they are expected to follow Madelung's rule without exceptions until element 120.[23]

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,[24] rather than the atomic orbital labels used for atoms and monatomic ions: hence, the electron configuration of the dioxygen molecule, O2, is written 1σg2 1σu2 2σg2 2σu2 3σg2 1πu4 1πg2,[25][26] or equivalently 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.

The electronic configuration of polyatomic molecules can change without absorption or emission of a photon through vibronic couplings.

Electron configuration in solids

In a solid, the electron states become very numerous. They cease to be discrete, and effectively blend into continuous ranges of possible states (an electron band). The notion of electron configuration ceases to be relevant, and yields to band theory.

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" (LCAO) approximation, using an ever-larger and more complex basis set of atomic orbitals as the starting point. The last step in such a calculation is the assignment of electrons among the molecular orbitals according to the Aufbau principle. Not all methods in calculational chemistry rely on electron configuration: density functional theory (DFT) is an important example of a method that discards the model.

For atoms or molecules with more than one electron, the motion of electrons are correlated and such a picture is no longer exact. A very large number of electronic configurations are needed to exactly describe any multi-electron system, and no energy can be associated with one single configuration. However, the electronic wave function is usually dominated by a very small number of configurations and therefore the notion of electronic configuration remains essential for multi-electron systems.

A fundamental application of electron configurations is in the interpretation of atomic spectra. In this case, it is necessary to supplement the electron configuration with one or more term symbols, which describe the different energy levels available to an atom. Term symbols can be calculated for any electron configuration, not just the ground-state configuration listed in tables, although not all the energy levels are observed in practice. It is through the analysis of atomic spectra that the ground-state electron configurations of the elements were experimentally determined.

