The periodic Hartree-Fock method and its implementation in the CRYSTAL code

The present chapter discusses the Hartree-Fock (HF) method for periodic systems with reference to its implementation in the CRYSTAL program. The HF theory is shortly recalled in its Closed Shell (CS), Unrestricted (UHF) and Restricted open shell (RHF) variants; its extension to periodic systems is illustrated. The general features of CRYSTAL, the periodic ab initio linear combination of atomic orbitals (LCAO) program, able to solve the CS, RHF and UHF, as well as Kohn-Sham equations, are presented. Three examples illustrate the capabilities of the CRYSTAL code and the quality of the HF results in comparison with those obtained with the Local Density Approximation using the same code and basis set: NiO in its ferro-magnetic and anti-ferromagnetic structure, trapped electron holes in doped alkaline earth oxides, and F-centres in LiF.