Doublet term

Lowering temperature to 200 K, the thermally induced ST at the central Fe(ll) site sets in with the appearance of two new doublets in the Mossbauer spectrum (1) the poorly resolved doublet termed LS refers to central Fe(ll) sites now being in the LS state, and (2) the doublet termed arises from the outer Fe(ll) sites of... 

CauUon has calculated the splitting of the doublet terms in cobalt(II) for a cr3 tal field consistent with a square pyramidal structure with a = 90°, and Fig. 34 shows the energy diagram drawn up using the appropriate values of the parameters for the species [Co(CN)5]3- 71). 

Fig. 1. Term system for Cr3 + in a ligand field of Oh symmetry, as depicted by Schlafer and Gliemann (2G is the only one of the doublet terms shown). Reprinted with permission from Ref. [1], p 44, Fig. A32...

The key point of this energy-level diagram is that the trigonal field is large with the orbital doublet term lower lying. The wavefunctions of the lower lying Kramers doublet are then of the form Ml,Ms) = 1, T, with corresponding g values ... 

To reduce this microstate table into its component free-ion terms, note that each of the terms described in the examples and in Exercise 11.2 consists of a rectangular array of microstates. To reduce the microstate table into its terms, all that is necessary is to find the rectangular arrays. This process is illustrated in Table 11.4. For each term, the spin multiplicity is the same as the number of columns of microstates a singlet term (such as D) has a single column, a doublet term has two columns, a triplet term (such as P) has three columns, and so forth. 

For boron, there are two terms to consider Ps/2 or P /2-These are both doublet terms, and both have L = 1. For the configuration, the p level is less than half-filled, and therefore the ground state level is the one with the lower value of J, i.e. Pin-... 

The existence of the doublet systems in the alkali metal elements requires another quantum number. This number was called the inner quantum number by Sommerfeld and is designated by the letter J and is used to distinguish the components of doublets. The S terms all have a J index of the P terms of and I and the D terms of f and f. Table 2-2 lists the J values for doublet terms. Analysis of the spectra of the alkali metals leads to the selection rule that AJ = 0 or 1, but also that the transition from J = 0 to J = 0 is excluded. 

The red cyanide bands, the a-bands of BO and the comet tail bands of CO exhibit a doublet splitting, which behaves like our case (a) as far as we know. It is the type of Heurling s bands with doublet series (Mecke s type II). This would mean that s =, if = 0. MuUiken has compared the common final term N of the cyanide bands (and the BO and CO bands) and the two initial terms A and B with the S-, P and S-term of the alkalis. From the nine outer electrons eight can form a closed shell and one can remain like in the alkalis. Our considerations lead to a construction of the bands which agrees with this. For instance the common end term N could correspond to the 5-groimd term of the alkalis, the doublet term A to the component U = 1 and the higher singlet term B to the component i/ = 0 of the P-term. Other interpretations are of course possible. 

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. 

The spin orbital if2sP could have been chosen instead of ir2sOi. We therefore have two states of equal energy. This doubly degenerate ground level corresponds to 5 = 1/2 (a doublet term), since the possible values of Ms are -I-1 /2 and —1/2. Since Mi = 0, the value of L is 0, the only value of / is 1/2, and the ground term symbol of lithium is Sy2-... 

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