Spin quantisation in triplet states

For an understanding of ESR in crystals, a detailed discussion of the molecular fundamentals is necessary. We deal with this primarily in Sections 7.2 and 7.3. There, the spin quantisation in triplet states, magnetic dipole-dipole couphng, zero-field splitting, Zeeman spHtting and fine structure are explained. These fundamentals apply both to isolated molecules and to excitons (Sects. 7.4 and 7.5). In the two later Sects. 7.6 and 7.7 of this chapter, the so called optical spin polarisation in excited triplet states and dynamic nuclear spin polarisation will be treated. 

The spin eigenfunctions of a system consisting of two coupled 7r-electrons i = 1 and 2 are, in the absence of an applied magnetic field (Bo = 0), given by the following four linearly-independent, orthonormal linear combinations of the products of the single-electron spin functions a() and fii) with the spin quantum number s=yi  

The physical properties of the four two-electron spin functions T (w = x,y,z) and I E follow from the action of the three vector components = s i + s 2 of the total spin operator S = 1 -1- 2 = S e -1- Sj, e -1- on the four two-electron spin functions (Eq. (7.1)). For the three functions T ), Ty), and Tz), these actions are collected in Table 7.2 and have the following physical significance  

The expectation value of the spins in every direction perpendicular to the direction w is for the three eigenfunctions T ) likewise equal to 0 (T S T )=0. 

For the function E) (Eq. (7.1d)), the relation S E) = 0 holds, i.e. E) is the spin eigenfunction for the singlet state with total spin quantum number 

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