Dear Marcos,
Thank you for your elucidative response. I learned a lot. I also apologize
for my not well defined questions and for that I did not provide my input
file for graphene.
Here it is. (that one that used initially)
NumberOfAtoms 2
NumberOfSpecies 1
%block ChemicalSpeciesLabel
1 6 C # Species index, atomic number, species label
%endblock ChemicalSpeciesLabel
Meshcutoff 800.00 Ry
LongOutput T
WriteDenchar T
AtomicCoordinatesFormat Ang
%block AtomicCoordinatesAndAtomicSpecies
0.000 0.000 0.000 1
1.42 0.00 0.000 1
%endblock AtomicCoordinatesAndAtomicSpecies
%block PAO.BasisSizes
C DZP
%endblock PAO.BasisSizes
LatticeConstant 2.459512147 Ang
%block LatticeVectors
0.866025403 0.5 0.0
0.866025403 -0.5 0.0
0.0 0.0 60.0
%endblock LatticeVectors
%block BandLines
1 0.0 -1.33333333 0.0
30 0.0 0.0 0.0
30 0.577350269 1.0 0.0
20 0.0 1.33333333 0.0
%endblock BandLines
I did what you suggested. I used the the content of STRUCT_NEXT_ITER files
to see the difference in structural parameters and here they are :
----------------------------------------------------------------
1) MD.VariableCell .false.; no k-point sampling; Meshcutoff=800 Ry
2.129999998 1.229756074 0.000000000
2.129999998 -1.229756074 0.000000000
0.000000000 0.000000000 147.570728820
2
1 6 0.000000000 -0.000000001 0.000000000
1 6 0.333333333 0.333333334 0.000000000
FE=2.916573
-----------------------------------------------------------------
2) MD.VariableCell .true.; no k-point sampling; Meshcutoff=800 Ry
2.129999998 1.229756074 0.000000000
2.129999998 -1.229756074 0.000000000
0.000000000 0.000000000 147.570728820
2
1 6 0.000000000 -0.000000001 0.000000000
1 6 0.333333333 0.333333334 0.000000000
FE=2.916573
-------------------------------------------------------------------
3) MD.VariableCell .true.;k-point sampling:
%block kgrid_Monkhorst_Pack
21 0 0 0.0
0 21 0 0.0
0 0 1 0.0
%endblock kgrid_Monkhorst_Pack ; Meshcutoff=800 Ry
2.129999998 1.229756074 0.000000000
2.129999998 -1.229756074 0.000000000
0.000000000 0.000000000 147.570728820
2
1 6 0.000000001 -0.000000001 0.000000000
1 6 0.333333334 0.333333335 0.000000000
FE=-3.788733
-------------------------------------------------------------------
4) MD.VariableCell .true.;k-point sampling:
%block kgrid_Monkhorst_Pack
6 0 0 0.0
0 6 0 0.0
0 0 1 0.0
%endblock kgrid_Monkhorst_Pack ; Meshcutoff=800 Ry
2.129999998 1.229756074 0.000000000
2.129999998 -1.229756074 0.000000000
0.000000000 0.000000000 147.570728820
2
1 6 0.000000001 0.000000000 0.000000000
1 6 0.333333334 0.333333335 0.000000000
FE=-3.785969
Is it that info that you asked for? So, if it is that, you may easily see
that there is no difference in cell vectors and atomic positions
regardless of the presence of the options you indicated. The only
significant difference is the Fermi Level (as it is expected). It is also
interesting that the band structure looks very similarly in all these
cases but the crossing points (at the K-points) are shifted and do not
tally with the calculated level of FE (in case without k-point sampling).
The fact that there is no difference in structure parameters may be the
simple consequence of that I used the initial geometry very closed to
equilibrium one. Is it so?
Now I have more questions.
1) Why do you want to compare these results? Are they indicative for what?
2) How to specify (what reasons or ideas to follow) the k-point sampling
in case of GNRs?
3) Why I got the more or less correct band structure (merely shifted with
respect to correct FE) for Zigzag NR without sampling and can not get the
same WITH k-point sampling along that ribbon?
4) Why I could not get the more or less reasoning BS for Armchair NR until
I used
%block kgrid_Monkhorst_Pack
45 0 0 0.0
0 1 0 0.0
0 0 1 0.0
%endblock kgrid_Monkhorst_Pack ?
5) How does k-point sampling influence the convergence of SCF loop?
6) Why the doubling of unit cell for Armchair NR (with the same or larger
k-point sampling along the ribbon) does not lead to convergence and any
reasonable results?
