Approximating H for solid-state structures

In Section 3.2.1, we discussed the two main sets of approximations available to us when considering the interaction terms present in the Hamiltonian operator. The first is ab initio theory, which has as its basis Hartree-Fock theory the second is density functional theory, which recasts the basic equations in terms of the electron density rather than the wavefunction directly. 

In principle, either method should be open to us to use in solid-state calculations. However, in practice the choice of a plane-wave basis set rather limits the use of any method within the framework of Fock theory. The problem is that the Slater determinant (Eq. 3.5) set up within the formalism of a plane-wave basis set is very large, and so impedes the performance of the calculations. Therefore, use of a plane-wave basis set, for the time being at least, limits the approximations made to H to those formalized in density functional theory. 

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