See also

Notes

  1. ^ a b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "configuration (electronic)". doi:10.1351/goldbook.C01248
  2. ^ a b In formal terms, the quantum numbers n, and m arise from the fact that the solutions to the time-independent Schrödinger equation for hydrogen-like atoms are based on spherical harmonics.
  3. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Pauli exclusion principle". doi:10.1351/goldbook.PT07089
  4. ^ Weisstein, Eric W. (2007). "Electron Orbital". wolfram.
  5. ^ Ebbing, Darrell D.; Gammon, Steven D. (2007-01-12). General Chemistry. p. 284. ISBN 978-0-618-73879-3.
  6. ^ Bohr, Niels (1923). "Über die Anwendung der Quantumtheorie auf den Atombau. I". Zeitschrift für Physik. 13: 117. Bibcode:1923ZPhy...13..117B. doi:10.1007/BF01328209.
  7. ^ Stoner, E.C. (1924). "The distribution of electrons among atomic levels". Philosophical Magazine. 6th Series. 48 (286): 719–36. doi:10.1080/14786442408634535.
  8. ^ Pauli, Wolfgang (1925). "Über den Einfluss der Geschwindigkeitsabhändigkeit der elektronmasse auf den Zeemaneffekt". Zeitschrift für Physik. 31: 373. Bibcode:1925ZPhy...31..373P. doi:10.1007/BF02980592. English translation from Scerri, Eric R. (1991). "The Electron Configuration Model, Quantum Mechanics and Reduction" (PDF). Br. J. Philos. Sci. 42 (3): 309–25. doi:10.1093/bjps/42.3.309.
  9. ^ a b Madelung, Erwin (1936). Mathematische Hilfsmittel des Physikers. Berlin: Springer.
  10. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "aufbau principle". doi:10.1351/goldbook.AT06996
  11. ^ Wong, D. Pan (1979). "Theoretical justification of Madelung's rule". Journal of Chemical Education. 56 (11): 714–18. Bibcode:1979JChEd..56..714W. doi:10.1021/ed056p714.
  12. ^ The similarities in chemical properties and the numerical relationship between the atomic weights of calcium, strontium and barium was first noted by Johann Wolfgang Döbereiner in 1817.
  13. ^ Scerri, Eric R. (1998). "How Good Is the Quantum Mechanical Explanation of the Periodic System?" (PDF). Journal of Chemical Education. 75 (11): 1384–85. Bibcode:1998JChEd..75.1384S. doi:10.1021/ed075p1384. Ostrovsky, V.N. (2005). "On Recent Discussion Concerning Quantum Justification of the Periodic Table of the Elements". Foundations of Chemistry. 7 (3): 235–39. doi:10.1007/s10698-005-2141-y.
  14. ^ Electrons are identical particles, a fact that is sometimes referred to as "indistinguishability of electrons". A one-electron solution to a many-electron system would imply that the electrons could be distinguished from one another, and there is strong experimental evidence that they can't be. The exact solution of a many-electron system is a n-body problem with n ≥ 3 (the nucleus counts as one of the "bodies"): such problems have evaded analytical solution since at least the time of Euler.
  15. ^ There are some cases in the second and third series where the electron remains in an s-orbital.
  16. ^ Melrose, Melvyn P.; Scerri, Eric R. (1996). "Why the 4s Orbital is Occupied before the 3d". Journal of Chemical Education. 73 (6): 498–503. Bibcode:1996JChEd..73..498M. doi:10.1021/ed073p498.
  17. ^ Scerri, Eric (7 November 2013). "The trouble with the aufbau principle". Education in Chemistry. Vol. 50 no. 6. Royal Society of Chemistry. pp. 24–26. Archived from the original on 21 January 2018. Retrieved 12 June 2018.
  18. ^ Meek, Terry L.; Allen, Leland C. (2002). "Configuration irregularities: deviations from the Madelung rule and inversion of orbital energy levels". Chem. Phys. Lett. 362 (5–6): 362–64. Bibcode:2002CPL...362..362M. doi:10.1016/S0009-2614(02)00919-3.
  19. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "relativistic effects". doi:10.1351/goldbook.RT07093
  20. ^ Pyykkö, Pekka (1988). "Relativistic effects in structural chemistry". Chem. Rev. 88 (3): 563–94. doi:10.1021/cr00085a006.
  21. ^ Miessler, G. L.; Tarr, D. A. (1999). Inorganic Chemistry (2nd ed.). Prentice-Hall. p. 38.
  22. ^ Scerri, Eric R. (2007). The periodic table: its story and its significance. Oxford University Press. pp. 239–240. ISBN 0-19-530573-6.
  23. ^ Hoffman, Darleane C.; Lee, Diana M.; Pershina, Valeria (2006). "Transactinides and the future elements". In Morss; Edelstein, Norman M.; Fuger, Jean. The Chemistry of the Actinide and Transactinide Elements (3rd ed.). Dordrecht, The Netherlands: Springer Science+Business Media. ISBN 1-4020-3555-1.
  24. ^ The labels are written in lowercase to indicate that they correspond to one-electron functions. They are numbered consecutively for each symmetry type (irreducible representation in the character table of the point group for the molecule), starting from the orbital of lowest energy for that type.
  25. ^ Levine I.N. Quantum Chemistry (4th ed., Prentice Hall 1991) p.376 ISBN 0-205-12770-3
  26. ^ Miessler G.L. and Tarr D.A. Inorganic Chemistry (2nd ed., Prentice Hall 1999) p.118 ISBN 0-13-841891-8

External links

Aufbau principle

The aufbau principle states that in the ground state of an atom or ion, electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. For example, the 1s shell is filled before the 2s subshell is occupied. In this way, the electrons of an atom or ion form the most stable electron configuration possible. An example is the configuration 1s2 2s2 2p6 3s2 3p3 for the phosphorus atom, meaning that the 1s subshell has 2 electrons etc.

Aufbau is a German noun that means construction or "building-up". The aufbau principle is sometimes called the building-up principle or the aufbau rule.

The details of this "building-up" tendency are described mathematically by atomic orbital functions. Electron behavior is elaborated by other principles of atomic physics, such as Hund's rule and the Pauli exclusion principle. Hund's rule asserts that even if multiple orbitals of the same energy are available, electrons fill unoccupied orbitals first, before reusing orbitals occupied by other electrons. But, according to the Pauli exclusion principle, in order for electrons to occupy the same orbital, they must have different spins (−1/2 and 1/2).

