Section 8.7.4.8. Comparison between theory and experiment

Since it is a measure of the imbalance between the densities associated with the two spin states of the electron, the spin-density function is a probe that is very sensitive to the exchange forces in the system. In an independent-particle model (Hartree–Fock approximation), the exchange mean field potential involves exchange between orbitals with the same spin. Therefore, if the numbers of and spins are different, one expects to be different from . The main consequence of this is the necessity to solve two different Fock equations, one for each spin state. This is known as the spin-polarization effect: starting from a paired orbital, a slight spatial decoupling arises from this effect, and closed shells do have a participation in the spin density.

It can be shown that this effect is hardly visible in the charge density, but is enhanced in the spin density.

Spin densities are a very good probe for calculations involving this spin-polarization effect: The unrestricted Hartree–Fock approximation (Gillon, Becker & Ellinger, 1983).

From a common spin-restricted approach, spin polarization can be accounted for by a mixture of Slater determinants (configuration interaction), where the configuration interaction is only among electrons with the same spin. There is also a correlation among electrons with different spins, which is more difficult to describe theoretically. There seems to be evidence for such effects from comparison of experimental and theoretical spin densities in radicals (Delley, Becker & Gillon, 1984), where the unrestricted Hartree–Fock approximation is not sufficient to reproduce experimental facts. In such cases, local-spin-density functional theory has revealed itself very satisfactorily. It seems to offer the most efficient way to include correlation effects in spin-density functions.

As noted earlier, analysis of the spin-density function depends more on modelling than that of the charge density. Therefore, in general, `experimental' spin densities at static densities and the problem of theoretical averaging is minor here. Since spin density involves essentially outer-electron states, resolution in reciprocal space is less important, except for analysis of the polarization of the core electrons.