7) What should I do now to circumvent all these hurdles?
I'm looking forward for you instructive (enlightening) advice.
Artem Baskin,
PhD student,
University of Illinois at Chicago
On Thu, April 22, 2010 7:35 pm, Marcos Veríssimo Alves wrote:
> Artem,
>
> Let's go step by step. The fact that you get "good" results with graphene
> only at the Gamma point seems extremely strange (weird might not sound so
> good, I acknowledge that) for the following.
>
> Graphene has an extremely small Fermi surface - actually, a *single*
> k-point,
> which is located at the high-symmetry point K of the Brillouin zone. To
> accurately sum over the bands of graphene, you need a specific k-point
> sampling, which includes the coordinates of K in reciprocal space, as well
> as a pretty dense k-point mesh in order to get the (linear, in the
> vicinity
> of K) dispersion of the bands in this region.
>
> Why is this important? Well, due to symmetry reasons, the Fermi level lies
> *
> exactly* at this point. Thus, it is important to accurately sample the
> region of the BZ close to K, both including this particular point in your
> sampling, *and* including enough k-points in order to accurately sum over
> the occupied states and get a good total energy, which is the variational
> quantity in DFT. Andf, as you may easily realize, Gamma-only sampling is
> not
> enough for that.
>
> You do not provide enough details on your graphene calculation, therefore
> I
> cannot know what you have done (this is the reason we always ask for the
> input files. Repetitive? Yes, but... an image is worth a thousand words,
> if
> you catch my drift). So, I propose the following test for you, in your
> graphene unit cell with two atoms. Start from ideal positions ((0,0,0) ;
> (0.3333333333,0.3333333333,0.3333333333) in fractional coordinates) for
> the
> C atoms, and the following cell:
>
> LatticeConstant 2.44 Ang
> %block LatticeParameters
> 1.00 1.00 10.0 90.0 90.0 60.0
> %endblock LatticeParameters
>
> (check the convention for the angles between the lattice vectors in
> crystallographic format in the manual, but I think this would be the
> correct
> setting). Now, do two calculations:
>
> 1) one with fixed cell, and only atomic coordinate relaxation
> (MD.VariableCell .false.), and
> 2) one with MD.VariableCell .true. .
>
> For those, check the cell parameters and angle between the cell vectors at
> the end of the second calculation.
>
> After this, do a third calculation, starting from the same ideal
> coordinates
> and with MD. VariableCell set to .true., but now using
>
> %block kgrid_Monkhorst_Pack
> 21 0 0 0.0
> 0 21 0 0.0
> 0 0 1 0.0
> %endblock kgrid_Monkhorst_Pack
>
> This is a sampling that, for the graphene cell described, includes the
> high-symmetry point K in the sampling, and has a rather dense k-point
> grid.
> As a final calculation, lower the Monkhorst-Pack grid to
>
> %block kgrid_Monkhorst_Pack
> 6 0 0 0.0
> 0 6 0 0.0
> 0 0 1 0.0
> %endblock kgrid_Monkhorst_Pack
>
> which still includes the high-symmetry point K, but has a much less dense
> grid. Do it still with MD.VariableCell .true., and look at the
> structural parameters. Use a 800 Ry cutoff in all of them, since this will
> help avoid the infamous egg-box effect. Please tell me if you see any
> difference in the structural parameters from each of the calculations. You
> can use, if you wish, an automatically generated DZP basis set with an
> EnergyShift 0.2 eV. An anticipation on the results: if there is no
> difference between these results, there is something wrong :)
>
> The fact that you use Stephan Roche's results as a benchmark is good - his
> calculations are very reliable. Nevertheless, I would say that you are
> somehow inadvertently forcing symmetry in your system, which is the cause
> of
> the - much likely fortuitous - agreement of whatever result you are
> obtaining in your calculations, with those of S. Roche.
>
> Some years ago, there were several posts on graphene on the list, with
> some
> very enlightening paricipations by Stephanie Reich. Search the list
> archives
> for these posts - you will learn a lot from them. I did, when I was still
> working with graphene.
>
> Later on we can deal with different beasts like GNRs.
>
> Cheers,
>
> Marcos
>
> On Thu, Apr 22, 2010 at 11:32 PM, Artem Baskin <abas...@uic.edu> wrote:
>
>> Dear Marcos,
>> Thanks for your help, but the situation looks really WEIRD or I don't
>> understand anything at all (that may be also true).
