Self-consistent field shielding calculations

By this method one obtains a simple analytic expression for the shielding potential. With the above values of pi and p2 this expression is hardly different from Hartree s self-consistent field calculated via incomparably difficult numerical techniques, and is even perhaps a bit more exact, as it lies between the self-consistent field with and without exchange in the case of the sodium atom. ... 

K. Ruud, T. Helgaker, R. Kobayashi, P. Jorgensen, K. Bak, H. Jensen, Multiconfigurational self-consistent field calculations of nuclear shieldings using london atomic orbitals, J. Chem. Phys. 100 (1994) 8178. 

The total electron density at the nucleus p(0) depends on the nature of the chemical bonding. Positive contributions to p(0) arise from the atomic 6s populations of the molecular orbitals on the gold ion, while a decrease in p(0) is caused by the atomic bd populations due to their shielding effects on s electrons. The relative magnitudes of the various contributions are known from the results of relativistic free-ion self-consistent field calculations for gold and for other d transition elements. The atomic 6p populations, on the other hand, yield only small contributions both by shielding of s electrons and by their relativistic density at the nucleus. Hence p(0) and consequently the isomer shift will mainly depend on the atomic 6s and 5[Pg.281]

An additional source of chemical shielding anisotropies is that of ab initio theoretical calculations.20 25 There has been considerable progress in this area of molecular quantum mechanics, particularly with the use of gauge-invariant atomic orbitals within the framework of self-consistent-field (SCF) perturbation theory.26 In many cases the theoretical quantities have been extremely accurate and have served not only as a corroboration of experimental quantities but also as a reliable source of new data for molecules of second-row atoms (i.e., Li through F). 

Figure 10.5 illustrates the chemical structure of a plane parallel PDR by giving the relative abundances of C+, C and CO as a function of the penetration depth into the model cloud [11]. We assumed a kinetic equilibrium and determined the relative abundances from a chemical network consisting of 38 different species formed and destroyed in 434 reactions. The PDR is illuminated from the left by the mean interstellar radiation field and extends from the predominantly atomic surface region to the point where almost all carbon is bound into CO. One of the difficulties in calculating the chemical and thermal structure of a PDR arises from the effect of self-shielding. Molecules already formed absorb UV photons which are able to dissociate the respective molecule. In other words they cast a shadow into the cloud which enhances the further formation of the respective molecule. This effects becomes especially important for the formation of key molecules like O2, H2 and CO. Our current research addresses the question under which physical conditions an instability due to shadowing effects could occur. Another difficulty concerns the effects of small-scale fluctuations of the UV radiation field on the chemical network. 

---