The Hartree-Fock Exchange for Crystalline Systems: The Implementation with an (All-Electron) Gaussian-Type Basis Set...

The treatment of the Hartree-Fock exchange (HFX) series in periodic systems is described when a Gaussian-type basis set is adopted, and its performance is documented with reference to the KCrF₃ perovskite. The computational scheme for the exchange, implemented in the CRYSTAL code in its general lines more than 35 years ago (Causà et al., J. Chem. Phys. 92, 909 (1988)), is here documented for the first time with reference to the variables essential for the description of many properties of periodic systems: truncation of the exchange series, reduction of point symmetry, change of space group, and dimension of the unit cell: these features are involved in the calculation of the total energy, the equilibrium geometry, the relative stability of phases, the Jahn-Teller splitting and orbital ordering, the ferromagnetic versus antiferromagnetic energy difference, the vibrational frequencies, and the IR and Raman intensities, to quote the most important properties of interest. The same computational scheme is used for both pure HF and for full-range or range-separated hybrid functionals, in which a variable percentage X of HFX is used. To document the role of X, a very recently defined functional is employed, PBE(X), such that PBE(0) = PBE and PBE(25) = PBE0. The high efficiency of the algorithms implemented in CRYSTAL permits to perform calculations for supercells of KCrF₃ containing, for example, 3430 atoms (7 × 7 × 7 supercell of the monoclinic cell, containing 10 atoms), when an all-electron basis set of triple-ζ quality is adopted.