Central-field approximation corrections

At this point one question must be answered Is the potential calculated in the manner above path independent [21] Equivalently, is the field given by Equation 7.33 curl-free For one-dimensional cases and within the central field approximation for atoms, it is. For other systems, there is a small solenoidal component [21,22] and we will see later that it arises from the difference in the kinetic energy of the true system and the corresponding Kohn-Sham system (in this case the HF system and its Kohn-Sham counterpart). For the time being, we explore whether the physics of calculating the potential in the manner prescribed above is correct in the cases where the curl of the field vanishes. 

The leading point-charge terms usually have to be augmented by correction terms AV, which may be formulated in a local, semilocal or nonlocal form. The advantage of these element-specific pseudopotentials is their economy regarding the number of necessary parameter sets to cover the whole Periodic Table. Once they have been generated for every element separately, they may be applied in calculations on compounds with arbitrary composition. Moreover, the pseudopotential adjustment itself is further simplified when the central-field approximation is used in the necessary atomic calculations. 

As we have seen there now exist significant measurements of PNC in four different atoms, carried out on five distinct magnetic-dipole absorption lines. In Table 3 we show the most recent result of each experiment together with the value predicted by the Weinberg-Salam weak interaction theory. The predicted values come from atomic calculations "" taking into account the major corrections to the central field approximation. We also show the values of Q defined in Eqs. (9) and (10) that may be inferred in each case from the experimental result and the atomic calculations. 

Corrections to the central-field approximation. Two important terms are omitted in the central-field approximation. The first is the residual electrostatic interactions represented by JC (equation (3.68)). This gives rise to non-central forces which cause the motion of the electrons to be correlated with one another, rather than completely independent as in the central-field approximation. The second terra is the magnetic spin-orbit interaction which was not included in equation (3.65) ... 

An accurate calculation in heavy atoms requires a thoroughgoing relativistic treatment. The central field-independent particle approximation gives a first-order answer, but corrections involving electron exchange, noncentral effects, and other electron-electron correlations are needed in many cases. Details of the calculations have been reviewed elsewhere ... 

How important the breakdown of the Born-Oppenheimer approximation is in limiting our ability to carry out ab initio simulations of chemical reactivity at metal surfaces is the central topic of this review. Stated more provocatively, do we have the correct theoretical picture of heterogeneous catalysis. This review will restrict itself to a consideration of experiments that have begun to shed light on this important question. The reader is directed to other recent review articles, where aspects of this field of research not mentioned in this article are more fully addressed.10-16... 

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