Enter (Heyd-Scuseria-Ernzerhof 2006). This hybrid functional, implemented efficiently in VASP (Vienna Ab initio Simulation Package), has become the gold standard for predictive simulations. It corrects the core errors of DFT without the prohibitive cost of methods like GW or Quantum Monte Carlo.
def run_hse06(alpha): with open('INCAR', 'w') as f: f.write(f"SYSTEM = HSE06 auto-alpha\n") f.write(f"LHFCALC = .TRUE.\n") f.write(f"AEXX = alpha\n") f.write(f"HFSCREEN = 0.2\n") f.write(f"PREC = Accurate\n") f.write(f"EDIFF = 1E-6\n") os.system("mpirun -np 4 vasp_std") return parse_dielectric()
Never use NCORE for large hybrid jobs; use KPAR to parallelize over k-points. Because HSE06 integrates over k-points, setting KPAR = 2 or 4 (up to number of irreducible k-points) yields near-linear scaling. vasp hse06
: Only the short-range part uses the expensive Hartree-Fock calculation, making it much faster than pure hybrid functionals like PBE0 while maintaining high accuracy. Key Advantages of Using HSE06 in VASP
The combination of and the HSE06 functional represents a pinnacle of accuracy in modern materials modeling. While the computational cost is high, the ability to predict electronic structures that align with experimental reality makes it an indispensable tool for physicists, chemists, and materials scientists worldwide. Enter (Heyd-Scuseria-Ernzerhof 2006)
Standard DFT functionals like the (a GGA functional) notoriously underestimate the band gap of materials—sometimes by as much as 50% or more. This happens because standard DFT doesn't fully account for the self-interaction error. HSE06 solves this by:
This calculates the exact Fock exchange only every 5 electronic steps, updating the Hamiltonian via Pulay mixing for the rest. This reduces cost by ~80% with almost no loss in convergence stability. def run_hse06(alpha): with open('INCAR', 'w') as f: f
To invoke HSE06 in VASP, specific tags must be set in the INCAR file. While VASP documentation provides the exhaustive list, the following are the non-negotiable parameters for a standard HSE06 run:
However, PBE0 is computationally expensive and, in solids, the long-range nature of the non-local exchange is often screened by the electron sea. This leads us to the screened hybrid functional.
$$ E_xc^HSE = E_x^PBE,SR(\omega) + E_x^HF,SR(\omega) + E_c^PBE $$