As we pass from one element to another of next higher atomic number, one electron is added each time to the atom.

The maximum number of electrons in any shell is 2n2, where n is the principal quantum number.

The maximum number of electrons in a subshell (s, p, d or f) is equal to 2(2ℓ+1) where ℓ = 0, 1, 2, 3...

Thus these subshells can have a maximum of 2, 6, 10 and 14 electrons respectively.

In the ground state the electronic configuration can be built up by placing electrons in the lowest available orbitals until the total number of electrons added is equal to the atomic number. Thus orbitals are filled in the order of increasing energy, using two general rules to help predict electronic configurations:-

1. Electrons are assigned to orbitals in order of increasing value of (n+ℓ).

2. For subshells with the same value of (n+ℓ), electrons are assigned first to the sub shell with lower n.A version of the aufbau principle known as the nuclear shell model is used to predict the configuration of protons and neutrons in an atomic nucleus.

Bent molecular geometry

In chemistry, the term "bent" can be applied to certain molecules to describe their molecular geometry. Certain atoms, such as oxygen, will almost always set their two (or more) covalent bonds in non-collinear directions due to their electron configuration. Water (H2O) is an example of a bent molecule, as well as its analogues. The bond angle between the two hydrogen atoms is approximately 104.45°. Nonlinear geometry is commonly observed for other triatomic molecules and ions containing only main group elements, prominent examples being nitrogen dioxide (NO2), sulfur dichloride (SCl2), and methylene (CH2).

This geometry is almost always consistent with VSEPR theory, which usually explains non-collinearity of atoms with a presence of lone pairs. There are several variants of bending, where the most common is AX2E2 where two covalent bonds and two lone pairs of the central atom (A) form a complete 8-electron shell. They have central angles from 104° to 109.5°, where the latter is consistent with a simplistic theory which predicts the tetrahedral symmetry of four sp3 hybridised orbitals. The most common actual angles are 105°, 107°, and 109°: they vary because of the different properties of the peripheral atoms (X).

Other cases also experience orbital hybridisation, but in different degrees. AX2E1 molecules, such as SnCl2, have only one lone pair and the central angle about 120° (the centre and two vertices of an equilateral triangle). They have three sp2 orbitals. There exist also sd-hybridised AX2 compounds of transition metals without lone pairs: they have the central angle about 90° and are also classified as bent.

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 complex. The d electron count is an effective way to understand the geometry and reactivity of transition metal complexes. The formalism has been incorporated into the two major models used to describe coordination complexes; crystal field theory and ligand field theory, which is a more advanced version based on molecular orbital theory.

Electron configurations of the elements (data page)

This page shows the electron configurations of the neutral gaseous atoms in their ground states. For each atom the subshells are given first in concise form, then with all subshells written out, followed by the number of electrons per shell. Electron configurations of elements beyond hassium (element 108) are predicted.

As an approximate rule, electron configurations are given by the Aufbau principle and the Madelung rule. However there are numerous exceptions; for example the lightest exception is chromium, which would be predicted to have the configuration 1s2 2s2 2p6 3s2 3p6 3d4 4s2, written as [Ar] 3d4 4s2, but whose actual configuration given in the table below is [Ar] 3d5 4s1.

Group 10 element

Group 10, numbered by current IUPAC style, is the group of chemical elements in the periodic table that consists of nickel (Ni), palladium (Pd), platinum (Pt), and perhaps also the chemically uncharacterized darmstadtium (Ds). All are d-block transition metals. All known isotopes of darmstadtium are radioactive with short half-lives, and are not known to occur in nature; only minute quantities have been synthesized in laboratories.

Like other groups, the members of this group show patterns in electron configuration, especially in the outermost shells, although for this group they are particularly weak, with palladium being an exceptional case. The relativistic stabilization of the 7s orbital is the explanation to the predicted electron configuration of darmstadtium, which, unusually for this group, conforms to that predicted by the Aufbau principle.

