[Pw_forum] Multiple issues with graphene supercell calculations
Gabriele Sclauzero
sclauzer at sissa.it
Mon Nov 22 12:01:11 CET 2010
Dear Singh,
i) in the hexagonal cell the forces vanish by symmetry, that's why they are perfectly zero. In the rectangular cell this is no more the case. I think the problem arises because you did not specify the celldm(1) parameter with enough significant digits, perhaps, hence the structure does not correspond exactly to the optimal one.
Then keep in mind that the cell is rectangular, thus in principle you should use a different number of k-points in the two directions.
ii) I do not see the point of moving to larger supercells if you are in trouble with the small one. No reason to try such a high wfc and density cutoff either, in my opinion.
iii) In the hexagonal cell the forces look good to me, for practical purposes they are sufficiently small to say that you are at the theoretical energy minimum. The energy is much closer to the one of the primitive cell because the k-point sampling is correct this time.
About the 72 atom cell, well, first are you sure about the structure? If so, you need to specify your input file, otherwise if will be difficult to judge.
HTH
GS
Il giorno 22/nov/2010, alle ore 04.08, DHRUV SINGH ha scritto:
> Dear PWSCF users,
>
> I use a hexagonal unit cell with 2 basis atoms and lattice parameter (C-C bond length) of 2.6868 a.u. - this value was arrived at by energy minimization over a range of lattice parameters near this value. With a 16x16x1 kpoint grid it is seen that the energy per atom converges to -11.395192 Ry and the forces on the 2 atoms are zero (atleast until a good precision). The ultrasoft pseudopotential with the RRKJ modification is used for C and the results obtained are in excellent agreement with Marzari and Mounet PRB 71, 205214, 2005.
> The essentials of the input file and the forces from the 2 atom unit cell are shown below
> --------------------------------------------------------------------------------
> &system
> ibrav=0,
> celldm(1)=2.6868,
> nat=2,
> ntyp=1,
> ecutwfc=40.0,
> ecutrho=480.0,
> degauss=0.03,
> nbnd=8
> /
> &electrons
> mixing_beta = 0.5
> conv_thr = 1.0d-8
> /
> ATOMIC_SPECIES
> C 12.0 C.pbe-rrkjus.UPF
>
> CELL_PARAMETERS {hexagonal}
> 1.5 0.866025404 0.0
> 1.5 -0.866025404 0.0
> 0.0 0.0 20
> ATOMIC_POSITIONS {crystal}
> C 0.0000000 0.0000000 0.0000000
> C 1/3.0 1/3.0 0.0000000
>
> atom 1 type 1 force = -0.00000000 -0.00000000 0.00000000
> atom 2 type 1 force = 0.00000000 0.00000000 0.00000000
> --------------------------------------------------------------------------------
>
> Using this lattice parameter I then try to do supercell calculations with rectangular and hexagonal supercells and I am facing the following problems in the supercell scf calculations :
>
> i) With a 4 atom rectangular supercell and the same lattice parameter of 2.6868 au, atomic coordinates and input shown below, I find that the energy/atom coverges to -11.395182 Ry(very close to the 2 atom unit cell) for a 8x8x1 k point grid but there seem to be non-negligible net forces on all 4 atoms as shown below,
> --------------------------------------------------------------------------------
>
> &system
> ibrav=0,
> celldm(1)=2.6868,
> nat=4,
> ntyp=1,
> ecutwfc=40.0,
> ecutrho=480.0,
> degauss=0.03,
> nbnd=16
> /
> &electrons
> mixing_beta = 0.5
> conv_thr = 1.0d-8
> /
>
> CELL_PARAMETERS {cubic}
> 3.0 0.0 0.0
> 0.0 1.732050808 0.0
> 0.0 0.0 14
> ATOMIC_POSITIONS {alat}
> C 0 0 0
> C 1 0 0
> C 1.5 0.866025404 0
> C 2.5 0.866025404 0
> --------------------------------------------------------------------------------
>
> atom 1 type 1 force = 0.00310476 0.00000000 0.00000000
> atom 2 type 1 force = -0.00310476 0.00000000 0.00000000
> atom 3 type 1 force = 0.00310476 0.00000000 0.00000000
> atom 4 type 1 force = -0.00310476 0.00000000 0.00000000
>
> ii) With a 48 atom rectangular supercell and 2x2x1 kpoint grid I find energy/atom of -11.395152 Ry (again very close to the 2 atom unit cell) but non negligible forces: Forces on atom 1 are shown below
> atom 1 type 1 force = 0.00274639 0.00000000 0.00000000
> The story is the same as I keep increasing the supercell size ... for 60 atoms the forces on atom 1 are
> atom 1 type 1 force = -0.00395744 0.00000000 0.00000000
> The forces do not change even if I increase ecutwfc to 80.0 and ecutrho to 800.0. They also do not change if I increase the kpoint grid resolution
>
> iii) Hexagonal supercells: I get slightly better answers with a hexagonal supercell in terms of forces. For example a 32 atom hexagonal supercell of graphene gives me an energy/atom of 11.395194 Ry for a 4x4x1 kpoint grid. The force on 1 of the atoms is
> atom 2 type 1 force = 0.00001419 0.00000887 0.00000000
> and the magnitude is similar for most other atoms. Once again I find that increasing ecutrho or ecutwfc doesnt matter.
>
> However a more serious problem is seen with the hexagonal supercell. I find that scf calculations do not converge for a 72 atom supercell, with the following trend:
>
> estimated scf accuracy < 7.42866516 Ry
> estimated scf accuracy < 2.47702692 Ry
> estimated scf accuracy < 0.05551173 Ry
> estimated scf accuracy < 0.02263262 Ry
> estimated scf accuracy < 0.01534456 Ry
> estimated scf accuracy < 0.00799064 Ry
> estimated scf accuracy < 0.00499060 Ry
> estimated scf accuracy < 0.00272207 Ry
> estimated scf accuracy < 0.00292201 Ry
> estimated scf accuracy < 0.00255637 Ry
> estimated scf accuracy < 0.00240574 Ry
> estimated scf accuracy < 0.00239154 Ry
> estimated scf accuracy < 0.00227859 Ry
> estimated scf accuracy < 0.00214441 Ry
> estimated scf accuracy < 0.00221359 Ry
>
> I also tried changing the parameters ecutrho to 600.0; nband to 400 (from 72*4); decreasing degauss to 0.03 and trying mixing_mode='local-TF' as suggested but that does not help convergence one bit.
>
> Please let me know if there is something else I could try which would help with these issues - decreasing the forces on each atom and helping convergence in the hexagonal supercell calculations.
>
> Thank you very much
> Dhruv Singh
> Graduate Student, Purdue University ME
>
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§ Gabriele Sclauzero, EPFL SB ITP CSEA
PH H2 462, Station 3, CH-1015 Lausanne
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