>> When I was calculating the BS for graphene and zigzag NR I did not use
>> any
>> specific supercell (I did not use the supercell block, the naive
>> supercell
>> factors were 6*6*1 for graphene (initially my elementary unit cell
>> consisted of 2 atoms) and 6*1*1 for Zigzag NR (with 22 atoms - 5 rings
>> width)). Of course, the SCF procedure converged in these two cases.
>> As to criterion to determine whether my calculations are good or not, I
>> used the comparison both with tight-bonding method results and the DFT
>> calculations that were already done (using Siesta) by Pr. Stephan Roche
>> and co-workers. My results tallied with the those ones perfectly.
>>
>> As to convergence in case with the zigzag NR (with k-point grid), double
>> unit cell of armchair NR and its flakes, the procedure did not
>> converged,
>> and I don't know how to have it converged. Moreover, form one step of
>> the
>> iteration to another one the charges on the edge H-atoms are fluctuating
>> getting more and more asymmetrical. This is another manifestation of the
>> non-zero dipole moment.
>>
>> Best,
>> Artem Baskin,
>> PhD student,
>> University of Illinois at Chicago
>>
>>
>> On Thu, April 22, 2010 1:16 pm, Marcos Veríssimo Alves wrote:
>> > Artem,
>> >
>> > Good results for graphene without any k-point sampling (only Gamma
>> point)?
>> > And also for a zigzag NR? Now THAT's weird... unless you are using a
>> huge
>> > supercell for each of them. What is your criterion for saying that
>> your
>> > calculation is good? For a zigzag NR you might get away with a smaller
>> > supercell, if it's a semiconductor (I guess it is, I don't remember it
>> > right
>> > now).
>> >
>> > What is your procedure for calculating the band structure? Are you
>> making
>> > sure you re-use the converged DM file?
>> >
>> > Marcos
>> >
>> >
>> > On Thu, Apr 22, 2010 at 8:06 PM, Artem Baskin <abas...@uic.edu> wrote:
>> >
>> >> Dear all users,
>> >> I am involved in band structure calculations for armchair and zigzag
>> >> nanoribbons and I have problems with the appropriate k-point
>> sampling.
>> >> My
>> >> problem is like this:
>> >> Initially, I calculated the band structure for graphene and zigzag NR
>> >> without specifying any k-points. The results (with Meshcutoff level
>> 800
>> >> Ry
>> >> and 400 Ry respectively) were quite good. But when I tried to
>> calculate
>> >> the band structure for armchair (5 rings width) NR I got absolutely
>> >> wrong
>> >> results, moreover, in spite of symmetrical configuration I obtained
>> the
>> >> non-zero significant dipole moment perpendicular to the ribbon (even
>> >> with 400 Ry MCutoff).
>> >> Then I generated a k-point grid using
>> >> %block kgrid_Monkhorst_Pack
>> >> 45 0 0 0.5
>> >> 0 1 0 0.5
>> >> 0 0 1 0.5
>> >> %endblock kgrid_Monkhorst_Pack
>> >> and I got correct results (no dipole moment and reasonable FE and
>> band
>> >> structure).
>> >>
>> >> FIRST problem that I encountered was that when I tried to recalculate
>> BS
>> >> for zigzag NR with the SAME k-point grid I got an enormous dipole
>> moment
>> >> (perpendicular to the ribbon) and wrong BS and FE level. Why is it
>> so?
>> >>
>> >> SECOND problem is that when I doubled the elementary cell for 5-rings
>> >> width armchair ribbon (using the SAME k-point grid and 400 Ry MCoff
>> >> level)
>> >> just to make sure that I will get the same good results I got again
>> an
>> >> enormous Dip moment and incorrect Band Structure.
>> >>
>> >> And THIRD (mysterious) problem is that when I tried to calculate Band
>> >> Structure for an isolated flake of armchair NR (3*5 rings size) I got
>> >> non
>> >> zero Dip moment (in this case for x- and y- directions) that is
>> >> nonsense.
>> >>
>> >> I guess, the problem is how to define correctly k-grid in these three
>> >> cases, but I don't know how. I performed the convergence test
>> increasing
>> >> the number of k-points but neither dipole moment nor FE level
>> >> demonstrate
>> >> the monotonic behaviour, so I could not reach the correct results.
>> >>
>> >> Any help will be appreciated.
>> >>
>> >> Artem Baskin,
>> >> PhD student,
>> >> University of Illinois at Chicago
>> >>
>> >>
>> >>
>> >>
>> >
>> >
>>
>>
>>
>
