Conclusions

The work presented here shows that it is possible to compare the energy partitions of density functionals with more conventional theories. This is achieved by using the Kohn-Sham single determinant as a reference. It is possible to use the same procedure to determine the spin orbital or density partitions of core/valence or $\alpha$ spin/$\beta$ spin (or indeed any partition into non-overlapping spin orbitals).

When applied to the LSDA functional, spin partition shows a strong overestimation of the parallel spin components (including spurious one-electron effects). Antiparallel correlation is also overestimated, but by a smaller factor. The core/valence partitioning reveals core correlation values which are much too large. These values also do not approach any limiting value as they should. One bonus of the LSDA functional, though, is that these core values remain fairly constant in moving from atom to molecule, allowing a systematic cancellation of errors for most chemical properties. The LSDA functional does, however, show better performance in the valence region, overestimating the antiparallel contributions by only a factor of two (there are still major errors for the parallel components here). However, the major failing of the LSDA functional is the relative contributions of $\alpha\alpha+\beta\beta$ and $\alpha \beta$ correlation to binding energies. The $\alpha \beta$ contribution to binding is usually too low, even though the LSDA functional generally overestimates the binding energy.

The partitioning method developed here is applicable to any energy functional, allowing a more detailed evaluation of a functional than was previously possible. Hopefully the study of the piecewise inadequacies of future functionals will allow the convergence towards an accurate, correct energy functional. The LYP functional, which is used to develop the empirical density functional of the following chapter, for example, does not have the spurious one-electron effects seen here for the LSDA functional.