Physics:Quantum atoms/electron configuration

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Short description: Arrangement of electrons in an atom's orbitals


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An electron configuration describes how electrons are distributed among the orbitals of an atom, molecule, or solid-state system.[1] It determines many physical and chemical properties of the atom, including bonding, spectra, periodic trends, and reactivity.

Example of electron configuration showing how electrons occupy orbitals in an atom.

Description

In atoms, electron configuration gives the occupation of shells, subshells, and orbitals. For example, the electron configuration of neon is 1s2 2s2 2p6, meaning that the 1s, 2s, and 2p subshells contain two, two, and six electrons respectively.

Electron configurations describe electrons as occupying quantum states in an average field produced by the nucleus and the other electrons. In more formal quantum mechanics, configurations may be represented by Slater determinants or configuration state functions.

Electrons can move from one configuration to another by absorbing or emitting a quantum of energy, usually a photon. This connects electron configuration directly to energy levels, spectroscopy, and atomic structure.

Shells and subshells

An electron shell is a set of allowed quantum states sharing the same principal quantum number n. The maximum number of electrons in the nth shell is 2n2. Thus the first shell can hold two electrons, the second shell eight electrons, and the third shell eighteen electrons.

A subshell is defined by the azimuthal quantum number l. The values l = 0, 1, 2, and 3 correspond to the s, p, d, and f subshells. The maximum number of electrons in a subshell is 2(2l + 1), giving two electrons in an s subshell, six in a p subshell, and ten in a d subshell.

These limits follow from quantum mechanics and the Pauli exclusion principle, which states that no two electrons in the same atom can have the same set of four quantum numbers.[2] A detailed treatment of atomic spectra and structure is given by Cowan.[3]

Notation

Electron configurations are written as a sequence of subshell labels with superscripts giving the number of electrons. Hydrogen is written as 1s1, lithium as 1s2 2s1, and phosphorus as 1s2 2s2 2p6 3s2 3p3.

The letters s, p, d, and f originated from early spectroscopic terms: sharp, principal, diffuse, and fundamental. Later labels continue alphabetically as g, h, i, and so on, although these orbitals are rarely needed in ordinary chemistry.[4][5]

For larger atoms, noble-gas shorthand is often used. For example, phosphorus may be written as [Ne] 3s2 3p3. Empty subshells may be omitted or explicitly written with a superscript zero, depending on context.[6]

Filling rules

Electron configurations follow several important rules:

  • the Pauli exclusion principle, which prevents two electrons in the same atom from sharing all four quantum numbers
  • Hund’s rule, which favors parallel spins in degenerate orbitals
  • the Aufbau principle, which fills lower-energy orbitals before higher-energy orbitals

The Aufbau principle states that a maximum of two electrons are placed into orbitals in order of increasing orbital energy.[7] In the Madelung rule, subshells are filled by increasing n + l; if two subshells have the same value, the one with lower n is filled first.[8][9]

The common filling sequence begins:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p

Ground and excited states

The configuration with the lowest electronic energy is the ground-state configuration. Any higher-energy configuration is an excited state. For example, sodium has the ground-state configuration 1s2 2s2 2p6 3s1. If the 3s electron is promoted to 3p, the atom enters an excited configuration.

Atoms can return from excited states to lower states by emitting photons. This is why electron configuration is essential for understanding emission spectra, absorption spectra, lasers, and atomic lamps.

History

The concept of electron arrangement developed from early atomic theory and spectroscopy. Irving Langmuir proposed a shell-like arrangement of electrons in 1919.[10] Niels Bohr later connected electron shells with periodicity in the elements.[11]

Richard Abegg described valence electrons in 1904.[12] E. C. Stoner improved the shell model by incorporating an additional quantum number.[13] Wolfgang Pauli introduced the exclusion principle in 1925, providing the key rule for shell and subshell occupation.[14]

The Schrödinger equation, published in 1926, supplied the modern quantum-mechanical basis for atomic orbitals and quantum numbers.

