## Overview

The simulation of materials has an important role to play both in understanding and interpreting experiment. Ideally, simulation would also be used to predict properties of materials, study materials under conditions which would be hard or impossible to recreate in a lab, or even discover new materials. Using computers to make predictions in this way drastically reduces the time and cost needed to develop and improve devices such as organic LEDs which are used in smartphone screens and TVs.

In order to make predictions, we need methods which doesn’t rely on experimental input, which are referred to as first principles or *ab initio* methods. In order to study realistic materials we have to make various approximations which are physical (approximations to the equations we want to solve) or numerical (how precisely we can solve the equations). When deciding which method to use the most important factors are therefore accuracy (how these approximations impact predictability), and computational cost (how much time a simulation will take). The most popular first principles approach is density functional theory (DFT), because of its balance between accuracy and computational efficiency.

In our group we develop new methods, primarily based on DFT, which aim to improve the accuracy by controlling or reducing the approximations made, and reduce the computational cost by using supercomputers more effectively. These methods include linear-scaling and multi-scale approaches which allow the simulation of thousands of atoms and therefore open up new possibilities for simulating complex materials. We develop various DFT codes in our group, and use these and others to simulate diverse materials ranging from molecular systems to nanostructures to solids.

## Codes we Develop

BigDFT is an open-source DFT code which uses a wavelet basis set and is designed to efficiently exploit supercomputers. As well as a conventional cubic-scaling approach, linear-scaling and fragment approaches are also implemented, allowing the treatment of systems containing tens of thousands of atoms.

ONETEP is a linear-scaling DFT code which uses a set of localized orbitals that are adapted to the local chemical environment within a given material. These orbitals are exploited to overcome the cubic-scaling limit of conventional DFT implementations, while maintaining a high level of accuracy.

MADNESS (Multiresolution ADaptive Numerical Environment for Scientific Simulation) is a general purpose numerical framework which combines a multiresolution approach with a parallel programming environment designed for petascale performance. There are a number of applications which use MADNESS, including a molecular DFT code.

## Wavelets and Density Functional Theory

For more information about some of the applications of (multi-)wavelets in density functional theory, see this tutorial I gave at the *KOSMOS Workshop on Numerical Methods in Quantum Chemistry* in Berlin in July 2018.