Exchange correlation,mesh cut off and k points

[huckelbuckel]

Although there are no of posts related to the same topic i just want to know briefly:

1. I want to calculate very accurate values of band gap of the given structure and the effect of electric field on the gap.As DFT generally underestimates the gap ... which exchange correlation is considered the best (LDA,LDA+u,GGA+u etc..) considering the accuracy of gap.

2.the mesh cut off can be tested for convergence by calculating total energy of the structure at different cut off points and selecting the one at which energy values start to saturate.Is there a similar test method available for deciding k-point or it is strictly dependent on geometry of the structure i.e, for a 2D graphene sheet 9 X9 X1 or 21 X 21 X 1 etc...can be selected.How the correct decision is made in k point selection.We have to re-run at various Kkpoints and then look for the changes??

Thanks

[Nordland]

1) The total energy can used as well, but as other properties can be slower to converge than the total energy with respect to the k-point, I normally look at the either the fermi level or Density of states.

2) If the structure is somewhat homogeneous, that being a molecule or bulk, then metaGGA is the best because it has a parameter C, that can be tuned to give the exact experimental answer or it without giving this parameter it is also quite good. metaGGA has it limitation when it comes to systems that consist of several domains,
where the material changes dramatically, where it loses some of it strength.
The runner-up is the LDA+U or GGA+U, which also have a parameter that will change the band gap, but in order for +U to work really well, you must have filled or almost shells of d-electron near the fermi level.

[GJK]

1) The total energy can used as well, but as other properties can be slower to converge than the total energy with respect to the k-point, I normally look at the either the fermi level or Density of states.

2) If the structure is somewhat homogeneous, that being a molecule or bulk, then metaGGA is the best because it has a parameter C, that can be tuned to give the exact experimental answer or it without giving this parameter it is also quite good. metaGGA has it limitation when it comes to systems that consist of several domains,
where the material changes dramatically, where it loses some of it strength.
The runner-up is the LDA+U or GGA+U, which also have a parameter that will change the band gap, but in order for +U to work really well, you must have filled or almost shells of d-electron near the fermi level.

Hi,
What does u mean in LDA+u and GGA+u

Thanks in advance

[zh]

"What does u mean in LDA+u and GGA+u"
U-->on-site Coulomb interaction parameter for the strong-correlated orbital in the Hubbard model.
Please go through a very recent review paper:
Hubbard-corrected DFT energy functionals: The LDA+U description of correlated systems
Burak Himmetoglu, Andrea Floris, Stefano de Gironcoli and Matteo Cococcioni,
International Journal of Quantum Chemistry, Volume 114, Issue 1, pages 14–49, 5 January 2014
http://onlinelibrary.wiley.com/doi/10.1002/qua.24521/abstract