Periodic table

The structure of the periodic table is closely related to electron configuration. Elements in the same group often have similar valence-shell configurations and therefore similar chemical properties.

The s, p, d, and f blocks of the periodic table correspond to the filling of s, p, d, and f subshells. Valence electrons largely determine bonding behavior, ionization energy, and chemical reactivity.

Exceptions and limitations

The Aufbau principle is approximate. Electron energies depend on the nuclear charge, electron-electron interactions, and the occupation of other orbitals. Transition metals and heavier elements often show exceptions to simple Madelung filling.

Chromium, copper, niobium, palladium, platinum, and other elements have configurations that differ from the simplest filling sequence. Explanations involving half-filled or filled subshells are useful but incomplete.[15] Orbital energies may shift with ionization, bonding, and chemical environment.[16][17]

Chemical environments can also change the effective configuration. For example, thorium ions and thorium compounds may show different orbital occupations.[18][19] In metals and compounds, configurations may be better described as mixtures or superpositions of several configurations.[20]

Relativistic effects become important for heavy elements and can shift orbital energies, especially for s and p orbitals.[21][22] Superheavy-element configurations are therefore partly predicted rather than experimentally verified.[23][24][25]

Open and closed shells

An open shell is a valence shell that is not completely filled, or that contains unpaired electrons. A closed shell is a filled shell or subshell and is usually especially stable.[26]

In molecules, open-shell systems contain unpaired electrons and often require special quantum-chemical treatment such as restricted open-shell or unrestricted Hartree–Fock methods.[27] Open-shell molecules are often more difficult to model computationally.[28]

Noble gas configuration

A noble gas configuration is a filled-shell electron configuration like those of helium, neon, argon, krypton, xenon, and radon. Main-group atoms often react in ways that move them toward a noble-gas-like valence shell. This is the basis of the octet rule for many simple compounds.

Molecules and solids

Electron configuration in molecules is more complex than in atoms because molecular orbitals extend over more than one nucleus. Molecular orbitals are labeled by symmetry rather than by atomic s, p, d, and f labels. The configuration of dioxygen, for example, explains its paramagnetism and was an important success of molecular orbital theory.[29][30]

In solids, the number of electron states becomes very large and the states form energy bands. In that context, the language of electron configuration gives way to band theory.

Applications

Electron configurations are used to understand:

  • the structure of the periodic table
  • chemical bonding and valence
  • atomic and molecular spectra
  • magnetic properties
  • lasers and semiconductors
  • computational chemistry and molecular orbital theory

In computational chemistry, configurations are often combined with molecular orbital theory and basis-set methods. Density functional theory uses a different framework but still connects electronic structure to observable properties.

Properties

  • distribution over energy levels
  • arrangement within orbitals
  • linked to spin and quantum numbers
  • determines valence behavior and periodic trends
  • important for spectroscopy and chemical bonding

See also

Table of contents (176 articles)

