Our research group focusses on developing new methods in electronic-structure theory. Understanding how electrons interact in molecules and materials is fundamental to understanding their chemical properties and reactivity.

## Extended Density-Functional Theories

#### Current-Density-Functional Theory

When a molecule is subjected to an external magnetic field, a situation commonplace in spectroscopic measurements and in practical devices, the standard formulation of DFT does not apply. In this case the universal density functional should depend on both charge-density *and* current-density.

New approximations for the exchange-correlation energy in weak to ultra-strong fields are required. We have shown how extended meta-GGA functionals can provide high accuracy results at relatively low cost in this regime. Functionals including current-dependence are now available at all rungs of Jacob’s ladder.

#### Orbital-Free Density-Functional Theory

Orbital-free density functional theory offers the potential to be the most efficient quantum mechanical simulation tool available. However, description of the kinetic energy (KE) of the electrons in terms of the electron density has been the pursuit of theoreticians since the 1920s.

Our work explores the properties of the KE functional, using tools based on highly accurate ab initio methods. In addition we have recently developed a very robust optimization approach for all-electron OF-DFT calculations — allowing use to further interrogate, develop and test new KE functionals.

## Ground-State Electronic Structure Methods

Our in-house program QUEST provides a wide range of electronic structure theories for calculating the ground state energies and properties of molecular systems. All of the methods implemented can be applied with either standard Gaussian basis sets or using London atomic orbitals to allow for studies in the presence of strong external electromagnetic fields. Density-fitting techniques may be used throughout to accelerate calculations.

#### Density Functional Approaches

- (Current)-Density-Functional Theory at LDA / GGA / mGGA / hybrid /range-separated hybrid / double-hybrid levels
- Orbital-Free Density-Functional Theory
- Optimized Effective Potential based Density-Functional Theory

#### Correlated Wavefunction Theories

- Møller-Plesset Theory: MP2, MP3
- Random Phase Approximation Techniques: dRPA, RPA, SOSEX
- Coupled Cluster Theory: drCCD, rCDD, CCD, CCSD, CCSD(T)

## Excited State Methods

QUEST also supports a broad range of approaches for calculating excitation energies in molecular systems and properties of excited states using .

- Linear Response Methods: TDA, RPA
- GW Theory: G
_{0}W_{0}, evGW, sc-evGW - Real-Time Electronic Structure Methods: RT-TD(C)DFT, RT-TDHF

## Using ab initio methods to Guide Density-Functional Theory

A challenge for density functional methods is the need to better understand the universal density functional F[rho]. Particularly the exchange-correlation component Exc[rho] but also the kinetic component T[rho]. To address this challenge QUEST includes a number of techniques to use highly accurate *ab initio* methods to study the density-functionals to high accuracy

- Constrained Search Methods
- The Lieb Variation Principle
- Adiabatic Connection Methods

## Molecular Properties and Spectroscopy

Our group has a long standing interest in magnetic response properties, such as

- Rotational g-tensors
- Magnetisabilities and Hyper-Magnetisabilities
- Spin-Rotation Constants
- NMR Shielding constants

Our work has provided benchmark data for testing electronic structure methods, improved density-functional approaches for calculating these properties and novel methods for related non-linear magnetic properties.

Recently our work on real-time approaches has allowed us to access electronic absorption, electronic circular dichroism and magnetic circular dichroism spectra both under standard conditions and in the presence of strong external electromagnetic fields.

## Embedded Fragment Methods

To study the effects of strong fields on molecular clusters and molecules inside such clusters we have constructed an embedded fragment approach using London atomic orbital based electronic structure methods.

This gives access to calculations on system sizes far beyond the reach of the constituent methods and and can be applied at the HF, DFT, Møller-Plesset and Coupled-Cluster levels in QUEST.

## Visualization

Recently we have developed a tool, *QMole*, which can render 3D visualisations of quantities such as the electron density, current-density, molecular orbitals etc. as well as quantities like the electron-localisation function.

These developments are powered by the Plotly package and provide user-firendly html outputs that can be opened in any browser. A recent example of a stagnation plot, which depicts lines separating vortices in the current vector field is shown below. The plots are interactive, allowing the user to zoom in and pan to examine details. Clicking on a particular type of point in the legend toggles whether is is shown in the plot.