First-principles simulation, meaning density-functional theory calculations with plane waves and pseudopotentials, has become a prized technique in condensed-matter theory. Here I look at the basics of the suject, give a brief review of the theory, examining the strengths and weaknesses of its implementation, and illustrating some of the ways simulators approach problems through a small case study. I also discuss why and how modern software design methods have been used in writing a completely new modular version of the CASTEP code.

https://iopscience.iop.org/article/10.1088/0953-8984/14/11/301/pdf

First-principles simulation: ideas, illustrations and the CASTEP code

The surface science of titanium dioxide

TiO2 photocatalysis and related surface phenomena

A surface science perspective on TiO2 photocatalysis

Oxygen vacancies in transition metal and rare earth oxides: Current state of understanding and remaining challenges

We present self-consistent ab initio total-energy calculations of the equilibrium relaxed structures and surface energies of the stoichiometric (1\ifmmode\times\else\texttimes\fi{}1) (110), (100), (001), and (011) surfaces of ${\mathrm{TiO}}_{2}$. The relaxations of atoms on these surfaces are found to be substantial, and are responsible for a large reduction of the calculated surface energies. A Wulff construction is used to display the relative energetics of these surfaces. The (100) surface is found to be stable with respect to forming macroscpic (110) facets, while the (001) surface is nearly unstable with respect to forming macroscopic (1\ifmmode\times\else\texttimes\fi{}1) (011) facets. These results shed light on published experimental results on the structures of these surfaces.

First-principles calculations of the energetics of stoichiometric TiO2 surfaces.

We present self-consistent ab initio total-energy calculations on ${\mathrm{TiO}}_{2}$ (110) surfaces for which the atomic geometry has been relaxed to equilibrium. For stoichiometric supercells we find no surface states in the bulk band gap, in accord with experiment. Oxygen vacancies on the surface give rise to Ti 3d-like surface states at the edge of the bulk conduction band. The relaxations of the atoms at the surface were found to be substantial, and those induced by a vacancy were localized in its vicinity. Bulk vacancies introduce states about 0.3 eV below the edge of the bulk conduction band.

Madhavan Ramamoorthy

Papers

First-principles calculations of the energetics of stoichiometric TiO2 surfaces.

Defects on TiO2 (110) surfaces.