Index

Full contents

1. Foundations (11)↑
  1. Physics:Quantum basics
  2. Physics:Quantum Postulates
  3. Physics:Quantum Hilbert space
  4. Physics:Quantum Observables and operators
  5. Physics:Quantum mechanics
  6. Physics:Quantum mechanics measurements
  7. Physics:Quantum state
  8. Physics:Quantum system
  9. Physics:Quantum superposition
  10. Physics:Quantum probability
  11. Physics:Quantum Mathematical Foundations of Quantum Theory
2. Conceptual and interpretations (13)↑
  1. Physics:Quantum Interpretations of quantum mechanics
  2. Physics:Quantum Wave–particle duality
  3. Physics:Quantum Complementarity principle
  4. Physics:Quantum Uncertainty principle
  5. Physics:Quantum Measurement problem
  6. Physics:Quantum Bell's theorem
  7. Physics:Quantum Hidden variable theory
  8. Physics:Quantum nonlocality
  9. Physics:Quantum contextuality
  10. Physics:Quantum Darwinism
  11. Physics:Quantum A Spooky Action at a Distance
  12. Physics:Quantum A Walk Through the Universe
  13. Physics:Quantum The Secret of Cohesion and How Waves Hold Matter Together
3. Mathematical structure and systems (13)↑
  1. Physics:Quantum Density matrix
  2. Physics:Quantum Exactly solvable quantum systems
  3. Physics:Quantum Formulas Collection
  4. Physics:Quantum A Matter Of Size
  5. Physics:Quantum Symmetry in quantum mechanics
  6. Physics:Quantum Angular momentum operator
  7. Physics:Quantum Runge–Lenz vector
  8. Physics:Quantum Approximation Methods
  9. Physics:Quantum Matter Elements and Particles
  10. Physics:Quantum Dirac equation
  11. Physics:Quantum Klein–Gordon equation
  12. Physics:Quantum pendulum
  13. Physics:Quantum configuration space
4. Atomic and spectroscopy (14)↑
    Quantum atomic structure and spectroscopy: orbitals, energy levels, and emission and absorption spectra.
  1. Physics:Quantum Atomic structure and spectroscopy
  2. Physics:Quantum Hydrogen atom
  3. Physics:Quantum number
  4. Physics:Quantum Multi-electron atoms
  5. Physics:Quantum Fine structure
  6. Physics:Quantum Hyperfine structure
  7. Physics:Quantum Isotopic shift
  8. Physics:Quantum defect
  9. Physics:Quantum Zeeman effect
  10. Physics:Quantum Stark effect
  11. Physics:Quantum Spectral lines and series
  12. Physics:Quantum Selection rules
  13. Physics:Quantum Fermi's golden rule
  14. Physics:Quantum beats
5. Wavefunctions and modes (9)↑
    A quantum wavefunction showing probability amplitude in space; the square of its magnitude gives the probability density.
  1. Physics:Quantum Wavefunction
  2. Physics:Quantum Superposition principle
  3. Physics:Quantum Eigenstates and eigenvalues
  4. Physics:Quantum Boundary conditions and quantization
  5. Physics:Quantum Standing waves and modes
  6. Physics:Quantum Normal modes and field quantization
  7. Physics:Number of independent spatial modes in a spherical volume
  8. Physics:Quantum Density of states
  9. Physics:Quantum carpet
6. Quantum dynamics and evolution (17)↑
  1. Physics:Quantum Time evolution
  2. Physics:Quantum Schrödinger equation
  3. Physics:Quantum Time-dependent Schrödinger equation
  4. Physics:Quantum Stationary states
  5. Physics:Quantum Perturbation theory
  6. Physics:Quantum Time-dependent perturbation theory
  7. Physics:Quantum Adiabatic theorem
  8. Physics:Quantum Scattering theory
  9. Physics:Quantum S-matrix
  10. Physics:Quantum tunnelling
  11. Physics:Quantum speed limit
  12. Physics:Quantum revival
  13. Physics:Quantum reflection
  14. Physics:Quantum oscillations
  15. Physics:Quantum jump
  16. Physics:Quantum boomerang effect
  17. Physics:Quantum chaos
7. Measurement and information (8)↑
  1. Physics:Quantum Measurement theory
  2. Physics:Quantum Measurement operators
  3. Physics:Quantum Projective measurement
  4. Physics:Quantum POVM
  5. Physics:Quantum Weak measurement
  6. Physics:Quantum Measurement collapse
  7. Physics:Quantum Zeno effect
  8. Physics:Quantum limit
8. Quantum information and computing (10)↑
  1. Physics:Quantum information theory
  2. Physics:Quantum Qubit
  3. Physics:Quantum Entanglement
  4. Physics:Quantum Gates and circuits
  5. Physics:Quantum Computing Algorithms in the NISQ Era
  6. Physics:Quantum Noisy Qubits
