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

The tetragonal to orthorhombic ferroelastic phase transition between rutile- and ${\text{CaCl}}_{2}$-type ${\text{SiO}}_{2}$ at high pressures is studied using first-principles calculations and the Landau free-energy expansion. The phase transition is systematically investigated in terms of characteristic phonon modes with ${\text{B}}_{1g}$ and ${\text{A}}_{g}$ symmetries, shear moduli, transverse-acoustic mode, rotation angle of the ${\text{SiO}}_{6}$ octahedra, spontaneous symmetry-breaking and volume strains, and enthalpy. The results show that these physical behaviors at the transition are well described using the Landau free-energy expansion parametrized by the first-principles calculations.

/pdf/first-principles-calculations-of-the-ferroelastic-transition-4b3qx4ec16.pdf

First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

Energetics and structure of stoichiometric SnO2 surfaces studied by first-principles calculations

It is thought that the Earth's outer core consists mainly of liquid iron and that the convection of this metallic liquid gives rise to the Earth's magnetic field. A full understanding of this convection is hampered, however, by uncertainty regarding the viscosity of theouter core. Viscosity estimates from various sources span no less than 12 orders of magnitude1,2, and it seems unlikely that thisuncertainty will be substantially reduced by experimental measurements in the near future. Here we present dynamical first-principles simulations of liquid iron which indicate that the viscosity of iron at core temperatures and pressures is at the low end of the range of previous estimates — roughly 10 times that of typical liquid metals at ambient pressure. This estimate supports the approximation commonly made in magnetohydrodynamic models that the outer core is an inviscid fluid3,4,5 undergoing small-scale circulation and turbulent convection6, rather than large-scale global circulation.

The viscosity of liquid iron at the physical conditions of the Earth's core

The adsorption of H2O on TiO2 and SnO2(110) studied by first-principles calculations

First-principles molecular-dynamics simulations based on density-functional theory and the projector augmented wave (PAW) technique have been used to study the structural and dynamical properties of liquid iron under Earth's core conditions. As evidence for the accuracy of the techniques, we present PAW results for a range of solid-state properties of low- and high-pressure iron, and compare them with experimental values and the results of other first-principles calculations. In the liquid-state simulations, we address particular effort to the study of finite-size effects, Brillouin-zone sampling, and other sources of technical error. Results for the radial distribution function, the diffusion coefficient, and the shear viscosity are presented for a wide range of thermodynamic states relevant to the Earth's core. Throughout this range, liquid iron is a close-packed simple liquid with a diffusion coefficient and viscosity similar to those of typical simple liquids under ambient conditions.

/pdf/structure-and-dynamics-of-liquid-iron-under-earth-s-core-3miya9ebf1.pdf

Structure and dynamics of liquid iron under Earth’s core conditions

First-principles calculations based on density–functional theory and pseudopotentials are used to calculate the energies and relaxed structures of five low-index surfaces of α-alumina. Evidence for the reliability of the theoretical methods is provided by calculations of the lattice parameters and internal coordinates of the perfect crystal, which agree very closely with experimental data. It is shown that, for some of the surfaces, relaxation effects reduce the surface energy by over a factor of two and lead to major changes of surface structure, with particularly large effects being found for the (0001) and (1010) surfaces. Results are also presented for the distribution of valence electron charge in the surface region. These results suggest that α-alumina is highly ionic even for ions at the surface.

M. J. Gillan

Papers

Energetics and structure of stoichiometric SnO2 surfaces studied by first-principles calculations

The viscosity of liquid iron at the physical conditions of the Earth's core

The adsorption of H2O on TiO2 and SnO2(110) studied by first-principles calculations

Structure and dynamics of liquid iron under Earth’s core conditions

Structure and Energetics of Alumina Surfaces Calculated from First Principles