# Electronic Structure

Principal investigators

We hold regular Electronic Structure Discussion Groups.

**Electronic structure research in TCM focuses on understanding
the behaviour of solids and liquids using quantum mechanics, through
so-called "first-principles" methods.**

First-principles methods take a fully quantum-mechanical view of electronic structure – treating a system at the level of individual electrons and nuclei – without fitting to experimental data. A leading approach to electronic structure along these lines is density-functional theory (DFT), which is used widely in TCM. DFT has provided scientists both in academia and industry with an unprecedented ability to probe a diverse range of systems, and the ability to make accurate first-principles predictions of a wide range of physical and chemical properties.

Beyond DFT, our research focuses on:

- developing new first-principles methods with greater accuracy (such as Quantum Monte Carlo), and applicability to strongly correlated systems
- developing new methods which allow the wider application of DFT (such as linear-scaling methods for DFT, first-principles molecular dynamics, and time-dependent DFT for non-adiabatic problems);
- creating methods for predicting experimental spectra (like NMR chemical shieldings and EELS spectra);
- developing methods based on first-principles techniques which allow us to predict the
atomic structure of materials (such as
*ab initio*random structure searching - AIRSS).

We are interested in applications of these methodologies in physics, biology, chemistry and materials science. Our recent successes include: the discovery of high-pressure phases of hydrogen and helium, insights into proteins, nano-crystals, alloy coatings, radiation damage, lithium ion battery anodes and point defects in cathodes, solvents, and water as both a liquid and a high-pressure solid.

TCM's electronic structure researchers hold regular fortnightly meetings at the Electronic Structure Discussion Group (ESDG) during term.

## Electronic structure codes

Members of TCM have been involved in developing a number of electronic structure codes in aid of their research:

- CASINO, a quantum monte carlo code
- CASTEP, a leading planewave pseudopotential DFT code
- ONETEP, a linear-scaling DFT code
- OptaDOS, for the calculation of high-quality theoretical DOS
- SIESTA, a DFT code employing atomic orbitals

## Density-functional theory in TCM

In quantum mechanics, the state of a system of *N* particles is described
by a many-body wave function. The full 3*N*-dimensional wavefunction is in general
a computationally intractable object for all but the smallest of systems. DFT, on the
other hand, harnesses techniques to calculate the electron density, a more computationally
feasible target. Our understanding of many atomic scale processes in the physical
sciences has been transformed by quantum mechanical simulations such as DFT.

The leading CASTEP code, which implements Kohn-Sham DFT using planewave basis sets and pseudopotentials, was first developed in TCM and continues to be expanded and updated by members of the group. More recent research in first-principles methods has focussed on linear-scaling DFT. Using the ONETEP (first produced in TCM) and SIESTA codes which are actively maintained by members of TCM, quantum mechanical calculations on systems containing many thousands of atoms are now possible. Applications are found in numerous biological and nano-material systems of ever-increasing size, for example in probing enzyme activity, and GaAs nanorods.

## First-principles method development

New first-principles method development is an endeavour which bridges condensed matter physics with other fields of science and technology; the new methods make use of novel approaches within condensed matter theory to expand the applicability of first-principles simulation methods in many fields. New methods being developed by members of TCM incude:

### Techniques for crystal structure prediction

It is very difficult to "see" the structure of materials over the
length scales that they work and very expensive to create prototype
materials. The theoretical prediction of even very simple structures
has, until recently, been out of bounds due to the huge number of
possible atomic arrangements. The
*ab initio* random structure searching method (AIRSS), first developed in TCM, uses a
stochastic approach to suggest different structural configurations
of atoms within a material. AIRSS has seen an enormous number of applications,
such as in
prototyping materials for battery design,
exploring
high pressure
phases of hydrogen and
planetary mantle materials, and in
defects in solids.

### Methods for calculating the anharmonic vibrational properties of solids

For systems at high temperature, in phase transitions, or with weak bonding, light atoms or in low dimensional systems, anharmonic vibrations can be significant and need to be taken into account to make accurate predictions. We have developed new approaches for including the effects of anharmonicity in first-principles calculations, and applied these techniques to study, for example, the relative stabilities of hexagonal and cubic ice. In this system, anharmonic effects have a considerable impact on calculated properties.

Now, techniques are emerging that allow us to sample the complex configuration spaces of biological molecules. Together, these methodologies will bring us to the beginning of the era of quantum mechanical prediction of biological function. For example, recent work has shown how many-body effects in the iron atom at the centre of haemoglobin allow it to transport oxygen through the bloodstream without being poisoned by carbon monoxide. Equally, nanomaterials offer us exciting new ways to control material properties, by varying material attributes which are not available in bulk systems. For example, in nano-crystals, growth conditions can be tuned to vary particle size, shape, surface terminations, composition and defect structure. Nanomaterials are thus the key to making a success of many emerging technologies. In order to both interpret experiments and to match our predicted structures to the real world, we develop techniques for predicting spectroscopic data from first-principles (such as NMR chemical shieldings and EELS spectra) using the CASTEP, OptaDOS and ONETEP codes that we develop.

## Quantum Monte Carlo in TCM

Beyond DFT, Quantum Monte Carlo offers an alternative and efficient approach which accurately describes the interactions between particles. Used in combination with other less-computationally expensive methods, it provides researchers with the final building block in an atomic scale micro-laboratory on their computer which can be used to simulate small parts of the real world. In the early 1990s, a project was initiated by TCM members to create a general-purpose QMC code. The result is the world-leading CASINO QMC code, which continues to be actively developed and maintained by former members of TCM.

## Current research topics in the group include:

- materials design and discovery (Conduit, Needs)
- crystal structure prediction through random sampling (AIRSS) (Needs)
- quantum monte carlo studies of systems (Conduit, Needs)
- vibrational properties of solids (Monserrat, Needs)
- pseudopotential development: ultracold atoms, dipolar interactions, correlated electron pseudopotentials (Conduit, Needs)
- electronic properties of superconductors through DFT (Artacho, Monserrat, Needs)
- linear-scaling DFT (Payne)
- topological materials (Monserrat)