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Chemistry · Glossary

What is Spectroscopic term, spin multiplicity, term symbol?

Also known as: spectroscopic term · spin multiplicity · term symbol

Definition 2.11 University Chemistry — Year 3 · Chapter 2 — Many-Electron Atoms and Term Symbols

A spectroscopic term is the set of the (2L+1)(2S+1)(2L+1)(2S+1) states of a configuration with given LL and SS. Its spin multiplicity is 2S+12S + 1. The term symbol is 2S+1L{}^{2S+1}L, with the letters S, P, D, F, G, H for L=0,1,2,3,4,5L = 0, 1, 2, 3, 4, 5; a state of given JJ is written 2S+1LJ{}^{2S+1}L_J — for example 3P2{}^{3}\mathrm{P}_{2}.

The ground configuration of carbon: one configuration, three terms (at their measured energies; the 3P term at the weighted mean of its levels, the configuration at the mean of all fifteen states) and five levels. The spin–orbit splitting of 3P (zoom, in cm-1) is a few hundred times smaller than the separations between terms.
The ground configuration of carbon: one configuration, three terms (at their measured energies; the 3{}^3P term at the weighted mean of its levels, the configuration at the mean of all fifteen states) and five levels. The spin–orbit splitting of 3{}^3P (zoom, in cm−1\mathrm{cm}^{-1}) is a few hundred times smaller than the separations between terms.

Examples

Example 2.15 (The terms of p2p^2)

Two electrons in pp (ml=1,0,−1m_l = 1, 0, -1) give (62)=15\binom62 = 15 determinants. Their table by MLM_L and MSM_S is:

MS=1M_S = 1MS=0M_S = 0MS=−1M_S = -1
ML=2M_L = 2–(1+,1−)(1^+,1^-)–
ML=1M_L = 1(1+,0+)(1^+,0^+)(1+,0−)(1^+,0^-), (1−,0+)(1^-,0^+)(1−,0−)(1^-,0^-)
ML=0M_L = 0(1+,−1+)(1^+,-1^+)(1+,−1−)(1^+,-1^-), (1−,−1+)(1^-,-1^+), (0+,0−)(0^+,0^-)(1−,−1−)(1^-,-1^-)
ML=−1M_L = -1(0+,−1+)(0^+,-1^+)(0+,−1−)(0^+,-1^-), (0−,−1+)(0^-,-1^+)(0−,−1−)(0^-,-1^-)
ML=−2M_L = -2–(−1+,−1−)(-1^+,-1^-)–

(with ml±m_l^\pm for ms=±12m_s = \pm\frac12). ML=2M_L = 2 occurs only with MS=0M_S = 0: a 1{}^1D term (5 states). The largest remaining ML=1M_L = 1 comes with MS=1M_S = 1: a 3{}^3P term (9 states). One state with ML=MS=0M_L = M_S = 0 remains: a 1{}^1S term. Indeed 5+9+1=155 + 9 + 1 = 15.

Example 2.16 (Carbon, measured)

The ground configuration 2p22p^2 of carbon gives the levels 3P0{}^{3}\mathrm{P}_{0}, 3P1{}^{3}\mathrm{P}_{1}, 3P2{}^{3}\mathrm{P}_{2} at 0, 16.4 and 43.4 cm−143.4\,\mathrm{cm}^{-1}, then 1D2{}^{1}\mathrm{D}_{2} at 10 193 cm−110\,193\,\mathrm{cm}^{-1} and 1S0{}^{1}\mathrm{S}_{0} at 21 648 cm−121\,648\,\mathrm{cm}^{-1}: the 3{}^3P term is lowest, as Hund’s rules predict.

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