  7. Physics:Quantum random access code
  8. Physics:Quantum pseudo-telepathy
  9. Physics:Quantum network
  10. Physics:Quantum money
9. Quantum optics and experiments (5)↑
    Experimental quantum physics: qubits, dilution refrigerators, quantum communication, and laboratory systems.
  1. Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy
  2. Physics:Quantum optics beam splitter experiments
  3. Physics:Quantum Ultra fast lasers
  4. Physics:Quantum Experimental quantum physics
  5. Physics:Quantum optics
    6. Template:Quantum optics operators
10. Open quantum systems (9)↑
  1. Physics:Quantum Open systems
  2. Physics:Quantum Master equation
  3. Physics:Quantum Lindblad equation
  4. Physics:Quantum Decoherence
  5. Physics:Quantum dissipation
  6. Physics:Quantum Markov semigroup
  7. Physics:Quantum Markovian dynamics
  8. Physics:Quantum Non-Markovian dynamics
  9. Physics:Quantum Trajectories
11. Quantum field theory (19)↑
    Structural dependency map of quantum field theory.
  1. Physics:Quantum field theory (QFT) basics
  2. Physics:Quantum field theory (QFT) core
  3. Physics:Quantum Fields and Particles
  4. Physics:Quantum Second quantization
  5. Physics:Quantum Harmonic Oscillator field modes
  6. Physics:Quantum Creation and annihilation operators
  7. Physics:Quantum vacuum fluctuations
  8. Physics:Quantum Propagators in quantum field theory
  9. Physics:Quantum Feynman diagrams
  10. Physics:Quantum Path integral formulation
  11. Physics:Quantum Renormalization in field theory
  12. Physics:Quantum Renormalization group
  13. Physics:Quantum Field Theory Gauge symmetry
  14. Physics:Quantum Non-Abelian gauge theory
  15. Physics:Quantum Electrodynamics (QED)
  16. Physics:Quantum chromodynamics (QCD)
  17. Physics:Quantum Electroweak theory
  18. Physics:Quantum Standard Model
  19. Physics:Quantum triviality
12. Statistical mechanics and kinetic theory (9)↑
  1. Physics:Quantum Statistical mechanics
  2. Physics:Quantum Partition function
  3. Physics:Quantum Distribution functions
  4. Physics:Quantum Liouville equation
  5. Physics:Quantum Kinetic theory
  6. Physics:Quantum Boltzmann equation
  7. Physics:Quantum BBGKY hierarchy
  8. Physics:Quantum Relaxation and thermalization
  9. Physics:Quantum Thermodynamics
13. Condensed matter and solid-state physics (13)↑
  1. Physics:Quantum Band structure
  2. Physics:Quantum Fermi surfaces
  3. Physics:Quantum Semiconductor physics
  4. Physics:Quantum Phonons
  5. Physics:Quantum Electron-phonon interaction
  6. Physics:Quantum Superconductivity
  7. Physics:Quantum Topological phases of matter
  8. Physics:Quantum well
  9. Physics:Quantum spin liquid
  10. Physics:Quantum spin Hall effect
  11. Physics:Quantum phase transition
  12. Physics:Quantum critical point
  13. Physics:Quantum dot
14. Plasma and fusion physics (8)↑
    Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.
  1. Physics:Quantum Fusion reactions and Lawson criterion
  2. Physics:Quantum Plasma (fusion context)
  3. Physics:Quantum Magnetic confinement fusion
  4. Physics:Quantum Inertial confinement fusion
  5. Physics:Quantum Plasma instabilities and turbulence
  6. Physics:Quantum Tokamak core plasma
  7. Physics:Quantum Tokamak edge physics and recycling asymmetries
  8. Physics:Quantum Stellarator
15. Timeline (8)↑
  1. Physics:Quantum mechanics/Timeline
  2. Physics:Quantum mechanics/Timeline/Pre-quantum era
  3. Physics:Quantum mechanics/Timeline/Old quantum theory
  4. Physics:Quantum mechanics/Timeline/Modern quantum mechanics
  5. Physics:Quantum mechanics/Timeline/Quantum field theory era
  6. Physics:Quantum mechanics/Timeline/Quantum information era
  7. Physics:Quantum mechanics/Timeline/Quantum technology era
  8. Physics:Quantum mechanics/Timeline/Quiz
16. Advanced and frontier topics (9)↑
  1. Physics:Quantum topology
  2. Physics:Quantum battery
  3. Physics:Quantum Supersymmetry
  4. Physics:Quantum Black hole thermodynamics
  5. Physics:Quantum Holographic principle
  6. Physics:Quantum gravity
  7. Physics:Quantum De Sitter invariant special relativity
  8. Physics:Quantum Doubly special relativity
  9. Physics:Quantum arithmetic geometry