Group 6 element

Group 6, numbered by IUPAC style, is a group of elements in the periodic table. Its members are chromium (Cr), molybdenum (Mo), tungsten (W), and seaborgium (Sg). These are all transition metals and chromium, molybdenum and tungsten are refractory metals. The period 8 elements of group 6 are likely to be either unpenthexium (Uph) or unpentoctium (Upo). This may not be possible; drip instability may imply that the periodic table ends around unbihexium. Neither unpenthexium nor unpentoctium have been synthesized, and it is unlikely that this will happen in the near future.

Like other groups, the members of this family show patterns in its electron configuration, especially the outermost shells resulting in trends in chemical behavior:

"Group 6" is the new IUPAC name for this group; the old style name was "group VIB" in the old US system (CAS) or "group VIA" in the European system (old IUPAC). Group 6 must not be confused with the group with the old-style group crossed names of either VIA (US system, CAS) or VIB (European system, old IUPAC). That group is now called group 16.

Group 8 element

Group 8 is a group of chemical element in the periodic table. It consists of iron (Fe), ruthenium (Ru), osmium (Os) and hassium (Hs). They are all transition metals. Like other groups, the members of this family show patterns in electron configuration, especially in the outermost shells, resulting in trends in chemical behavior.

"Group 8" is the modern IUPAC name for this group; the old style name was group VIIIB in the CAS, US system or group VIIIA in the old IUPAC, European system.

Group 8 should not be confused with the old-style group name of VIIIA by CAS/US naming. That group is now called group 18.

Group 9 element

Group 9, numbered by IUPAC nomenclature, is a group of chemical element in the periodic table. Members are cobalt (Co), rhodium (Rh), iridium (Ir) and perhaps also the chemically uncharacterized meitnerium (Mt). These are all transition metals in the d-block. All known isotopes of meitnerium are radioactive with short half-lives, and it is not known to occur in nature; only minute quantities have been synthesized in laboratories.

Like other groups, the members of this family show patterns in electron configuration, especially in the outermost shells, resulting in trends in chemical behavior; however, rhodium deviates from the pattern.

Hund's rule of maximum multiplicity

Hund's rule of maximum multiplicity is a rule based on observation of atomic spectra, which is used to predict the ground state of an atom or molecule with one or more open electronic shells. The rule states that for a given electron configuration, the lowest energy term is the one with the greatest value of spin multiplicity. This implies that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs. The rule, discovered by Friedrich Hund in 1925, is of important use in atomic chemistry, spectroscopy, and quantum chemistry, and is often abbreviated to Hund's rule, ignoring Hund's other two rules.

Isoelectronicity

Isoelectronicity is the phenomenon of two or more chemical species (atoms, molecules, radicals, ions etc.) differing in the atoms of which they are formed but having the same number of valence electrons and the same structure (that is, the same number of atoms with the same connectivity). The species concerned are termed isoelectronic.

This definition is sometimes termed valence isoelectronicity, in contrast with various alternatives. At one extreme these require identity of the total electron count and with it the entire electron configuration. More usually, alternatives are broader, and may extend to allowing different numbers of atoms in the species being compared.The importance of the concept lies in identifying significantly related species, as pairs or series. Isoelectronic species can be expected to show useful consistency and predictability in their properties. (Slight differences of, for example, structural formula, such as a double versus single bond, commonly have major effects.)

Electron-density calculations have been performed on many common substances, resulting in reaction predictions. Identifying a new, rare or odd compound as isoelectronic with one already characterised offers clues to possible properties and reactions.

Mercury(IV) fluoride

Mercury(IV) fluoride, HgF4, is the first mercury compound to be reported with mercury in the oxidation state IV. Mercury, like the other group 12 elements (cadmium and zinc), has an s2d10 electron configuration and generally only forms bonds involving its 6s orbital. This means that the highest oxidation state mercury normally attains is II, and for this reason it is usually considered a post-transition metal instead of a transition metal. HgF4 was first reported from experiments in 2007, but its existence remains disputed; experiments conducted in 2008 could not replicate the compound.

