How to accurately calculate Density of States(DOS) for 2D systems

[ph]

Dear Sir,
1)To calculate DOS, whether we have to keep  the k-points in the DFT calculator (e.g,13X13X1) and  in the k-points in the DOS analysis function(e.g,13X13X13) are same or different?
2)For the  above 2D system, if we  want to calculate Band structure and DOS, is it necessary to maintain same k-points for Band structure and DOS ?
3) What is the influence of points per segment in DFT-calculator on Band structure and DOS?
4)What is the importance of Projected DOS for a given system? or When we need to use PDOS?
5)What are  the general  thumb rules for  calculating accurate DOS of a system?

Best Regards
Ph       

[Anders Blom]

1. So, this is a 2D system. In that case it's sufficient to use NAxNBX1 in all cases, calculator and DOS. But you may need more k-points for the DOS, to get an accurate value.
2. The k-points for the band structure are not really related to this, they are along high-symmetry lines in the Brillouin zone, and it is well known that you do not get an accurate DOS by sampling only these lines. But as mentioned, they are not really related, at least not in terms of how you specify them, since the numbers NA, NB, NC for DOS are used to generate a Monkhorst-Pack grid.
3. There are no points per segment for DOS. For band structure, it gives smoother curves. Imagine plotting sin(x) with 10 points or 100 points, one curve is smoother than the other.
4. You use this if you want to know what orbitals contribute to the DOS at a given energy.
5. Many k-points. More than you think

[ph]

Dear Sir,
Thanks a lot for your kind reply.

1)So , for the given 2D system, To calculate DOS, the K-points(NAXNBX1)  in calculator are different from the K-points(NAXNBXNC) in the DOS analysis function(i.e, Monkhorst-Pack grid), to have a accurate DOS,  is it right?
2)What is the  approximate size of Monkhorst-pack grid(i.e, mesh thickness), interms of NAxNBXNC,  for  the given system size, interms of number of atoms(i.e, structure with 20 atoms, 40 atms, 100, 500, 700, 1000, etc) for reasonably good DOS calculation ?

Best Regards
Ph

[Anders Blom]

1. At least NC=1 for a 2D system (if you have vacuum in C). But yes, you may need different values for DOS and calculation.

2. It's not related to the number of atoms, it has to do with how rapidly the electron density changes in k-space, so it's system dependent, and strongly influenced by things like if you have d or f electrons. Of course the unit cell size matters, but the only sensible approach is to start at a reasonable value and increase until there are no significant changes anymore.

Note that DOS calculations parallelize extremely well, basically linearly, so there is a lot of time to be saved by running DOS (and transmission etc) in parallel (MPI).

[ph]

Dear Sir,
I am really thankful to your good Tips.

1) What additional changes do we need to make  for Band structure and DOS calculations if we use  two or three   layer (each one 2D layer or 2D unit cell) systems. Will our discussion so far obey, even  for two layer and three layer  systems ?

Best Regards
Ph
 

[Anders Blom]

That shouldn't change anything.

[ph]

Sir, Thanks a lot for your kind and valuble answers.