Band Gap/Band Structure Calculations

[tommy91779]

Hello all,


I am new to VASP and wish to use it to determine the band gap of bulk silicon at the special k points. Can anyone share with me a systematic way to determine the band gap and the band structure using VASP?


Thank you in advance

Tom

[admin]

1) please do a fully self-consistent calculation. This includes
-- optimizing the parameter sets (KPOINTS, ENCUT, PREC)
-- with that parameter set, optimize the geometry (either automatically, by using ISIF=3, PREC=Acc, ENCUT= 1.3*max (ENMAX), ENMAX is given in the POTCAR file you use, or by hand (doing an E/V fit). As convergence criterium for the geometry, please choose eg EDIFFG=-0.01 (the maximum forces/pressure is 0.01 eV/Ã…)
-- for the fully optimized geometry, please keep CONTCAR (=POSCAR of the optimized geometry), CHGCAR and WAVECAR of the last step.

2) BAND STRUCTURE runs:
please
-- use
the last CONTCAR (as POSCAR), the last CHGCAR (which gives the self-consistent potential/charge density of the system)
-- in INCAR set ICHARG=11
IBRION=-1
NSW=0
-- as KPOINTS file please choose the format which generates k-points along the high-symmetry lines of the BZ: like eg
points for bandstructure
10
line
reciprocal
0.50000 0.50000 0.50000 1
0.00000 0.00000 0.00000 1

0.00000 0.00000 0.00000 1
0.00000 0.50000 0.50000 1......

take a look at the EIGENVAL file of this run to get the KS-eigenvalues at the special k-points (for a cubic cell, these would be R, Gamma and M in the given cell) to find the gap witdth.

3) the DOS-run:
please again use
-- CHGCAR (ICHARG=11)
-- a KPOINTS file with a denser grid as you used for the scf run, please choose a mesh which includes the Gamma point and the points at the edges of the BZ (usually odd grids do).
-- do one step (IBRION=-1; NSW=0) choosing the Tetrahedron BZ-integration method (ISMEAR=-5)
-- if you want to get the local DOS, please set LORBIT=11 in addition. the DOSCAR file gives the DOS.

please also have a look at the VASP-workshop excercise Nr. 2, which was on the electronic properties of bulk Si (2.1 -- 2.6). You can download the input files and the transparancies with the discussion from http://cms.mpi.univie.ac.at/vasp-workshop , Handson2.tgz (all inputs) and handsonII.pdf (discussion)

[sankh]

Hi forum,

Thanks for explanation about how VASP does Band structure and DOS calculations. However, I have got a few specific questions related to this topic. I am currently using VASP 5.2.8 for 48-atoms Anatase and Rutile systems within LSDA and spin polarized GGA formalisms of theory. I am interested in obtaining 1. Accurate geometry, 2. Accurate bulk total energy, 3. DOS and PDOS (LDOS) and 4. Band structure.

For obtaining 1. accurate geometry what I do is:
a. INCAR with ENCUT = max(ENMAX) from POTCAR, PREC = Accurate, ISPIN = 2, ISIF = 3, EDIFF = 1E-05, EDIFFG = 1E-03, ISMEAR = 0, POTCAR with PAW_PBE potentials supplied by VASP, and KPOINTS with automatic MP mesh of size 8*8*8.
b. Move CONTCAR to POSCAR without changing INCAR and KPOINTS files and re-optimize the geometry.

Could someone comment the quality of my geometry including the internal co-ordinates and cell parameters and volume? Why do I need to increase ENCUT to 3*max(ENMAX) at stage "b", if I would need to do so, at all?

For obtaining accurate bulk energy what I do:

a. Move CONTCAR to POSCAR from last run "b". Read WAVECAR from last step of Geom Opt, set NSW = 0, ICHARG = 0, IBRION = -1, ENCUT = unchanged, ISMEAR = 0 ISPIN = 2, save new WAVECAR and KPOINTS file with 8*8*8 MP automatic mess.

b. Read WAVECAR from a, in INCAR NSW = 0, IBRION = -1, ENCUT = unchanged, ISPIN = 2, ISMEAR = -5 (I am NOT reading charge density as VASP manual discourages this for spin-polarization calculations), in KPOINTS file now 8*8*8 Gamma centred mesh (keeping in mind Tetrahedron method uses Gamma centred k-points)
A quick question is why in OUTCAR Blöchl energy corrections are priting as "*****"?

c. Now again read the WAVECAR and same INCAR, KPOINTS, POSCAR and POTCAR, I repeat a single point calculation to obtain total energy.

Could someone comment on the quality of this bulk total-energy, please?

And now I want to obtain DOS and LDOS using the final WAVCAR and/or charge density. Shall I use the following?
In INCAR, ISPIN = 2, ICHARG = 0, NSW = 0, IBRION = -1, ISMEAR = -5, same ENCUT, EDIFF and EDIFFG, LORBIT = 12

In KPOINTS, Automatic Gamma Centered mesh of size either 8*8*8 or 16*16*16

I guess setting ICHARG = 11 with ISPIN = 2 won't work. Am I correct?

