We study three structures of tungsten oxide (WO_{3}) using the Quantum Espresso (QE) planewave Density functional theory (DFT) code and the effects of different primary parameters including: functional/pseudopotential, relaxed geometry, planewave cutoff (ecut), and k-grid density. The three structures of WO_{3} we consider are: simple cubic (space group Pm-3m), tetragonal (P4/nmm), and monoclinic (P2_{1}/n). For each structure, we simulate using the following pairs of W/O pseudopotentials with given exchange-correlation and formulation. This gives nine structure/functional variations.
W.pz-bhs.UPF Perdew-Zunger (LDA) exchange-correlation Bachelet-Hamann-Schlueter and derived O.pz-mt.UPF |
W.pw91-nsp-van.UPF Perdew-Wang 91 gradient-corrected functional nonlinear core-correction semicore state s in valence semicore state p in valence Vanderbilt ultrasoft O.pw91-van_ak.UPF |
74w.14.hgh.UPF translated from 74w.14.hgh (Abinit) Perdew-Wang 92 (LDA) functional Hartwigsen-Goedecker-Hutter (HGH) 8o.6.hgh.UPF translated from 8o.6.hgh (Abinit) |
We begin by determining an sufficiently converged planewave cutoff for a fixed k-grid density and non-optimal geometry
struct/xc, ecut (Ry) | PZ | PW92 | PW91 |
---|---|---|---|
Cubic | 180 | 280 | 260 |
Tetragonal | 220 | 300 | 160 |
Monoclinic | 180 | 300 | 260 |
Using these values for ecut we select k-grid densities compromising between accuracy and performance that are Monkhorst-Pack meshes of dimensions 8x8x8, 6x6x8, and 2x2x2 for the cubic, tetragonal, and monoclinic structures respectively.
We relax the structures using the variable cell (vc-relax) calculation in QE and calculate the band structures of these optimized geometries.
Examining the convergence of total energy as the value of ecut is increased is a basic verification in simulating electronic structure. When this is applied rigorously, insight can be gained to validate and identify problems with simulation parameters.
We begin by validating the translation of the Abinit 8o.6.hgh and 74w.14.hgh pseudopotentials to the Quantum Espresso UPF format. This validation uses the energy_versus_ecut_plot plugin to compare two datasets with simulations varying ecut and comparing the total energy curve. The difference in these datasets is that one is simulating using Abinit with the original HGH pseudopotential files and the other is simulated using QE with the UPF translation files.
This plot shows the two dataset total energy versus ecut curves. Qualitatively they are in fine agreement. The next table gives the numerical values for comparison.
Ecut | E_{QB} | E_{AB} | |dE | |
---|---|---|---|
110 | 0.19237 | 0.19245 | 0.00008 |
120 | 0.13910 | 0.13916 | 0.00006 |
130 | 0.10096 | 0.10101 | 0.00005 |
140 | 0.07297 | 0.07301 | 0.00004 |
150 | 0.05312 | 0.05315 | 0.00003 |
160 | 0.03868 | 0.03870 | 0.00002 |
170 | 0.02811 | 0.02813 | 0.00002 |
180 | 0.02048 | 0.02050 | 0.00002 |
190 | 0.01493 | 0.01494 | 0.00001 |
200 | 0.01086 | 0.01087 | 0.00001 |
210 | 0.00787 | 0.00787 | 0 |
220 | 0.00567 | 0.00567 | 0 |
230 | 0.00405 | 0.00406 | 0.00001 |
240 | 0.00286 | 0.00286 | 0 |
250 | 0.00197 | 0.00198 | 0.00001 |
260 | 0.00133 | 0.00133 | 0 |
270 | 0.00084 | 0.00084 | 0 |
280 | 0.00048 | 0.00047 | 0.00001 |
290 | 0.00020 | 0.00020 | 0 |
300 | 0 | 0 | 0 |
In our ecut parametrization tests on WO_{3} using the PW91 ultrasoft pseudopotential a problem with the convergence in total energy was present in all three structures. We show this result for only the cubic geometry.
Again, using the energy_versus_ecut_plot plugin for an order of magnitude in different values of ecut,
the features of this plot is that while there may be a few local minimum areas in which the difference in total energy between consecutive ecuts may be small; the overall convergence is still not reached.
Another perspective of this result is looking at the stress tensor that is a derivative of the total energy; these plots clearly show oscillation in non-zero stress tensor components.
Functional | Basis | a (Å) | V (Å^{3}/WO_{3}) | gap (eV) |
---|---|---|---|---|
PW92 | PW | 3.78 | 54.01 | 0.58 |
PZ | PW | 3.76 | 53.16 | 0.42 |
PW91 (US) | PW | 3.83 | 56.18 | 0.62 |
EXP | 3.77 | 53.7 | ||
LDA | FP-LMTO | 3.78 | 0.3 | |
PW91 | PW (US) | 3.84 | 56.5 | 0.41 |
Table. Lattice Parameters, Equilibrium Volume, and Band Gap of Simple Cubic WO3
Functional | Basis | a (Å) | c (Å) | V (Å^{3}/WO_{3}) | gap (eV) |
---|---|---|---|---|---|
PW92 | PW | 5.30 | 3.87 | 54.3 | 0.56 |
PZ | PW | 5.22 | 4.00 | 54.5 | 0.46 |
PW91 (US) | PW | 5.36 | 3.98 | 56.3 | 0.61 |
EXP | 5.25 | 3.92 | 54.0 | ||
PW91 | PW (US) | 5.36 | 3.98 | 57.1 | 0.40 |
Table. Lattice Parameters, Equilibrium Volume, and Band Gap of Tetragonal WO3
Functional | Basis | a (Å) | b (Å) | c (Å) | γ (°) | V (Å^{3}/WO_{3}) | gap (eV) |
---|---|---|---|---|---|---|---|
PW92 | PW | 7.38 | 7.60 | 7.43 | 90.2 | 52.05 | 1.29 |
PZ | PW | 7.40 | 7.61 | 7.43 | 90.15 | 52.35 | 1.11 |
PW91 (US) | PW | 7.65 | 7.66 | 7.64 | 90.07 | 56.08 | 1.24 |
EXP | 7.31 | 7.54 | 7.69 | 90.9 | 53.0 | 2.6-3.2 | |
PW91 | PW (US) | 7.50 | 7.73 | 7.80 | 90.3 | 56.5 | 1.35 |
Table. Lattice Parameters, Equilibrium Volume, and Band Gap of Monoclinic WO3
Cubic WO_{3} PW92 |
Cubic WO_{3} PZ |
Cubic WO_{3} PW91 |
Tetragonal WO_{3} PW92 |
Tetragonal WO_{3} PZ |
Tetragonal WO_{3} PW91 |
Monoclinic WO_{3} PW92 |
Monoclinic WO_{3} PZ |
Monoclinic WO_{3} PW91 |
Structure | Short URL |
---|---|
Cubic | http://goo.gl/d5rjI |
Monoclinic | http://goo.gl/2rv2a |
Tetragonal | http://goo.gl/kAIZJ |
Comments
masoud2600
Tue, 02/04/2014 - 07:11
Permalink
dear sir
dear sir
i'm working with wo3 in QE code.but my results especially fermi energy is similar to exprimental resultes.
if u need,i can present my letter to upload this.
*Yours sincerely*
*Masoud Mansouri