Angular coupling

This form of Vsr is particularly efficient for rod-shaped, elongated molecules. For such molecules a direct expansion of Vsr in terms of Pl(cos0) would have a prohibitively slow convergence because of the strong radial-angular coupling of the PES. However, the as a... 

Fig. 15. Polar differential cross section calculated semi-classically for the charge transfer process Na + I - Na+ + I, (a) Calculation with the complete interference structure with omission of the primary rainbow. (b) Approximate semi-classical calculation taking into account only interferences from net repulsive and net attractive scattering, (c) The full bars indicate maxima observed experimentally for net attractive scattering, the dashed bars for net repulsive scattering. H12(RC) = 0-065 eV angular coupling was neglected. (Delvigne and Los, 1973.)...

Finally, an example in which all three types of coupling (radial, rotational and spin-orbit) are operative is the charge-transfer reaction Ar ( P)-l- H- Ar( S)-l-H. All three have been calculated as a function of intemuclear separation. The entrance channel correlates with B 2, a Il, A II and b Z states, while the outgoing channel possesses only Z symmetry. (The angular coupling involves the term with a maximum around 0.4 a.u. the radial coupling is only about half of this and finally the spin-orbit operator couples the output channel X Z with the upper state of the ingoing partners. 

For a coupled spin system, the matrix of the Liouvillian must be calculated in the basis set for the spin system. Usually this is a simple product basis, often called product operators, since the vectors in Liouville space are spm operators. The matrix elements can be calculated in various ways. The Liouvillian is the conmuitator with the Hamiltonian, so matrix elements can be calculated from the commutation rules of spin operators. Alternatively, the angular momentum properties of Liouville space can be used. In either case, the chemical shift temis are easily calculated, but the coupling temis (since they are products of operators) are more complex. In section B2.4.2.7. the Liouville matrix for the single-quantum transitions for an AB spin system is presented. 

Figure B2.5.13. Schematic representation of the four different mechanisms of multiphoton excitation (i) direct, (ii) Goeppert-Mayer (iii) quasi-resonant stepwise and (iv) incoherent stepwise. Full lines (right) represent the coupling path between the energy levels and broken arrows the photon energies with angular frequency to (Aco is the frequency width of the excitation light in the case of incoherent excitation), see also [111].

When the molecule is not in a S state there is an interaction between the rotation of the molecule and S and/or L, and the details of coupling the angular momenta are involved. Most nonsinglet molecules with electronic orbital angular momentum A = 0 obey Hund s case (b) coupling. In Case (b), the electronic orbital angular momentum combines with the nuclear orbital angular... 

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