References

  1. ↑ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "configuration (electronic)". doi:10.1351/goldbook.C01248
  2. ↑ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Pauli exclusion principle". doi:10.1351/goldbook.PT07089
  3. ↑ Cowan, Robert D. (2020). The Theory of Atomic Structure and Spectra. University of California Press. ISBN 9780520906150. 
  4. ↑ Weisstein, Eric W. (2007). "Electron Orbital". wolfram. http://scienceworld.wolfram.com/physics/ElectronOrbital.html. 
  5. ↑ Ebbing, Darrell D.; Gammon, Steven D. (2007-01-12). General Chemistry. Cengage Learning. p. 284. ISBN 978-0-618-73879-3. https://books.google.com/books?id=_vRm5tiUJcsC&pg=PA284. 
  6. ↑ Rayner-Canham, Geoff; Overton, Tina (2014). Descriptive Inorganic Chemistry (6 ed.). Macmillan Education. pp. 13–15. ISBN 978-1-319-15411-0. 
  7. ↑ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "aufbau principle". doi:10.1351/goldbook.AT06996
  8. ↑ Madelung, Erwin (1936). Mathematische Hilfsmittel des Physikers. Berlin: Springer. 
  9. ↑ Wong, D. Pan (1979). "Theoretical justification of Madelung's rule". Journal of Chemical Education 56 (11): 714–18. doi:10.1021/ed056p714. Bibcode: 1979JChEd..56..714W. 
  10. ↑ Langmuir, Irving (June 1919). "The Arrangement of Electrons in Atoms and Molecules". Journal of the American Chemical Society 41 (6): 868–934. doi:10.1021/ja02227a002. Bibcode: 1919JAChS..41..868L. https://zenodo.org/record/1429026. 
  11. ↑ Bohr, Niels (1923). "Über die Anwendung der Quantumtheorie auf den Atombau. I". Zeitschrift für Physik 13 (1): 117. doi:10.1007/BF01328209. Bibcode: 1923ZPhy...13..117B. 
  12. ↑ Abegg, R. (1904). "Die Valenz und das periodische System. Versuch einer Theorie der Molekularverbindungen". Zeitschrift für Anorganische Chemie 39 (1): 330–380. doi:10.1002/zaac.19040390125. https://zenodo.org/record/1428102. 
  13. ↑ Stoner, E.C. (1924). "The distribution of electrons among atomic levels". Philosophical Magazine. 6th Series 48 (286): 719–36. doi:10.1080/14786442408634535. 
  14. ↑ Pauli, Wolfgang (1925). "Über den Einfluss der Geschwindigkeitsabhändigkeit der elektronmasse auf den Zeemaneffekt". Zeitschrift für Physik 31 (1): 373. doi:10.1007/BF02980592. Bibcode: 1925ZPhy...31..373P.  English translation from Scerri, Eric R. (1991). "The Electron Configuration Model, Quantum Mechanics and Reduction". The British Journal for the Philosophy of Science 42 (3): 309–25. doi:10.1093/bjps/42.3.309. http://www.chem.ucla.edu/dept/Faculty/scerri/pdf/BJPS.pdf. 
  15. ↑ Scerri, Eric (2019). "Five ideas in chemical education that must die". Foundations of Chemistry 21: 61–69. doi:10.1007/s10698-018-09327-y. 
  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. doi:10.1021/ed073p498. Bibcode: 1996JChEd..73..498M. 
