Bridge to Analytic Forms The Harris Functional

It should be understood that the Kohn-Sham orbitals are strictly good only for generating the electron densities that enter Eqs. [5] or [8], and the eigenvalues for the one-electron orbitals are not necessarily the same values that would be obtained from an exact solution for the many-body wavefunction. Nonetheless, the orbital energies are often used to estimate reasonable values for quantities such as electron affinities and electronegativities. 

Whereas the Kohn-Sham orbital approach is in principle exact, it requires knowing the exchange-correlation energy and potential. A widely used approximation is called the local density approximation (LDA) in which the ex-change-correlation functional is given by 

Working independently, Harris as well as Foulkes and Haydock showed that the electronic energy calculated from a single iteration of the energy functional 

Comparison of the aluminum (111) surface energy given by a Harris functional and self-consistent density functional calculations have been carried out 

The Harris functional, together with other related simplifying approximations, has also been used to model a wide range of cluster and surface structures for silicon and carbon. With careful choice of nonspherical atomic orbitals used to construct the input density, these studies have demonstrated that the Harris functional can yield energies and structures that match self-consistent results relatively well. Furthermore, because these calculations are relatively efficient, this approach has been used to model full atomistic dynamics. 

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