This lesson aims at showing how to get converged values for the following physical properties :
You will also finish to read the abinit_help file.
This lesson should take about 1 hour.
We studied the H2 molecule in a big box. We used 10 Ha as cut-off energy, a 10x10x10 Bohr^3 supercell, the local-density approximation (as well as the local-spin-density approximation) in the Teter parametrization (ixc=1, the default), and a pseudopotential from the Goedecker-Hutter-Teter table.
At this stage, we compared our results :
2.1.a Computing the bond length and corresponding atomisation energy in one run.
Before beginning, you might consider to work in a different subdirectory as
for lesson_base1. Why not "Work2" ?
Because we will compute many times the bond length and atomisation energy, it is worth to make a single input file that will do all the associated operations. You should try to use 2 datasets (try to combine ~abinit/tests/tutorial/Input/tbase1_3.in with ~abinit/tests/tutorial/Input/tbase1_5.in !). Do not try to have the same position of the H atom as one of the H2 atoms in the optimized geometry.
The input file ~abinit/tests/tutorial/Input/tbase2_1.in is an example of file that will do the job, while ~abinit/tests/tutorial/Refs/tbase2_1.out is an example of output file. You might use ~abinit/tests/tutorial/Input/tbase2_x.files as "files" file (do not forget to modify it, like in lesson 1), although it does not differ from ~abinit/tests/tutorial/Input/tbase1_x.files. The run should take less than one minute.
You should obtain the values :
etotal1 -1.1058360644E+00 etotal2 -4.7010531489E-01and
xcart1 -7.6091015760E-01 0.0000000000E+00 0.0000000000E+00 7.6091015760E-01 0.0000000000E+00 0.0000000000E+00
These are similar to those determined in lesson 1,
although they have been obtained in one run. You can also check that the residual
forces are lower than
Convergence issues are discussed in
of the abinit_help file.
You should read it. By the way, you have read many parts of the abinit_help file ! You are missing the sections 2, 5, 8. You are also missing the description of many input variables. We suggest that you finish reading entirely the abinit_help file now, while the knowledge of the input variables will come in the long run.
2.1.b Many convergence parameters have already been identified. We will focus only on ecut and acell. This is because
2.2.a You have likely seen a big increase of the CPU time needed to do the calculation (now, about one minute on a PC 3 GHz). You should also look at the increase of the memory needed to do the calculation (go back to the beginning of the output file). The output data are as follows :
etotal11 -1.1058360644E+00 etotal12 -4.7010531489E-01 etotal21 -1.1218716100E+00 etotal22 -4.7529731401E-01 etotal31 -1.1291943792E+00 etotal32 -4.7773586424E-01 etotal41 -1.1326879404E+00 etotal42 -4.7899908214E-01 etotal51 -1.1346739190E+00 etotal52 -4.7972721653E-01 etotal61 -1.1359660026E+00 etotal62 -4.8022016459E-01 xcart11 -7.6091015760E-01 0.0000000000E+00 0.0000000000E+00 7.6091015760E-01 0.0000000000E+00 0.0000000000E+00 xcart12 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 xcart21 -7.5104912643E-01 0.0000000000E+00 0.0000000000E+00 7.5104912643E-01 0.0000000000E+00 0.0000000000E+00 xcart22 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 xcart31 -7.3977108831E-01 0.0000000000E+00 0.0000000000E+00 7.3977108831E-01 0.0000000000E+00 0.0000000000E+00 xcart32 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 xcart41 -7.3304273322E-01 0.0000000000E+00 0.0000000000E+00 7.3304273322E-01 0.0000000000E+00 0.0000000000E+00 xcart42 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 xcart51 -7.3001570260E-01 0.0000000000E+00 0.0000000000E+00 7.3001570260E-01 0.0000000000E+00 0.0000000000E+00 xcart52 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 xcart61 -7.2955902118E-01 0.0000000000E+00 0.0000000000E+00 7.2955902118E-01 0.0000000000E+00 0.0000000000E+00 xcart62 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00The corresponding atomisation energies and interatomic distances are :
ecut atomisation interatomic distance (Ha) energy (Ha) (Bohr) 10 .1656 1.522 15 .1713 1.502 20 .1737 1.480 25 .1747 1.466 30 .1753 1.460 35 .1756 1.459In order to obtain 0.2% relative accuracy on the bond length or atomisation energy, one should use a kinetic cut-off energy of 30 Ha. We will keep in mind this value for the final run.
Well, 30 Ha is a large kinetic energy cut-off ! The pseudopotential that we are using for Hydrogen is rather "hard" ...
2.3 The convergence in acell
The same technique as for ecut
should be now used for the convergence in acell.
We will explore acell starting
8 8 8 to
18 18 18, by step of
2 2 2.
We keep ecut 10 for this study.
