Hugh Burton

Recent News

02-03-2022:   Theory Seminar at CFEL-DESY

I enjoyed presenting my latest work on the Energy Landscape of State-Specific Electronic Structure for the theory seminar at the Center for Free-Electron Laser Science, based in Hamburg. It was a great opportunity to discuss the connections with their theoretical simulations on the interaction of molecules with intense x-ray radiation and hear about the amazing experimental advances in x-ray imaging.

18-02-2022:   Energy Landscape of State-Specific Electronic Structure

I am excited to share my latest research looking at the mathematical structure of the exact landscape, which is now out in J. Chem. Theory Comput. On this exact energy landscape, ground and excited electronic states form stationary points constrained to the surface of a hypersphere. We investigate how this exact energy landscape controls the type of excited states that can be found using various wave function approximations. These insights establish a proper theoretical foundation for developing new types of computational methods for exploring excited states in electronic systems.

01-10-2021:   Gabriela and Antoine join the group

A big welcome to Gabriela Oprea who joins the group as a Part II undergraduate research student for the 2021–2022 academic year, and Antoine Marie who joins as a visiting student for five months from ENS Lyon. It's great to have them both in the team and we are excited to see the amazing results of their research.

23-09-2021:   57th Symposium on Theoretical Chemistry

It was great to present my latest work on Electronic Structure as an Energy Landscape at the 57th Symposium on Theoretical Chemistry organised virtually in Würzburg. Despite being another online event, it was a brilliant opportunity to learn more about the exciting research underway throughout Germany, Switzerland, and Austria.

15-07-2021:   Outstanding Thesis Award in Theoretical Chemistry

I am honoured to announce that I have been awarded the 2020 Outstanding Thesis Award in Theoretical Chemistry from the University of Cambridge for my work Holomorphic Hartree–Fock Theory: Moving Beyond the Coulson–Fischer Points. I am incredibly grateful to everyone who helped and inspired me along the way, including my supervisor Dr Alex Thom, the Cambridge theoretical chemisty community, and the Cambridge Trust for their financial support.

12-07-2021:   Yi Sun joins for a Summer Research Project

A big welcome to Yi Sun who joins the group for a six-week undegraduate research project this summer as part of the Hertford College Summer Research Studentship scheme. Yi Sun will be looking at the mathematical properties of finite-temperature perturbation theory in the complex plane.

09-07-2021:   Virtual Visits to the University of Duisburg–Essen and the University of Cardiff

I was delighted to present my latest work on the Energy Landscape of Electronic Structure Theory to the Theoretical Physics Colloquium at the University of Duisburg–Essen (11-06-2021) and the Computational Chemistry Seminar at the University of Cardiff (09-07-2021). It is always great to meet like-minded researchers around the world, especially those in the closely related areas of theoretical physics and applied computational chemistry.

16-04-2021:   Generalised Nonorthogonal Matrix Elements

My latest research on nonorthogonality in quantum chemistry is now out in J. Chem. Phys.. I develop an entirely generalised approach to compute nonorthogonal matrix elements for electronic configurations represented with different sets of orbitals. This work unifies two well-established theories — the generalised Slater–Condon rules and Wick's theorem — to create a universal framework for deriving and evaluating matrix elements in quantum chemistry.

29-03-2021:   Faraday Joint Interest Group Conference 2021

It was an honour to present my PhD research on the development of holomorphic Hartree–Fock and nonorthogonal configuration interaction at the 2021 Faraday Joint Interest Group Conference organised by the Royal Society of Chemistry. As always, it was amazing to get the opportunity to meet with theoretical chemists from across the UK and discuss the latest developments in theoretical, computational, and experimental chemistry.

15-03-2021:   Critical Nuclear Charge in Hartree–Fock Theory

My recent work investigating the ionisation threshold for two-electron atoms using Hartree–Theory has now been published as a Communication in J. Chem. Phys. as part of the 2021 JCP Emerging Investigators Special Collection. This work uses high-accuracy Hartree–Fock calculations in the complete-basis-set limit to identify the nuclear charge at which one of the electrons in a Helium-like atom becomes unbound. I find this critical nuclear charge depends on the type of symmetries that are fixed in the Hartree–Fock wave function. Specifically, the closed-shell restricted Hartree–Fock approximation can bind two electrons to a lower nuclear charge than the unrestricted approximation, but a fractional-spin error becomes increasingly dominant for small nuclear charges. These results emphasise the role of static correlation for weakly-bound negative ions.

