Case Study: Tungsten Oxide (Quantum Espresso)

Introduction

We study three structures of tungsten oxide (WO3) 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 WO3 we consider are: simple cubic (space group Pm-3m), tetragonal (P4/nmm), and monoclinic (P21/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
Perdew-Zunger (LDA) exchange-correlation
Martins-Troullier

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
Perdew-Wang 91 gradient-corrected functional
Vanderbilt ultrasoft

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)
Perdew-Wang 92 (LDA) functional
Hartwigsen-Goedecker-Hutter (HGH)

Methods

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.

Results

Ecut Parametrization

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 EQB EAB |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 WO3 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.

Lattice Parameters

Functional Basis a (Å) V (Å3/WO3) 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 (Å3/WO3) 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 (Å3/WO3) 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

Band Structures

Cubic WO3 PW92
Cubic WO3 PZ
Cubic WO3 PW91
Tetragonal WO3 PW92
Tetragonal WO3 PZ
Tetragonal WO3 PW91
Monoclinic WO3 PW92
Monoclinic WO3 PZ
Monoclinic WO3 PW91

References

  1. Fenggong Wang, Cristiana Di Valentin, and Gianfranco Pacchioni. Electronic and structural properties of wo3: A systematic hybrid dft study. The Journal of Physical Chemistry C, 115(16):8345–8353, 2011.
    http://pubs.acs.org/doi/abs/10.1021/jp201057m

Data Links

Structure Short URL
Cubic http://goo.gl/d5rjI
Monoclinic http://goo.gl/2rv2a
Tetragonal http://goo.gl/kAIZJ

Comments

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