Indeed, it is a rather general rule that there is little cross-influence between
the convergence of ecut and the
convergence of acell. The file
~abinit/tests/tutorial/Input/tbase2_3.in can be used as an example. The CPU time needed
is also on the order of one minute.
The output data (~abinit/tests/tutorial/Refs/tbase2_3.out)
are as follows :
etotal11 -1.1188128741E+00 etotal12 -4.8074164402E-01 etotal21 -1.1058360644E+00 etotal22 -4.7010531489E-01 etotal31 -1.1039109441E+00 etotal32 -4.6767804802E-01 etotal41 -1.1039012761E+00 etotal42 -4.6743724199E-01 etotal51 -1.1041439319E+00 etotal52 -4.6735895176E-01 etotal61 -1.1042058195E+00 etotal62 -4.6736729718E-01 xcart11 -7.8427127284E-01 0.0000000000E+00 0.0000000000E+00 7.8427127284E-01 0.0000000000E+00 0.0000000000E+00 xcart12 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 xcart21 -7.6091015760E-01 0.0000000000E+00 0.0000000000E+00 7.6091015760E-01 0.0000000000E+00 0.0000000000E+00 xcart22 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 xcart31 -7.5472588642E-01 0.0000000000E+00 0.0000000000E+00 7.5472588642E-01 0.0000000000E+00 0.0000000000E+00 xcart32 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 xcart41 -7.5491961064E-01 0.0000000000E+00 0.0000000000E+00 7.5491961064E-01 0.0000000000E+00 0.0000000000E+00 xcart42 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 xcart51 -7.5427730675E-01 0.0000000000E+00 0.0000000000E+00 7.5427730675E-01 0.0000000000E+00 0.0000000000E+00 xcart52 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 xcart61 -7.5415348434E-01 0.0000000000E+00 0.0000000000E+00 7.5415348434E-01 0.0000000000E+00 0.0000000000E+00 xcart62 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00The corresponding atomisation energies and interatomic distances are :
In order to reach 0.2% convergence on the interatomic distance, one needs
acell 12 12 12.
The atomisation energy needs
acell 14 14 14 to be converged at that level.
12 12 12, the difference is
.0009 Ha=0.024eV, which
is sufficiently small for practical purposes.
We will use
acell 12 12 12 for the final run.
For most solids the size of the unit cell will be smaller than that. We are treating a lot of vacuum in this supercell ! So, the H2 study, with this pseudopotential, turns out to be not really easy. Of course, the number of states to be treated is minimal ! This allows to have reasonable CPU time still.
We now use the correct values of both ecut
and acell. Well, you should
modify the tbase2_3.in file to make a calculation
acell 12 12 12
You can still use the double loop feature with
1 2 (which reduces to a single loop), to minimize the modifications to
the file. The file ~abinit/tests/tutorial/Input/tbase2_4.in can be taken as an example of input
file, and ~abinit/tests/tutorial/Refs/tbase2_4.out as an example of output file.
Since we are doing the calculation at a single (ecut, acell) pair, the total CPU time is not as much as for the previous determinations of optimal values through series calculations. However, the memory needs have still increased a bit.
The output data are :
etotal11 -1.1329372051E+00 etotal12 -4.7765320721E-01 xcart11 -7.2662135225E-01 0.0000000000E+00 0.0000000000E+00 7.2662135225E-01 0.0000000000E+00 0.0000000000E+00 xcart12 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00
0.1776 Ha = 4.833 eV
ixc=1. Other expressions for the local (spin) density approximation
ixc=2, 3 .. 7are possible. The values 1, 2, 3 and 7 should give about the same results, since they all start from the XC energy of the homogeneous electron gas, as determined by Quantum Monte Carlo calculations.
ixc=4, 5, 6are older local density functionals, that could not rely on these data.
We will use the Perdew-Burke-Ernzerhof functional, proposed in Phys. Rev. Lett. 77, 3865 (1996).
In principle, for GGA, one should use another pseudopotential than for LDA. However, for the special case of Hydrogen, and in general pseudopotentials with a very small core (including only the 1s orbital), pseudopotentials issued from the LDA and from the GGA are very similar.
So, we will not change our pseudopotential. This will save us lot of time, as we should not redo an ecut convergence test (ecut is often characteristic of the pseudopotentials that are used in a calculation).
Independently of the pseudopotential, an acell convergence test should not be done again, since the vacuum is treated similarly in LDA or GGA.
So, our final values within GGA will be easily obtained, by setting ixc to 11 in the input file tbase2_4.in. See ~abinit/tests/tutorial/Input/tbase2_5.in for an example.
etotal11 -1.1621428502E+00 etotal12 -4.9869631917E-01 xcart11 -7.1204535408E-01 0.0000000000E+00 0.0000000000E+00 7.1204535408E-01 0.0000000000E+00 0.0000000000E+00 xcart12 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00
0.1647 Ha = 4.482 eV
Do not forget that the typical accuracy of LDA and GGA varies with the class of materials studied...