Open shell states with both spin and orbital angular momentum

Open shell states with both spin and orbital angular momentum 

Many free radicals in their electronic ground states, and also many excited electronic states of molecules with closed shell ground states, have electronic structures in which both electronic orbital and electronic spin angular momentum is present. The precession of electronic angular momentum, L, around the intemuclear axis in a diatomic molecule usually leads to defined components, A, along the axis, and states with A =0, 1, 2, 3, etc., are called , n, A, t , etc., states. In most cases there is also spin angular momentum S, and the electronic state is then labelled 2,s+1 Id, 2,s+1 A, etc. 

Questions arise immediately concerning the coupling of L, S and the nuclear rotation, R The possible coupling cases, first outlined by Hund, are discussed in detail in chapter 6. Here we will adopt case (a), which is the one most commonly encountered in practice. The most important characteristic of case (a) is that A, the component of L along the intemuclear axis, is indeed defined and we can use the labels , Id, A, etc., as described above. The spin-orbit coupling can be represented in a simplified form by the Hamiltonian term 

If we are dealing with a 2n state, the possible values of the projection quantum numbers are as follows  

The rigid body rotational Hamiltonian can be written in the form 

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