19-02-2021:   Perturbation Theory in the Complex Plane

Delighted to share our latest review on understanding the performance of perturbation theory using complex-valued non-Hermitian Hamiltonians, now published in J. Phys.: Condens. Matter. Working with long-time collaborator Pierre-François Loos (Université de Toulouse) and his student Antoine Marie, we investigate how the convergence of electronic perturbation theory is determined by the structure of the ground and excited electronic energy surfaces in the complex plane. Specifically, discrete energy levels become unified as one continuous Riemman surface and are connected by exceptional points that control whether the perturbation series converges or not. Furthermore, we illustrate how these exceptional points can be used to relate the divergence of perturbation theory to the exotic phenomena of quantum phase transitions and electronic symmetry breaking.

17-02-2021:   Virtual Visit to New Brunswick

Enjoyed sharing a combination of my work on holomorphic Hartree Fock, nonorthogonal configuration interaction, and the geometry of electronic structure theory with Stijn De Baerdemacker and his quantum chemistry group at the University of New Brunswick. It was great to meet such an enthusiastic group of theoretical quantum chemists, share ideas on challenging problems, and hear all about the amazing research they are working on.

29-12-2020:   Energy Landscapes for Electronic Structure

Our work on the properties of multiple Hartree-Fock solutions continues. In this paper, now out in J. Chem. Theory Comput., we apply molecular energy landscape methods to explore the minima and saddle points on the Hartree–Fock wave function energy surface. We use the simple H4 model to study the effect of orbital symmetry constraints, basis sets, and molecular structure on the number of HF minima and the index-1 saddles that connect them. The pathways connecting local minima form the orbital analogy of reaction transition states, and show fundamental symmetry conservation rules. Finally, we identify the connectivity between symmetry-pure spin states using the generalised HF wave function, providing the most complete picture of the HF solution space. We expect that our results will create new guiding principles for developing algorithms to locate multiple HF solutions, encouraging their use in mean-field excited state approximations and multi-reference methods.

20-11-2020:   Holomorphic Density Functional Theory

Our project deriving a holomorphic extension to density functional theory (DFT) is now out in J. Chem. Theory Comput. Working with Rhiannon Zarotiadis (now at ETH Zürich), we investigate the existence of multiple solutions in DFT and explore how these are connected to the solutions located using the Hartree–Fock (HF) potential. We find that multiple DFT solutions can coalesce and vanish in exactly the same way as multiple HF solutions. By deriving a holomorphic DFT approach, we show how these DFT solutions can be analytically continued across all molecular geometries or approximate exchange-correlation functionals. This work opens a new frontier in understanding and exploiting multiple DFT solutions to understand chemical processes and describe multi-configurational systems while retaining the computational efficiency of density functional methods.

01-10-2020:   Joining New College, Oxford

I have joined New College, Oxford as the Astor Junior Research Fellow in Chemistry. New College is among the oldest and largest of the colleges that make up the University of Oxford, U.K. In this position, I will be affiliated with the Theoretical Chemistry group in the Department of Chemistry, where I will continue my research into the mathematical breakdown of electronic structure approximations. I hope to bring you many new scientific developments over the upcoming years!

19-08-2020:   Nonorthogonal CI Perturbation Theory

Our work on a second-oder perturbative correction to nonorthogonal configuration interaction (NOCI) is now published in J. Chem. Theory Comput. In this paper, we derive a rigorous second-order perturbation theory that allows dynamic correlation to be captured on top of a statically correlated reference NOCI wave function. Our NOCI-PT2 approach provides the nonorthogonal analogue to CASPT2 and yields quantitative energy surfaces for molecular systems with strong static and dynamic correlation effects. In principle, any set of nonorthogonal Slater determinants can be used to define the reference NOCI wave function, making the approach highly flexible and extendable. We choose to build our NOCI wave functions using multiple Hartree–Fock solutions and make use of the holomorphic Hartree–Fock approach to define smooth and continuous energy surfaces across all molecular geometries.

13-07-2020:   Website Launches

My research website has launched! On this site I will keep you updated with my latest research and scientific developments. I hope you enjoy learning more about my work, and I would be happy to answer any of your questions.