Hybrid functionals implemented in wien2k

Presentation

The hybrid functionals combine semilocal functionals with Hartree-Fock theory for the strongly correlated electrons .

The hybrid functionals implemented in wien2k are classified into two types: full hybrid funcionals and onsite hybrid functionals.

For solids, the full hybrid functionals are computationally very expensive. On-site methods → As cheap as LDA/GGA.

Both functionals are available in wien2k.

The Onsite hybrid functionals are applied only inside atomic spheres of selected atoms and electrons of a given angular momentum ℓ.

For the hybrid methods only exchange is corrected. In contrast to DFT+U where both exchange and Coulomb are corrected.

How to run  on-site hybrid calculation?

1. Create the input files:
◮ case.ineece for on-site hybrid functionals (case.indm created automatically):

2. Run the job (can only be run with runsp lapw):
◮ Hybrid: runsp lapw -eece . . .

For a calculation without spin-polarization (ρ↑ = ρ↓): runsp_c_lapw -orb/eece . . .

Input file case.ineece

On-site hybrid functional PBE0 applied to the 4f electrons of atoms No. 2 and 4:

---------------------------------------------------------------------
-12.0 2               emin, natorb
2 1 3                  iatom, nlorb, lorb
4 1 3                  iatom, nlorb, lorb HYBR HYBR/EECE
0.25                   fraction of exact exchange
----------------------------------------------------------------------

Full hybrid functionals

Full hybrid functionals are necessary (but expensive) for solids with delocalized electrons (e.g., in sp-semiconductors)

Two types of full hybrid functionals available in WIEN2k1 :

◮ unscreened: Exc = E DFT xc + α E HF x − E DFT x

◮ screened (short-range), 1 |r−r ′ | → e −λ|r−r ′ | |r−r ′ | : Exc = E DFT xc + α E SR−HF x − E SR

−DFT x screening leads to faster convergence with k-points sampling

technical details

◮ 10-1000 times more expensive than LDA/GGA
◮ k-point and MPI parallelization
◮ Approximations to speed up the calculations:
◮ Reduced k-mesh for the HF potential. Example: For a calculation with a 12 × 12 × 12 k-mesh, the reduced k-mesh for the HF potential can be: 6 × 6 × 6, 4 × 4 × 4, 3 × 3 × 3, 2 × 2 × 2 or 1 × 1 × 1
◮ Non-self-consistent calculation of the band structure
◮ Underlying functionals for unscreened and screend hybrid:

• ◮ LDA 
• ◮ PBE 
• ◮ WC 
• ◮ PBEsol 
• ◮ B3PW91 
• ◮ B3LYP 

input file case.inhf

Example for YS-PBE0 (similar to HSE06 from Heyd, Scuseria and Ernzerhof1 )

------------------------------------------------------------------------------------------------
0.25           fraction α of HF exchange
T                screened (T, YS-PBE0) or unscreened (F, PBE0)
0.165         screening parameter λ 20 number of bands for the 2nd Hamiltonian
6                GMAX
3                lmax for the expansion of orbitals
3                lmax for the product of two orbitals
1d-3           radial integrals below this value neglected
--------------------------------------------------------------------------------------------

Important: The computational time will depend strongly on the number of bands, GMAX, lmax and the number of k-points

How to run full hybrid functionals? 

1. init lapw
2. Recommended: run(sp) lapw for the semilocal functional
3. save lapw
4. init hf lapw (this will create/modify input files)

• 4.1 adjust case.inhf according to your needs 
• 4.2 reduced k-mesh for the HF potential? Yes or no 
• 4.3 specify the k-mesh 

5. run(sp) lapw -hf (-redklist) (-diaghf) ...

SCF cycle of full hybrid functionals in WIEN2k 

How to calculate the band structure ?

Use    run bandplothf_lapw    for band structure


Reference: http://susi.theochem.tuwien.ac.at/events/ws2015/Tran-talk_xc.pdf