Spectroscopic notation

This article is about the notation for atomic and molecular orbitals. It is not to be confused with the Russel–Saunders term symbol, a similar notation that describes multi-electron systems, which is often referred to as "spectroscopic notation" as well.

Spectroscopic notation provides various ways to specify atomic ionization states, as well as atomic and molecular orbitals.

Ionization states

Spectroscopists customarily refer to the spectrum arising from a given ionization state of a given element by the element's symbol followed by a Roman numeral. The numeral I is used for spectral lines associated with the neutral element, II for those from the first ionization state, III for those from the second ionization state, and so on.[1] For example, 'He I' denotes lines of neutral helium, and 'C IV' denotes lines arising from the third ionization state, C3+, of carbon. This notation is used for example to retrieve data from the NIST Atomic Spectrum Database.

Atomic and molecular orbitals

Before atomic orbitals were understood, spectroscopists discovered various distinctive series of spectral lines in atomic spectra, which they identified by letters. These letters were later associated with the azimuthal quantum number, l. The letters, "s", "p", "d", and "f", for the first four values of l were chosen to be the first letters of properties of the spectral series observed in alkali metals. Letters for subsequent values of l were assigned in alphabetical order, omitting the letter "j"[2][3][4] because some languages do not distinguish between the letters "i" and "j":[5]

letter name l
s sharp 0
p principal 1
d diffuse 2
f fundamental 3
g 4
h 5
i 6
k 7
l 8
m 9
n 10
o 11
q 12
r 13
t 14
u 15
v 16
... ...

This notation is used to specify electron configurations and to create the term symbol for the electron states in a multi-electron atom. When writing a term symbol, the above scheme for a single electron's orbital quantum number is applied to the total orbital angular momentum associated to an electron state.[4]

Molecular Spectroscopic Notation

Main article: Molecular term symbol

The spectroscopic notation of molecules uses Greek letters to represent the modulus of the orbital angular momentum along the internuclear axis. The quantum number that represents this angular momentum is Λ.

Λ=0,1,2,3,... Symbols: Σ,Π,Δ,Φ

For Σ states, one denotes if there is a reflection in a plane containing the nuclei (symmetric), using the + above. The - is used to indicate that there is not.

For homonuclear diatomic molecules, the index g or u denotes the existence of a center of symmetry (or inversion center), and indicates the parity of the total wave function. States of even parity with respect to inversion are denoted g for gerade (German for even), and states of odd parity are denoted u for ungerade (German for odd).

See also

References

  1. ↑ p. 92, Guide to the Sun, Kenneth J. H. Phillips, Cambridge, UK: Cambridge University Press, 1992. ISBN 0-521-39788-X.
  2. ↑ §12-7, An Introduction to Quantum Physics, Anthony Philip French and Edwin Floriman Taylor, CRC Press, 1979. ISBN 0-7487-4078-3.
  3. ↑ §7.12, Stellar Atmospheres, Jeremy B. Tatum, online book. Accessed on line September 19, 2007.
  4. 1 2 Spectroscopic notation, web page at http://hyperphysics.phy-astr.gsu.edu/, accessed on line September 19, 2007.
  5. ↑ P.Atkins et al. Quanta, Matter, and Change: A Molecular Approach to Physical Chemistry (Oxford University Press) p.106
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