Off-Diagonal Matrix Elements of Total Hamiltonian between Unsymmetrized Basis Functions

Born-Oppenheimer approximation perturbation AA AE AS AH spin-orbitalsrf 

The final three terms of the rotational operator in Eq. (3.1.13), which couple the orbital, spin, and total angular momenta, are responsible for perturbations between different electronic states  

+(l/2pf 2)L S F gives rise to homogeneous (Aft = 0) spin-electronic perturbations between basis functions of the same ft and S, but different A and E. 

— (l/2/xi 2)J FS is responsible for heterogeneous (Aft = 1) electronic-rotational perturbations between basis states of different ft having identical values of S and A, but different values of E. This operator is called the S-uncoupling operator. 

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Table 3.2 Off-Diagonal Matrix Elements of Total Hamiltonian between Unsymmetrized Basis Functions... 

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