Nitrene

In chemistry, a nitrene (R–N:) is the nitrogen analogue of a carbene. The nitrogen atom has only 6 valence electrons and is therefore considered an electrophile. A nitrene is a reactive intermediate and is involved in many chemical reactions. The simplest nitrene, HN, is also called imidogen.

Organoscandium chemistry

Organoscandium chemistry is the chemistry of organometallic compounds containing a carbon to scandium chemical bond. The interest in organoscandium compounds is mostly academic but several compound classes find practical application in catalysis, especially in polymerization. A common precursor is scandium chloride.

As with the other elements in group 3 – e.g. yttrium, forming organoyttrium compounds – and the lanthanides, the dominant oxidation state for scandium in organometallic compounds is +3 (electron configuration [Ar] 3d14s2). The members of this group also have large ionic radii with vacant s,p and d orbitals (88 pm for Sc3+ compared to 67 pm for Al3+) and as a result they behave as hard Lewis acids and tend to have high coordination numbers of 9 to 12. The metal to ligand chemical bond is largely ionic.

Periodic table

The periodic table, also known as the periodic table of elements, is a tabular display of the chemical elements, which are arranged by atomic number, electron configuration, and recurring chemical properties. The structure of the table shows periodic trends. The seven rows of the table, called periods, generally have metals on the left and non-metals on the right. The columns, called groups, contain elements with similar chemical behaviours. Six groups have accepted names as well as assigned numbers: for example, group 17 elements are the halogens; and group 18 are the noble gases. Also displayed are four simple rectangular areas or blocks associated with the filling of different atomic orbitals.

The organization of the periodic table can be used to derive relationships between the various element properties, and also to predict chemical properties and behaviours of undiscovered or newly synthesized elements. Russian chemist Dmitri Mendeleev published the first recognizable periodic table in 1869, developed mainly to illustrate periodic trends of the then-known elements. He also predicted some properties of unidentified elements that were expected to fill gaps within the table. Most of his forecasts proved to be correct. Mendeleev's idea has been slowly expanded and refined with the discovery or synthesis of further new elements and the development of new theoretical models to explain chemical behaviour. The modern periodic table now provides a useful framework for analyzing chemical reactions, and continues to be widely used in chemistry, nuclear physics and other sciences.

The elements from atomic numbers 1 (hydrogen) through 118 (oganesson) have been discovered or synthesized, completing seven full rows of the periodic table. The first 94 elements all occur naturally, though some are found only in trace amounts and a few were discovered in nature only after having first been synthesized. Elements 95 to 118 have only been synthesized in laboratories or nuclear reactors. The synthesis of elements having higher atomic numbers is currently being pursued: these elements would begin an eighth row, and theoretical work has been done to suggest possible candidates for this extension. Numerous synthetic radionuclides of naturally occurring elements have also been produced in laboratories.

Tanabe–Sugano diagram

Tanabe–Sugano diagrams are used in coordination chemistry to predict absorptions in the UV, visible and IR electromagnetic spectrum of coordination compounds. The results from a Tanabe–Sugano diagram analysis of a metal complex can also be compared to experimental spectroscopic data. They are qualitatively useful and can be used to approximate the value of 10Dq, the ligand field splitting energy. Tanabe–Sugano diagrams can be used for both high spin and low spin complexes, unlike Orgel diagrams, which apply only to high spin complexes. Tanabe–Sugano diagrams can also be used to predict the size of the ligand field necessary to cause high-spin to low-spin transitions.

In a Tanabe–Sugano diagram, the ground state is used as a constant reference, in contrast to Orgel diagrams. The energy of the ground state is taken to be zero for all field strengths, and the energies of all other terms and their components are plotted with respect to the ground term.

