Angular momentum coupling spin-orbit

Their symmetry labels can be obtained by vector coupling (see Appendix G) the spin and orbital angular momenta of the two subsystems. The orbital angular momentum coupling... 

Section treats the spatial, angular momentum, and spin symmetries of the many-electron wavefunctions that are formed as antisymmetrized products of atomic or molecular orbitals. Proper coupling of angular momenta (orbital and spin) is covered here, and atomic and molecular term symbols are treated. The need to include Configuration Interaction to achieve qualitatively correct descriptions of certain species electronic structures is treated here. The role of the resultant Configuration Correlation Diagrams in the Woodward-Hoffmann theory of chemical reactivity is also developed. 

Angular momentum coupling is just a mathematical device, which does not explain why the two states actually have different energies. The theory does, however, make some useful predictions. When an atom with spin-orbit coupling is subjected to a magnetic field, it is the total angular momentum that can take a variety of orientations, and the number allowed is given the formula (2j + 1), in line with the similar formulae for s and l. For example, the levels j = f and i split into four and two states, respectively, which can... 

The mechanism by which spin-orbit coupling can impact molecular bonding becomes more obvious if the wave function is reformulated in terms of molecular spinors (Hund s case c coupling). One should keep in mind, however, that even for the heaviest elements the angular momentum coupling is generally intermediate between case a and case c, and the following picture is therefore an oversimplification. 

When great accuracy is desired, and in certain cases when only ordinary accuracy is required, it is necessary to consider the coupling between electronic and nuclear motions, and especially between the electronic angular momentum (either spin or orbital) and the rotation of the molecule. We shall not discuss these questions,1 but shall treat only the simplest problems in the complex field of molecular structure and molecular spectra in the following sections. Some further discussion is also given in Chapter XII and in Section 48 of Chapter XIV. 

The orbital angular momentum and the spin angular momentum couple to yield a total angular momentum characterized by a quantum number J. 

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