Quartet, term symbol

In the case of less symmetric complexes, the above states may be split into further ones (except A states), although the basic electron population and the spin designation remain. To avoid dealing with a multitude of term symbols, some authors adopt the practice of designating states as S, D, Q, etc., for singlet, doublet and quartet, with subscripts to be explained in Section 7.3.2.2.I. 

The letter in the term symbol is the letter code describing the value of L. The left superscript is the multiplicity of the state, 2S + 1, and is called singlet, doublet, triplet, quartet, and so on. The right subscript is the value of J. Sometimes the principal quantum number of the state is written before the term symbol. 

This is called a term symbol. It represents a set of energy levels, called a term in spectroscopic parlance. States with a multiplicity of 1 are called singlet states, states with a multiplicity of 2 are called doublet states, states with a multiplicity of three are called triplets, states with a multiplicity of 4 are called quartets and so on. Hence, S is called singlet S, and is called triplet P. 

A left superscript with the value 25 - -1 is attached to the term symbol. For two electrons we can have 5 = 0, giving a superscript of 1 (a singlet term), or we can have 5=1, giving a superscript of 3 (a triplet term). For a single electron we can have only 5 = 1/2, giving a superscript of 2 (a doublet term). If 5 = 3/2, the superscript equals 4 (a quartet term), and so on. The value of the left superscript is called the multiplicity of the term. A right subscript can be attached to the term symbol to specify the value of 7, but is sometimes omitted. 

To investigate values of L, we use the complex orbitals that are eigenfunctions of L. We have assigned one electron to each of the i 2p space orbitals. The only possibility is Ml = 1 - - 0 — 1 = 0. The only value of L compatible with the maximum value of S is zero. The only possible value of J is equal to S, so the ground-level term symbol is 53/2 ( quartet S three-halves ). 

Figure 3.10 Partial energy level diagram for the Fe3+ or Mn2+ ions with 3tfi configurations in high-spin states in an octahedral crystal field. Only sextet and quartet spectroscopic terms and crystal field states are shown. Note that the same energy level diagram applies to the cations in tetrahedral crystal fields (with g subscripts omitted from the state symbols for the acentric coordination site).

The quantity 25 -h 1 is called the electron-spin multiplicity (or the multiplicity) of the term. If L 5, the possible values of/in (11.62) range from L + SioL- S and are 25 -I- 1 in number if L 5, the spin multiplicity gives the number of levels that arise from a given term. For L < 5, the values of J range from S + LtoS - L and are 2L + 1 in number in this case, the spin multiplicity is greater than the number of levels. For example, if L = 0 and 5 = 1 (a 5 term), the spin multiplicity is 3, but there is only one possible value for 7, namely,/ = 1. For 25 -t 1 = 1,2,3,4,5,6,..., the words singlet, doublet, triplet, quartet, quintet, sextet, are used to designate the spin multiplicity. The level symbol is read as triplet P one. ... 

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