The role of the exact Hartree-Fock exchange in the investigation of defects in crystalline systems

The role of the exact Hartree-Fock (HF) exchange in determining the band gap and other properties of defects in crystalline solids is investigated. Two defects in diamond, VH^d₁ and VH^q₁ (one first neighbour of the vacancy is saturated with hydrogen, and the three unpaired electrons combine to give a quadruplet, 3 spin up, or a doublet, two spin up and one down), are used as test cases. The results obtained with a gradient corrected functional, PBE, one range separate hybrid, HSE06, two full range hybrids, B3LYP and PBE0, and the Hartree-Fock Hamiltonian are compared. The crucial role of the exact HF exchange emerging from this comparison is confirmed by a set of calculations with a variable functional, PBE(X), in which X is the percentage of HF exchange, which is varied from 0 to 100, where PBE(0) coincides with PBE, and PBE(25) with PBE0.