What is the difference between PBE and HSE06 in DFT?
For what type of calculation/materials do we employ PBE and HSE06?
Thank You in advance.
PBE is the default exchange-correlation functional or default GGA.while HSE06 is a hybrid functional (XC) class of DFT that uses GGA but nonlocal-exchange-correlation functional. For bandgap, HSE06 is often considered a very accurate XC. However, it is much more time-consuming and demanding in computer power. you can quickly calculate structural properties with PBE and use HSE06 for electronic properties .
for better understanding, you can read this:
https://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/content/modules/castep/tskcastepsetelecxc.htm
Md. Yasir Zamil and @Zhaoxi Sun have already mentioned most of the things, I just wanted to add a little more, that how it is being used differently in DFT calculations.
As we know, Many-body Hamiltonian consists of Kinetic energy term (T), potential energy term having the interaction of electrons with the ions, and another term is an exchange-correlation term (V_HXC), due to which Hamiltonian can't be precisely defined and we follow the self-consistent procedure to determine the converged Hamiltonian or converged density, which is then used to determine the bands or DOS non-self consistently.
But, determining the converged Hamiltonian self-consistently, and band calculations non-self consistently is applicable only in GGA or GGA+U calculations, not in Hybrid ones.
Since, in GGA calculations,
V_HXC is a functional of density, so just making a guess on the density and iterating it self-consistently to get the converged density, will provide us with the converged Hamiltonian, and can be used to calculate the energy bands along the high symmetry directions non-self consistently. If you use VASP, you might notice that we keep CHGCAR in going from scf to nscf calculations, i.e., we are providing it the converged charge densities or converged hamiltonians to calculate the energy eigenvalues.
While in HSE calculations, this is not the case. Our KPOINTS file is not similar to the ones which we use in GGA, instead, we provide the explicit values of KPOINTS to calculate the band structure.
This is because in HSE, V_HXC is a function of psi_nk, which depends on n (band index) and k (kpoint), so for each band and each kpoint wave function would be different, so accordingly potential would be different, hence the Hamiltonian, so we need to consider self-consistency of each value of n and k, as one density term can't serve our purpose here, so we don't use any copying of Charge densities like in GGA or GGA+U.
Hope this helps!
PBE is an exchange-correlation functional, while HSE06 is a hybrid functional (XC) class of DFT that uses GGA but nonlocal-exchange-correlation functional. For bandgap, HSE06 is often considered a very accurate XC. you can use PBE for geometry optimization and use HSE06 for electronic properties as like as band structure and band gap .
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