Tantalum(IV) sulfide

Tantalum(IV) sulfide is the inorganic compound with the formula TaS2. It is a layered compound with three-coordinate sulfide centres and trigonal prismatic metal centres. It is structurally similar to the more famous material molybdenum disulfide, MoS2. TaS2 is a semiconductor with d1 electron configuration. Although an obscure material otherwise, TaS2 has been the subject of numerous studies because it is a versatile host for intercalation of electron donors, and because it exhibits unusual phase transitions at low temperatures.

Term symbol

In quantum mechanics, the term symbol is an abbreviated description of the (total) angular momentum quantum numbers in a multi-electron atom (however, even a single electron can be described by a term symbol). Each energy level of an atom with a given electron configuration is described by not only the electron configuration but also its own term symbol, as the energy level also depends on the total angular momentum including spin. The usual atomic term symbols assume LS coupling (also known as Russell-Saunders coupling or spin-orbit coupling). The ground state term symbol is predicted by Hund's rules.

The use of the word term for an energy level is based on the Rydberg-Ritz combination principle, an empirical observation that the wavenumbers of spectral lines can be expressed as the difference of two terms. This was later explained by the Bohr quantum theory, which identified the terms (multiplied by hc, where h is the Planck constant and c the speed of light) with quantized energy levels and the spectral wavenumbers (again multiplied by hc) with photon energies.

Tables of atomic energy levels identified by their term symbols have been compiled by the National Institute of Standards and Technology. In this database, neutral atoms are identified as I, singly ionized atoms as II, etc. Neutral atoms of the chemical elements have the same term symbol for each column in the s-block and p-block elements, but may differ in d-block and f-block elements, if the ground state electron configuration changes within a column. Ground state term symbols for chemical elements are given below.

Tolman's rule

Tolman's rule states that, in a certain chemical reaction, the steps involve exclusively intermediates of 18- and 16 electron configuration. The rule is an extension of the 18-electron rule. This rule was proposed by American chemist Chadwick A. Tolman. As stated above, Tolman's rule, even for reactions that proceed via 2e− steps, is incorrect because many reactions involve configurations of fewer than 16 e−.

Many examples of homogeneous catalysis involving organometallic complexes involve shuttling of complexes between 16 and 18 electron configurations. 16-electron complexes often form adducts with Lewis bases and, if low-valent, undergo oxidative addition.

CH3I + cis-[Rh(CO)2I2]− → [(CH3)Rh(CO)2I3]−Conversely, complexes of 18 electron configuration tend to dissociate ligands or undergo reductive elimination:

[Rh(PPh3)3ClH2 → [Rh(PPh3)3Cl + H2

Valence electron

In chemistry, a valence electron is an outer shell electron that is associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed; in a single covalent bond, both atoms in the bond contribute one valence electron in order to form a shared pair. The presence of valence electrons can determine the element's chemical properties, such as its valence—whether it may bond with other elements and, if so, how readily and with how many. For a main group element, a valence electron can exist only in the outermost electron shell; in a transition metal, a valence electron can also be in an inner shell.

An atom with a closed shell of valence electrons (corresponding to an electron configuration s2p6) tends to be chemically inert. Atoms with one or two more valence electrons than are needed for a "closed" shell are highly reactive due to the following reasons:

1) It requires relatively low energy (compared to the lattice enthalpy) to remove the extra valence electrons to form a positive ion.

2) Because of their tendency either to gain the missing valence electrons (thereby forming a negative ion), or to share valence electrons (thereby forming a covalent bond).

Similar to an electron in an inner shell, a valence electron has the ability to absorb or release energy in the form of a photon. An energy gain can trigger an electron to move (jump) to an outer shell; this is known as atomic excitation. Or the electron can even break free from its associated atom's valence shell; this is ionization to form a positive ion. When an electron loses energy (thereby causing a photon to be emitted), then it can move to an inner shell which is not fully occupied.

Valence energy levels correspond to the principal quantum numbers (n = 1, 2, 3, 4, 5 ...) or are labeled alphabetically with letters used in the X-ray notation (K, L, M, …).

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