I used LORBIT = 11, and it does not give DOS for spin-up and spin-down and nor it produced two PROCAR files and nor two PROROOT, and nor two sets of eigenvalues for up and down spins in EIGENVALE files and nor DOS0, DOS1, DOS2, .... Could someone please comment on these?

Do I need to set odd Gamma centered k-mess (say 15*15*15) in KOINTS instead of 8*8*8 0r 16*16*16 when calculating DOS/LDOS and accurate bulk energy? If yes, why?

What would be the quality of bulk energy and DOS/LDOS if one uses tetrahedon method, i.e. ISMEAR =-5 with Monkhorst-Pack k-mesh instead of Gamma centered k-mesh?

Finally, for band-structure calculations within spin-polarized description, what do I need to do? I guess, ISMEAR = -5 also gives better band-structure, right? I guess for Band structure calculation it is always better to use the WAVECAR or charge density from DOS calculation as they are better in quality if DOS was done with denser k-points. Am I right? For band structure calculations, doesn't VASP need any particular K-point sampling?

I am sorry to bother with long text-torturing and with so many questions, but I suppose one would agree with me that it is better to understand a code properly than abusing it as a black box! So, I look forwad to receiving the feedback. Thanks a lot for this in advance.

Best regards,
Sankh

[tlchan]

For geometry optimization and total energy evaluation, the procedures that you described are complicated just because you choose to relax unit cell shape and volume automatically. With a fixed number of basis set, there is Pulay stress when volume changes. The steps that you described are ways to minimize the error. Depending on your project, it is better to do a series of constant volume calculations. Please see the VASP manual for details.

[quote author= max(ENMAX) from POTCAR, PREC = Accurate, ISPIN = 2, ISIF = 3, EDIFF = 1E-05, EDIFFG = 1E-03, ISMEAR = 0, POTCAR with PAW_PBE potentials supplied by VASP, and KPOINTS with automatic MP mesh of size 8*8*8.
b. Move CONTCAR to POSCAR without changing INCAR and KPOINTS files and re-optimize the geometry.

Could someone comment the quality of my geometry including the internal co-ordinates and cell parameters and volume? Why do I need to increase ENCUT to 3*max(ENMAX) at stage "b", if I would need to do so, at all?
[/quote]
You simply need to take your optimized geometry from above, and evaluate the total energy using the ENCUT and the k-point sampling scheme that you want for your project.


[quote="sankh"]
For band structure calculations, doesn't VASP need any particular K-point sampling?
[/quote]
To calculate band structure, there is no k-point sampling. VASP reads in the self-consistent charge density from a previous calculation, and then evaluate the eigenvalues for each k-point that you specified in the KPOINT file.

[sankh]

Thanks for the suggestions and comments. Going through VASP manual and all various comments/discussions, I am quite confused about the strategies for full geometry optimization, accurate bulk energy, DOS/LDOS and band structure calculations within VASP with publication quality.

First issue that I would address is that spin-polarization formalism (ISPIN = 2) within VASP, especially for accurate energy, DOS/LDOS and band-structure is not very clear, not well documented and is very confusing. It is a well known fact that these 3 types of calculations should be done using converged density matrices (alpha and beta densities in spin-unrestricted cases) that were obtained from a previous SCF run, and using Tetrahedron method of integration with Blochl's correction. Now this is straight forward for ISPIN = 1 case by setting ICHARG = 11. It seems to me that ICHARG = 11 uses Harris functional method which is not compatible with spin-orbital description. Could someone please clarify whether or not ICHARG = 11 indeed uses Harris functional method, and whether or not CHARGCAR contains both alpha and beta charge densities from an SCF calculation with ISPIN = 2?

I think that VASP manual at some point warns the users to avoid using charge densities (reading CHARGCAR, i.e. ICHARG =1) for restarting a geometry optimization (i.e. ISTART = 1 and IBRION=1/2/3) from a previous run in case of ISPIN =2, as well, and rather advises to use previously optimized wavefunctions (i.e. reading WAVECAR using ICHARG = 0) to construct initial density matrices.

Then how would one perform a static type calculation (DOS, Energy, Band, etc.) for spin polarized cases (ISPIN =2) within VASP?

Since Tetrahedron method within VASP uses Gamma centered k points, I guess, one can't directly use the optimized set of k points and wavefunctions (plane wave coefficients) that were obtained from a past geometry optimization, unless the past geometry optimization was also done with Gamma centered k mesh. But use of Tetrahedron method for a static calculation to obtain accurate energy or DOS/LDOS is advised. Therefore, I have been again reoptimizing them at fixed nuclear displacement vectors and cell parameters (stationary cell geometry) before making them use for further static calculations such as energy, DOS, band, optical properties, etc. However, if someone feels I am incorrect, please do advise me up.

Thanks once again for reading and co-operating with the issues I have raised.

Best regards,
Sankh
<span class='smallblacktext'>[ Edited Mon Dec 27 2010, 09:54PM ]</span>