Matthew J. P. Hodgson- Doctor of Philosophy
- Lecturer at University of York
Matthew J. P. Hodgson
- Doctor of Philosophy
- Lecturer at University of York
Developing reliable density-functional based methods for calculating electron excitation properties.
About
54
Publications
6,646
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461
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Introduction
My research focuses on the fundamentals of quantum theory and its application to modelling the electron excitation properties of materials. My research contributions include the authorship of the iDEA code, a comprehensive Python software library for exploring and understanding many‑body quantum mechanics, fundamental insights into the calculation of excited electron states with density functional theory, and the development of a method for accurately simulating many‑electron real‑time dynamics.
Current institution
Additional affiliations
November 2019 - August 2021
Position
- Researcher
Description
- I was a visiting researcher in the group of Dr Nikitas Gidopoulos. Together we worked on developing efficient methods for calculating electron excitation energies using density functional theory. I published six articles in leading scientific journals during my time at Durham, including my first solo-author publication.
November 2016 - August 2019
Position
- Researcher
Description
- As a researcher at the Max Planck Institute, I had the opportunity to work independently and in collaboration with Prof. Eberhard Gross on electron excitation within many-body quantum theory. Our efforts resulted in fundamental insights into the calculation of exact excited electron states within density functional theory (DFT). I also proposed a novel method for accurately and efficiently simulating electron currents in molecular junctions using time-dependent DFT.
Education
October 2012 - October 2016
October 2008 - October 2012
Publications
Publications (54)
We introduce a new functional for simulating ground-state and time-dependent
electronic systems within density-functional theory. The functional combines an
expression for the exact Kohn-Sham (KS) potential in the limit of complete
electron localization with a measure of the actual localization. We find
accurate self-consistent charge densities, ev...
Knowledge of exact properties of the exchange-correlation (xc) functional is important for improving the approximations made within density functional theory. Features such as steps in the exact xc potential are known to be necessary for yielding accurate densities, yet little is understood regarding their shape, magnitude and location. We use syst...
The local density approximation (LDA) constructed through quantum Monte Carlo calculations of the homogeneous electron gas (HEG) is the most common approximation to the exchange-correlation functional in density functional theory. We introduce an alternative set of LDAs constructed from slab-like systems of one, two and three electrons that resembl...
By propagating the many-body Schrödinger equation, we determine the exact time-dependent Kohn-Sham potential for a system of strongly correlated electrons which undergo field-induced tunneling. Numerous features are entirely absent from the approximations commonly used in time-dependent density-functional theory. The self-interaction correction is...
We obtain the exact Kohn-Sham potentials V_KS of time-dependent density-functional theory for 1D Hubbard chains, driven by a d.c. external
field, using the time-dependent electron density and current density obtained from exact many-body time-evolution. The exact V_xc is compared to the adiabatically-exact V_xc^ad and the "instantaneous
ground stat...
CCP9 connects several UK research groups and facilitates UK participation in other European networks. My talk at the 2022 conference, "Should discontinuities in the Kohn-Sham potential be avoided or exploited?", discussed the origin of the infamous discontinuous features of the exact Kohn-Sham potential and what modern techniques can be used to cap...
I was invited by Nankai University, China to present at their online symposium "Modern Techniques in Theory and Calculation". My talk "Should discontinuities in the Kohn-Sham potential be avoided or exploited?" discusses the origin of the infamous discontinuous features of the exact Kohn-Sham potential and what modern techniques can be used to capt...
Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of particles. As such, they are unable to reproduce some crucial and fundamental aspects, such as the explicit depe...
Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of particles. As such, they are unable to reproduce some crucial and fundamental aspects, such as the explicit depe...
Popular approximations to the exchange-correlation (xc) energy of density functional theory do not yield the spatial `step' structures in the exact xc potential which are necessary to describe dissociation and electron excitation with the Kohn-Sham (KS) system. Via the discontinuity in the derivative of the xc energy as a function of electron numbe...