  17. ↑ Scerri, Eric (7 November 2013). "The trouble with the aufbau principle". Education in Chemistry (Royal Society of Chemistry) 50 (6): 24–26. https://eic.rsc.org/feature/the-trouble-with-the-aufbau-principle/2000133.article. Retrieved 12 June 2018. 
  18. ↑ Langeslay, Ryan R.; Fieser, Megan E.; Ziller, Joseph W.; Furche, Philip; Evans, William J. (2015). "Synthesis, structure, and reactivity of crystalline molecular complexes of the {[C5H3(SiMe3)23Th}1− anion containing thorium in the formal +2 oxidation state"]. Chem. Sci. 6 (1): 517–521. doi:10.1039/C4SC03033H. PMID 29560172. 
  19. ↑ Wickleder, Mathias S.; Fourest, Blandine; Dorhout, Peter K. (2006). "Thorium". in Morss, Lester R.; Edelstein, Norman M.; Fuger, Jean. The Chemistry of the Actinide and Transactinide Elements. 3 (3rd ed.). Dordrecht, the Netherlands: Springer. pp. 52–160. doi:10.1007/1-4020-3598-5_3. ISBN 978-1-4020-3555-5. http://radchem.nevada.edu/classes/rdch710/files/thorium.pdf. 
  20. ↑ Ferrão, Luiz; Machado, Francisco Bolivar Correto; Cunha, Leonardo dos Anjos; Fernandes, Gabriel Freire Sanzovo. "The Chemical Bond Across the Periodic Table: Part 1 – First Row and Simple Metals". ChemRxiv. doi:10.26434/chemrxiv.11860941. https://figshare.com/articles/The_Chemical_Bond_Across_the_Periodic_Table_Part_1_First_Row_and_Simple_Metals/11860941. Retrieved 23 August 2020. 
  21. ↑ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "relativistic effects". doi:10.1351/goldbook.RT07093
  22. ↑ Pyykkö, Pekka (1988). "Relativistic effects in structural chemistry". Chemical Reviews 88 (3): 563–94. doi:10.1021/cr00085a006. 
  23. ↑ Umemoto, Koichiro; Saito, Susumu (1996). "Electronic Configurations of Superheavy Elements". Journal of the Physical Society of Japan 65 (10): 3175–9. doi:10.1143/JPSJ.65.3175. Bibcode: 1996JPSJ...65.3175U. https://journals.jps.jp/doi/pdf/10.1143/JPSJ.65.3175. Retrieved 31 January 2021. 
  24. ↑ 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 978-1-4020-3555-5. 
  25. ↑ Pyykkö, Pekka (2016). "Is the Periodic Table all right ("PT OK")?". Nobel Symposium NS160 – Chemistry and Physics of Heavy and Superheavy Elements. https://www.epj-conferences.org/articles/epjconf/pdf/2016/26/epjconf-NS160-01001.pdf. 
  26. ↑ "Periodic table". http://www.newi.ac.uk/buckleyc/periodic.htm. 
  27. ↑ "Chapter 11. Configuration Interaction". AMPAC™ 10 User Guide. Semichem, Inc.. http://www.semichem.com/ampacmanual/ci.html. 
  28. ↑ "Laboratory for Theoretical Studies of Electronic Structure and Spectroscopy of Open-Shell and Electronically Excited Species – iOpenShell". http://iopenshell.usc.edu/. 
  29. ↑ Levine I.N. Quantum Chemistry (4th ed., Prentice Hall 1991) p.376 ISBN 0-205-12770-3
  30. ↑ Miessler G.L. and Tarr D.A. Inorganic Chemistry (2nd ed., Prentice Hall 1999) p.118 ISBN 0-13-841891-8


Author: Harold Foppele




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