# Research

This page discusses my research interests. I also suggest you examine the research posts in the blog (a selection of which are highlighted below), and the papers page, which contains an in-depth look at my research in each specific paper. Over time, additional content will be added to this page.

My research interests primarily relate to molecular electronic structure theory, and its application to studying the spectroscopic properties of molecules. In electronic structure theory, we take only the simplest information about a molecule (basically, a simple schematic representation of a molecule, so can we "draw" it). From this information, we attempt to deduce the observable properties of these molecules. For example, the atomisation energies, ionisation potentials, reaction barrier heights, equilibrium and transition-state structures, bond dissociation energies etc can all be computed from electronic structure theory.

Perhaps more importantly, we can also predict and rationalise the spectroscopic properties of molecules. For example, we are able to compute NMR shielding constants and chemical shifts for any active nuclei, spin-spin coupling constants, IR and Raman vibrational wave numbers and intensities, UV/vis transition energies and intensities, and also luminescence, both fluorescence and phosphorescence, circular dichroism, etc.

Those of you who are familiar with this field of research will be aware of the difficulties associated with electronic structure theory. On one hand, we are, in principle, able to compute all of these properties exactly. Unfortunately, to do so we would require an infinitely powerful computer or an infinite amount of time. Neither of which is particularly practical. In order to make the calculations that underpin our predictions feasible, we have to make approximations.

Our research is primarily concerned with improving these approximations. In particular, we are seeking to improve the approximations available to us so that we can predict emission in technologically relevant molecules that are relevant to OLED design.

A large thread of my research has concerned the understanding and development of methods in density functional theory (DFT), which is a computationally efficient first-principles approach to solving the electronic structure problem. DFT is widely used in both the chemistry and physics communities to study the fundamental properties of molecules and solids.

Problems in theoretical spectroscopy are of particular interest, not least because the accurate evaluation of spectroscopic parameters from first-principles can be particularly demanding; much of my more recent work has been concerned with understanding and remedying problems in the description of excited states.

My research career began with an assessment of the Yanai, Tew and Handy CAM-B3LYP functional. This functional was specifically designed to study the excited states of molecules, by attenuating the amount of exact orbital exchange within a functional (functionals of this type are often referred to as either Coulomb-attenuated or range-separated hybrids). As a follow-up, we conducted a systematic examination of the dependence of this type of functional on the parameters involved.

Our work on excited states continued with a major assessment of the ability of TDDFT to describe the singlet excited states of "difficult" organic molecules, and the introduction of the Lambda diagnostic, which provides a simple mechanism of determining when excitation energies will be poorly predicted in TDDFT due to low-overlap problems, in Excitation energies in DFT: An evaluation and a diagnostic test. This paper has had over 400 citations, and the diagnostic has been implemented in a number of commercial and open-source electronic structure packages.

We later followed this up with work on triplet excited states, and highlighted the issue of "the triplet instability problem" on the accuracy of both triplet and singlet excited states. We proposed a simple mechanism for using the Hartree-Fock triplet stability measures to identify when triplet stabilities would cause large errors in excited states. Following this, we also connected the stability with Lambda, and proposed a new benchmark set against which we can measure the accuracy of TDDFT methods.

Along-side our work in excited states, we have also considered the OEP method and how to accurately compute NMR shielding constants for Coulomb-attenutated functionals, how we can model the adiabatic connection to develop new functionals, the evaluation of the Kohn-Sham kinetic energy from a single molecular orbital, how we can approach the calculation of negative electron affinities using potential walls, together with numerous applications of DFT and TDDFT methods to problems of experimental interest.

Time-dependent density functional theory allows us to consider excited states, and thus to rationalise and predict the absorption and emission spectra (and thus the colour) of molecules. The accuracy with which we can routinely achieve this is usually sufficient to rationalise the absorption spectra of a molecule, but there are significant deficiencies in the method's ability to predict the emission properties of molecules. This is primarily caused by the change in geometry; as we move away from the ground state geometry to an excited state geometry, the accuracy of many electronic structure methods decreases, sometimes catastrophically so. The result can be a completely unphysical picture of a molecule.

The basis of the research programme we are developing at Lancaster aims to redress these problems. If we are able to improve the accuracy of these methods, we will be able to predict, in advance of synthesising and characterising a molecule, what its properties are, and thus we can begin to use theoretical/ computational techniques to design molecules with specific properties.

I am incredibly fortunate that I have had the opportunity to collaborate with some world-leading scientists (in alphabetical order):

Nick Besley | Nottingham |

Aron Cohen | Cambridge |

Frank De Proft | Brussels |

Hardy Gross | MPI Halle |

Nicholas Handy | Cambridge |

Trygve Helgaker | Oslo |

David O'Hagan | St. Andrews |

Kenneth Ruud | Trumsø |

Andy Teale | Nottingham/ Oslo |

David Tozer | Durham |

Gareth Williams | Durham |

Chemistry at Lancaster is a relatively new Department, opening in late 2012, with its first intake of undergraduate students starting in October 2013. As part of our expanding research activities within the Department, Chemical theory and computation (CTC) is becoming a major area of research. We already have three members of academic staff whose research falls into this area, and we are currently seeking to appoint another this year. The university is investing heavily in providing equipment and custom-designed space to support our growing research activities in this area.