Crystal Structure:

CIF Source:
Acta Crystallographica B47 (1991) 462-468
Structural and thermal parameters for rutile and anatase
Locality: synthetic
_database_code_amcsd 0019093
http://rruff.geo.arizona.edu/AMS/CIF_text_files/11272_cif.txt

Simulated Powder XRD using VESTA:

X-Ray Wavelength: 1.54059 Angstrom

Simulation 1: GGA

Pseudopotential Used:
Ti.pbe-spn-rrkjus_psl.1.0.0.UPF
O.pbe-nl-rrkjus_psl.1.0.0.UPF

PP Type: Ultrasoft
Exchange Correlation Functional: PBE-GGA
Non-linear core corrections are used.

Total Energy vs Cutoff:

E-Cutoff(Ry)    Total E(Ry)

10                  -674.97884493
15                  -720.42529095
20                  -733.86047790
25                  -738.17214180
30                  -739.43060835
35                  -739.70149419
40                  -739.75957365
45                  -739.77545989
50                  -739.78366106
54                  -739.78915969
55                  -739.79040617
56                  -739.79157928
60                  -739.79553659
62                  -739.79708585

Wavefunction Energy Cutoff: 54 Ry
Charge Density Energy Cutoff: 600 Ry
k – mesh: 8x8x8
Run Type: GGA-PBE

Optimized Coordinates and Lattice Parameters:

Lattice Parameters: a= b= 3.80034 A, c= 9.70793 A
alpha=beta=gamma=90 degrees

ATOMIC_POSITIONS {angstrom}
Ti 0.000000   0.000000   0.000000
Ti 1.900170   1.900170   4.853964
Ti 0.000000   1.900170   2.426988
Ti 1.900170   0.000000   7.280940
O 0.000000   0.000000   2.005006
O 1.900170   1.900170   6.858963
O 0.000000   1.900170   4.431988
O 1.900170   0.000000   9.285942
O 1.900170   1.900170   2.848965
O 0.000000   0.000000   7.702922
O 1.900170   0.000000   5.275940
O 0.000000   1.900170   0.421986

Bandstructure:

High Symmetry points: G-X-M-G-Z-R-A-Z (Brillouin Zone integration along these points)

Density of States(DOS):

Input Files:

TiO2 Anatase Input Files

Simulation 2: GGA + U(Hubbard Correction)

The Hubbard parameter provides on-site Coulomb corrections to the highly localized electrons.
It can usually be determined by the linear response approach.

Variation of Band Gap with Hubbard Parameter U:

using simplified version of Cococcioni and de Gironcoli, PRB 71, 035105 (2005), using Hubbard_U

U(eV)        Band-Gap(eV)
1                2.2182
2                2.2974
3                2.3862
4                2.4892
5                2.6094
6                2.7540
7                2.9287
8                3.1443
9                3.4117

Therefore, the rest of the calculations will be run using U=8eV:
(NOTE: Just because U=8eV provided a good picture of the band-gap doesn’t mean that it will provide a good picture for all other properties. Such a high correction can change other properties and therefore, the parameter should be suitably determined. For more info read the article attached in the References section of this article.)

Bandstructure:

Density of States(DOS):

Input Files:

TiO2 Anatase Input Files

Acknowledgements:

I acknowledge the use of the following tools and packages in order to produce the above simulations.
Quantum Espresso(for DFT based simulations): http://www.quantum-espresso.org/
BURAI(for visualization and as a GUI for QE): http://nisihara.wixsite.com/burai
VESTA(for visualization and XRD simulations): http://jp-minerals.org/vesta/en/

References and Resources:

https://www.researchgate.net/publication/51554133_DFT_U_Calculations_of_Crystal_Lattice_Electronic_Structure_and_Phase_Stability_under_Pressure_of_TiO2_Polymorphs