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

Abstract

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.