LDA+U convergence problem

[lzhao10]

Hi, I'm doing LDA+U calculations of rutile TiO2 recently and had difficulties for DFT convergence. I want to consider not only U_d for Titanium, but also U_p for oxygen, so I set the basis like this:

Code: python

basis_set = [LDABasis.Oxygen_DoubleZetaPolarized(hubbard_u=[0.0, 6.0, 0.0, 6.0, 0.0]*eV),
    LDABasis.Titanium_DoubleZetaPolarized(hubbard_u=[8.0, 0.0, 0.0, 0.0, 0.0]*eV)]

I cannot reach convergence for the default 100 steps of DFT calculations, which is unusual. LDA usually converges in 11-14 steps. Then I tried different combinations of Ud and Up, I found for Ud=8eV and Up=-8~2eV, calculations all converge in less than 15 steps. For Ud=8eV and Up>=3eV, it doesn't converge in 100 steps. Next I tried to modify the structure and potential directly from the NiO tutorial on the website. But still has the same convergence problem. The structure is like this:

Code: python

a=4.570
c=2.920
u=0.303
    
lattice = SimpleTetragonal(a*Angstrom, c*Angstrom)

# Define elements
elements = [Titanium, Titanium, Oxygen, Oxygen, Oxygen, Oxygen]

# Define coordinate
fractional_coordinates = [[ 0., 0., 0.],
                      		[ 0.5, 0.5, 0.5],
                      		[ u, u, 0.],
                      		[ 1-u, 1-u, 0.],
                      		[ 0.5+u, 0.5-u, 0.5],
                      		[ 0.5-u, 0.5+u, 0.5]]
             		
# Set up configuration
bulk_configuration = BulkConfiguration(
    bravais_lattice=lattice,
    elements=elements,
    fractional_coordinates=fractional_coordinates
    )

[zh]

These may suggest that the values of U (Ud=8eV and Up>=3e) chosen in your calculations may not be reasonable.  You had better check the electronic structure of TiO2 calculated by Ud=8eV and Up=-8~2eV.

[Nordland]

In ATK 10.8.2 it always fills the shells using a spherical-symmetric initial density for each atom. However studies have shown that in order to get good convergence for the +U
it sometimes requires that you use an anisotropic initial density.

In the ATK 11.2 version, you can give a keyword called Anisotropic, and the initial density will be setup to be anisotropic, and our test have shown that this greatly improves convergence for the harder systems with +U.

[kstokbro]

I would also recommend to only include the U for the single zeta orbitals, it seems that for O you include the U for both p orbitals.

It might even be that you should  only include the U for the d orbital in Ti.  I am not sure if the O states are sufficiently localized for the U correction to be meaningfull.