Atomic spin-orbit coupling

The small values of the spin-orbit coupling in molecules containing first-and second-row elements does not mean, however, that spin-orbit coupling is unimportant. It will be shown in the next section that intersystem crossing can be efficient even for molecules with small spin-orbit coupling. 

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The Wlc total atomization energy at 0 K of aniline, 1468.7 kcal/mol, is in satisfying agreement with the value obtained from heats of formation in the NIST WebBook 39), 1467.7 0.7 kcal/mol. (Most of the uncertainty derives from the heat of vaporization of graphite.) The various contributions to this result are (in kcal/mol) SCF limit 1144.4, valence CCSD correlation energy limit 359.0, connected triple excitations 31.7, inner shell correlation 7.6, scalar relativistic effects -1.2, atomic spin-orbit coupling -0.5 kcal/mol. Extrapolations account for 0.6, 12.1, and 2.5 kcal/mol, respectively, out of the three first contributions. 

Second, it is a good approximation for an ion like HeAr+ to assume that the spin-orbit coupling operator is the same as that for the free Ar+ ion, L S, where f is the atomic spin orbit coupling constant. If the basis functions are confined to those arising from the 2P3/2 and 2Pi/2 states, the spin-orbit operator is also diagonal in a case (e) basis... 

With the exception of Ligand Field Theory, where the inclusion of atomic spin-orbit coupling is easy, a complete molecular treatment of relativity is difficult although not impossible. The work of Ellis within the Density Functional Theory DVXa framework is notable in this regard [132]. At a less rigorous level, it is relatively straightforward to develop a partial relativistic treatment. The most popular approach is to modify the potential of the core electrons to mimic the potential appropriate to the relativistically treated atom. This represents a specific use of so-called Effective Core Potentials (ECPs). Using ECPs reduces the numbers of electrons to be included explicitly in the calculation and hence reduces the execution time. Relativistic ECPs within the Hartree-Fock approximation [133] are available for all three transition series. A comparable frozen core approximation [134] scheme has been adopted for... 

The heavy atom effect is traditionally studied by physicists as redistribution of electron transition rates in the presence of bromine or iodine atoms. In the presence of heavy atoms spin-orbit coupling in the molecules is substantial.1,2 The spin-orbit interaction fulfils the role of the disturbance factor that removes the multiplicity prohibition. 

Nag-Chaudhuri J, Stoessell L, McGlynn S.P. External heavy-atom spin-orbital coupling effect. II. Comments on the effect of ferric acetylacetonate on the spectra of polyacenes. J Chem Phys 1963 38 2027-8. 

Numerical ab initio calculations for selected examples with polarized basis sets and Cl of reasonably size confirmed that the size of the matrix elements within the active space matrix is negligible. In contrast, the elements of that involve both the active and inner shells are large, since is primeuily due to the shielding of nuclei by inner-shell electrons [11]. It is therefore common practice in many semiquantitative applications, to account for the effect of the fixed-core electrons by replacing the factor gPgZ r in by the empirical value of the atomic spin-orbit coupling constant valence p orbitals on... 

The fine structure constant A was determined indirectly from the perturbations by the riy state of the observed Zeeman shifts in the state, A= -177.3 5.6 cm" [2]. A splitting of 160 30 cm was derived from an asymmetry of the vibrational components of three photoelectron bands [1]. A = ( )188cm was calculated from the atomic spin-orbit coupling constants and from the F hyperfine coupling constant [2]. The method used was described in... 

Table 8.3 Atomic spin-orbit coupling parameters (cm...

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