Hi all,

I have encountered a puzzling problem when running siesta calculations for a 
graphene arm-chair nano-ribbon, with width of 5 C atoms (basically 2 benzene 
rings), terminated by H atoms on the sides. The calculation is thus supposed to 
be 1D, periodic in Z-direction. The system has 14 atoms in rectangular 
(cartesian) lattice cell. 

To make sure the cell size is big enough in x and y dimension for the 1D 
calculation, I calculated total energies of an unrelaxed system (with fixed 
coordinates) with different cell dimensions, 41 kpoints in z directions, and 
mesh cut off of 900 Ry (these are converged values, more on the mesh below).  

The basis I am using is SZ. I need to use the minimum basis to get result that 
could be used to compare with results from another tight-binding code. When 
scanning the output files, I did not notice any warnings or errors in the basis 
set, and maximum cut-off for automatically generated H and C orbitals are both 
around 5.1 Bohr.

The basis settings are given by:

PAO.BasisSize       SZ
PAO.EnergyShift     200 meV

Here are the results:

For x cell dimension, with y dimension fixed at 10 Ang. (the nano-ribbon is 
flat in y-plane, so I assumed 10 Ang would be enough as an initial guess)

# Cell x dim (Ang) |  Total Energy (eV)
10.000000  -1594.828815
15.000000  -1594.855952
20.000000  -1594.856570
25.000000  -1594.856598
30.000000  -1594.856603
35.000000  -1594.856581
40.000000  -1594.856600
45.000000  -1594.856593
50.000000  -1594.856601
60.000000  -1594.856596
70.000000  -1594.856608

And for y cell dimension, with x dimension fixed to be 30.0 Ang:

# Cell y dim (Ang) |  Total Energy (eV)
 5.000000  -1594.558893
10.000000  -1594.856603
15.000000  -1594.860901
20.000000  -1594.861861
25.000000  -1594.862136
30.000000  -1594.862229
40.000000  -1594.862260
50.000000  -1594.862274

I set the DM.Tolerance to 1.d-6, so was expecting an energy tolerance of at 
least 1e-5 eV or better for each calculation. It is therefore puzzling to see 
there is still noticeable energy difference for such large x and y cell 
dimensions, especially for y, which I would expect to be flat after 10 Ang, as 
from the output, the maximum orbital and potential cutoff radii are about 5.1 ~ 
5.2 bohr.

I used the C.psf and H.psf files downloaded from siesta website, and also tried 
out my own ones generated using Opium. But all give the same problems.

I have also tried the same calculations with Soft-confinement options turned on:

PAO.BasisSize       SZ
PAO.EnergyShift     200 meV
PAO.SoftDefault     T
PAO.SoftInnerRadius  0.9
PAO.SoftPotential   40.0 Ry

But the results were even worse:

# Cell x dim (Ang) |  Total Energy (eV)
10.000000  -1595.419901
15.000000  -1595.445128
20.000000  -1595.445689
25.000000  -1595.445734
30.000000  -1595.445739
35.000000  -1595.445493
40.000000  -1595.445765
45.000000  -1595.445729
50.000000  -1595.445735
60.000000  -1595.445707
70.000000  -1595.445516

# Cell y dim (Ang) |  Total Energy (eV)
 5.000000  -1595.287697
10.000000  -1595.445739
15.000000  -1595.449755
20.000000  -1595.450680
25.000000  -1595.450917
30.000000  -1595.450999
40.000000  -1595.451061
50.000000  -1595.451042

If anyone have a solution to my problem I would very grateful. This has been 
bugging me for over a week now, and I need to get thing as basic as this 
correct or understood to be confident of my calculated results. 

I have a feeling that it may have something related to the integration grid, as 
at the moment I am also having problem converging the mesh, even with the 
egg-box corrections set to:

%block GridCellSampling
 0.5     0.5     0.5
%endblock GridCellSampling

as shown below (in all cases DM.Tolerance = 1.d-6, and it appeared the SCF 
calculations converged within 20 iterations):

# GNR Armchair N=5 pbc Siesta SZ LDA mesh
# Planewave equivalent mesh cutoff (Ry) | (eV) |  Total Energy (eV)
50.000000   680.279626  -1597.529386
100.000000   1360.559253  -1597.523020
150.000000   2040.838879  -1597.524000
200.000000   2721.118506  -1597.524111
300.000000   4081.677759  -1597.523661
400.000000   5442.237012  -1597.523763
500.000000   6802.796265  -1597.523767
600.000000   8163.355518  -1597.523812
700.000000   9523.914771  -1597.523724
800.000000   10884.474024  -1597.523694
900.000000   12245.033277  -1597.523779
1000.000000   13605.592530  -1597.523773
1100.000000   14966.151783  -1597.523767
1200.000000   16326.711036  -1597.523733
1300.000000   17687.270289  -1597.523751
1400.000000   19047.829542  -1597.523751
1500.000000   20408.388795  -1597.523765

I apologise for the long email, and thank you all for your time and help in 
advance.

Best regards,

Lianheng


==========================================================
Lianheng Tong                                                             Tel: 
+44 20 7679 3302
London Centre For Nanotechnology                       Fax: +44 20 7679 0595
University College London                                        
[email protected]
17–19 Gordon Street, London WC1H 0AH, U.K.
==========================================================


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