Atomic orbital

In quantum mechanics, an atomic orbital (/ˈɔːrbɪtəl/) is a function describing the location and wave-like behavior of an electron in an atom.^[1] This function describes the electron's charge distribution around the atom's nucleus, and can be used to calculate the probability of finding an electron in a specific region around the nucleus.^[2]

Each orbital in an atom is characterized by a set of values of the three quantum numbers $n$ , $ℓ$ , and $m ℓ$ , which respectively correspond to the electron's energy, its orbital angular momentum, and its orbital angular momentum projected along a chosen axis (magnetic quantum number). The orbitals with a well-defined magnetic quantum number are generally complex-valued. Real-valued orbitals can be formed as linear combinations of $m ℓ$ and $-m ℓ$ orbitals, and are often labeled using the associated harmonic polynomials (e.g., xy, x² − y²) which describe their angular structure.

An orbital can be occupied by a maximum of two electrons, each with its own projection of spin $m_{s}$ . The simple names s orbital, p orbital, d orbital, and f orbital refer to orbitals with angular momentum quantum number $ℓ = 0, 1, 2,$ and $3$ respectively. These names, together with the value of $n$ , are used to describe the electron configurations of atoms. They are derived from the description by early spectroscopists of certain series of alkali metal spectroscopic lines as sharp, principal, diffuse, and fundamental. Orbitals for $ℓ > 3$ continue alphabetically (g, h, i, k, ...),^[3] omitting j^[4]^[5] because some languages do not distinguish between the letters "i" and "j".^[6]

Atomic orbitals are the basic building blocks of the atomic orbital model (or electron cloud or wave mechanics model), a modern framework for visualizing the submicroscopic behavior of electrons in matter. In this model the electron cloud of an atom may be seen as being built up (in approximation) in an electron configuration that is a product of simpler hydrogen-like atomic orbitals. The repeating periodicity of blocks of 2, 6, 10, and 14 elements within sections of the periodic table arises naturally from the total number of electrons that occupy a complete set of s, p, d, and f orbitals, respectively, though for higher values of quantum number $n$ , particularly when the atom bears a positive charge, the energies of certain sub-shells become very similar and so the order in which they are said to be populated by electrons (e.g., Cr = [Ar]4s¹3d⁵ and Cr²⁺ = [Ar]3d⁴) can be rationalized only somewhat arbitrarily.

^ Orchin, Milton; Macomber, Roger S.; Pinhas, Allan; Wilson, R. Marshall (2005). "1. Atomic Orbital Theory" (PDF). The Vocabulary and Concepts of Organic Chemistry (2nd ed.). Wiley. Archived (PDF) from the original on 9 October 2022.
^ Daintith, J. (2004). Oxford Dictionary of Chemistry. New York: Oxford University Press. pp. 407–409. ISBN 978-0-19-860918-6.
^ Griffiths, David (1995). Introduction to Quantum Mechanics. Prentice Hall. pp. 190–191. ISBN 978-0-13-124405-4.
^ Levine, Ira (2000). Quantum Chemistry (5 ed.). Prentice Hall. pp. 144–145. ISBN 978-0-13-685512-5.
^ Laidler, Keith J.; Meiser, John H. (1982). Physical Chemistry. Benjamin/Cummings. p. 488. ISBN 978-0-8053-5682-3.
^ Atkins, Peter; de Paula, Julio; Friedman, Ronald (2009). Quanta, Matter, and Change: A Molecular Approach to Physical Chemistry. Oxford University Press. p. 106. ISBN 978-0-19-920606-3.

[1] Orchin, Milton; Macomber, Roger S.; Pinhas, Allan; Wilson, R. Marshall (2005). "1. Atomic Orbital Theory" (PDF). The Vocabulary and Concepts of Organic Chemistry (2nd ed.). Wiley. Archived (PDF) from the original on 9 October 2022.

[2] Daintith, J. (2004). Oxford Dictionary of Chemistry. New York: Oxford University Press. pp. 407–409. ISBN 978-0-19-860918-6.

[3] Griffiths, David (1995). Introduction to Quantum Mechanics. Prentice Hall. pp. 190–191. ISBN 978-0-13-124405-4.

[4] Levine, Ira (2000). Quantum Chemistry (5 ed.). Prentice Hall. pp. 144–145. ISBN 978-0-13-685512-5.

[5] Laidler, Keith J.; Meiser, John H. (1982). Physical Chemistry. Benjamin/Cummings. p. 488. ISBN 978-0-8053-5682-3.

[6] Atkins, Peter; de Paula, Julio; Friedman, Ronald (2009). Quanta, Matter, and Change: A Molecular Approach to Physical Chemistry. Oxford University Press. p. 106. ISBN 978-0-19-920606-3.

[1]

[2]

[3]

[4]

[5]

[6]