tolerance setting

[jerry]

Dear,
    I am a little confused by the tolerance setting in the iteration control panel. Does the tolerance correspond to total energy or other parameters?
    Thank you very much！
                                                                                Jerry

[zh]

Usually, it corresponds to the total energy. 

[jerry]

Thanks a lot!
I have another question. It is said that the zig-zag graphene nanoribbon is metallic and the armchair graphene nanoribbon is semiconducting. But when i calculate the band structure for an armchair nanoribbon (without H atoms adsorbed at the edge, actually is a graphene sheet), the results show that the ribbon is metallic. Am i wrong?

[Anders Blom]

In ATK 10.8 and later the tolerance is primarily defined with respect to the Hamiltonian. The manual (http://quantumwise.com/documents/manuals/latest/ReferenceManual/index.html/ref.iterationcontrolparameters.html) contains a quite detailed explanation of this, but the short story is that if you set tolerance to for instance 1e-5, it means the calculation will be converged when the largest change dH in any Hamiltonian matrix element is 1e-5 Hartree.

In rare cases, you can have dH<tolerance and the calculation still continues for a bit, because there is actually an additional check on the Mulliken populations (for semi-empirical models) or the total energy (for DFT).

So, if you set the tolerance to 1e-5, you can be sure (for DFT) that the total energy is converged to dE=1e-5 Hartree, although in reality dE is normally even smaller once you reach dH=1e-5. You can see the obtained energy accuracy in the output log, in the final iteration report.

[Anders Blom]

A graphene sheet is not the same as a ribbon, even if you remove the hydrogen. A ribbon is finite in 2 directions (one atom layer thin, and finite across, with a vacuum gap), and only periodic in one direction. A graphene sheet is a graphene sheet, and no matter in which direction you look it will be metallic (but you need a lot of k-points to get an accurate band structure).

[Nordland]

At zero kelvin, graphene is a semi-metallic, as the band gap is only zero in the dirac point (and has a linear  dispersion around).
This means that you will many k-points to simulate the metallic properties of graphene.

[jerry]

Thanks a lot!
    When i calculate a armchair graphene ribbon with its H atoms removed ((4,0) with 1 repetition in z axis, the k point sampling is (1*1*50), the unit cell padding is 5), the band structure shows that it is metallic rather than semiconducting. Is this right?

[Anders Blom]

If by (4,0) you mean the indices used in the Ribbon builder in VNL, then this is an armchair ribbon, so it should be semiconducting. Removing the hydrogens is not a good idea, they make sure to saturate dangling bonds which give unreasonable results.

[jerry]

Yes, you are right! When remove the H atoms, its band structure changes a lot and the ribbon become metallic! Thanks you very much!