Coupling constants lowest order

In order to find the relevant conformers, the authors employed a Monte Carlo/minimization strategy that is described in more detail in the next chapter - in practice, (2/ , 4S )-l-hydroxy-2,4-dimethylhex-5-ene is sufficiently small that one could survey every possible torsional isomer by brute force, but it would be very tedious. Table 2.2 shows, for the nine lowest energy conformers, their predicted energies, their contribution to the 300 K equilibrium population, their individual 1 Jcc coupling constants between atoms C(2)C(5), C(2)C(8), C( 1 )C(4), and C(4)C(7), and the mean absolute error in these coupling... 

Several methods exist for calculating g values. The use of crystal field wave functions and the standard second order perturbation expressions (22) gives g = 3.665, g = 2.220 and g = 2.116 in contrast to the experimentaf values (at C-band resolution) of g = 2.226 and g 2.053. One possible reason for the d screpancy if the use of jperfXirbation theory where the lowest excited state is only 5000 cm aboye the ground state and the spin-orbit coupling constant is -828 cm. A complete calculation which simultaneously diagonalizes spin orbit and crystal field matrix elements corrects for this source of error, but still gives g 3.473, g = 2.195 and g = 2.125. Clearly, covalent delocalization must also be taken into account. 

The leading quantum electrodynamic effects to be accounted for in electronic structure calculations are the radiative corrections known as electron self-energy interaction and vacuum polarization. For the energy of electronic systems, the latter is usually small compared to the former, but only the latter can be expressed in terms of an effective additive potential to be included in the electronic structure calculations. The total vacuum polarization potential can be expanded into a double power series in the fine structure constant a and the external coupling constant Za. The lowest-order term, the Uehling potential, can be expressed as [110-112] ... 

The first term which is independent of nuclear spin dominates by several orders of magnitude in heavy elements over the second, nuclear spin dependent, term. In the above expression a and T are the standard Dirac matrices and o is the Pauli spin matrix (see e.g. Sakurait78]) stands for any nucleon either proton or neutron and the coupling constants C take on the following form in lowest order in... 

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