Accurately describing excited states within Kohn–Sham (KS) density functional theory (DFT), particularly those which induce ionization and charge transfer, remains a great challenge. Common exchange-correlation (xc) approximations are unreliable for excited states owing, in part, to the absence of a derivative discontinuity in the xc energy (Δ), wh...
I find the analytic solutions to the time-dependent Schrödinger equation for the one-dimensional quantum harmonic oscillator which is perturbed by a uniform electric field.
Capturing the discontinuous shift by ∆ in the exact exchange-correlation (xc) potential is the standard proposal for calculating the fundamental gap, Eg, from the Kohn-Sham (KS) gap, εg, within KS density functional theory (DFT), as Eg = εg + ∆, yet this discontinuity is absent from existing approximations. The 'N-centered' formulation of ensemble...
Capturing the discontinuous shift by $\Delta$ in the exact exchange-correlation (xc) potential is the standard proposal for calculating the fundamental gap, $E_\mathrm{g}$, from the Kohn-Sham (KS) gap, $\varepsilon_\mathrm{g}$, within KS density functional theory (DFT), as $E_\mathrm{g} = \varepsilon_\mathrm{g} + \Delta$, yet this discontinuity is...
Accurately describing excited states within Kohn-Sham (KS) density functional theory (DFT), particularly those which induce ionization and charge transfer, remains a great challenge. Common exchange-correlation (xc) approximations are unreliable for excited states owing, in part, to the absence of a derivative discontinuity in the xc energy (∆), wh...
We review and expand on our work to impose constraints on the effective Kohn Sham (KS) potential of local and semi-local density functional approximations. In this work, we relax a previously imposed positivity constraint, which increased the computational cost and we find that it is safe to do so, except in systems with very few electrons. The con...
We review and expand on our work to impose constraints on the effective Kohn Sham (KS) potential of local and semi-local density functional approximations. In this work, we relax a previously imposed positivity constraint, which increased the computational cost and we find that it is safe to do so, except in systems with very few electrons. The con...
The exact static and time-dependent Kohn-Sham (KS) exchange-correlation potential is extremely challenging to approximate as it is a local multiplicative potential that depends on the electron density everywhere in the system. The KS approach can be generalized by allowing part of the potential to be spatially nonlocal. We take this nonlocal part t...
The exact static and time-dependent Kohn-Sham (KS) exchange-correlation potential is extremely challenging to approximate as it is a local multiplicative potential that depends on the electron density everywhere in the system. The KS approach can be generalized by allowing part of the potential to be spatially nonlocal. We take this nonlocal part t...
Watch on YouTube: https://www.youtube.com/watch?v=JaSVguMFA-M
The European Theoretical Spectroscopy Facility (ETSF) Young Researchers' Meeting (YRM) is held annually for scientists with non-permanent positions. I attended the conference this year, 2019, in San Sebastián, Spain.
Reprinted with permission from M. J. P. Hodgson et al. J. Phys. Chem. Lett., 2017, 8, pp 5974-5980. Copyright 2017 American Chemical...
This year, 2019, I gave a talk at the Hebrew University of Jerusalem. The workshop was focused on the exact factorisation theory which offers way to go beyond the Born-Oppenheimer approximation within electronic structure prediction. I was invited along with other speakers to attend the workshop and present my work with the aim of developing collab...
The self-screening error in electronic structure theory is the part of the self-interaction error that would remain within the GW approximation if the exact dynamically screened Coulomb interaction W were used, causing each electron to artificially screen its own presence. This introduces error into the electron density and ionization potential. We...
For properties of interacting electron systems, Kohn-Sham (KS) theory is often favored over many-body perturbation theory (MBPT), owing to its low computational cost. However, the exact KS potential can be challenging to approximate, for example in the presence of localized subsystems where the exact potential is known to exhibit pathological featu...
In this poster we present a detailed look at the connection between the interatomic step in the Kohn-Sham (KS) potential, which forms to correctly distribute charge throughout complex systems, and the derivative discontinuity which manifests in the KS potential as a "jump" by a constant shift as the number of electrons in the system infinitesimally...
For properties of interacting electron systems, Kohn-Sham (KS) theory is often favored over many-body perturbation theory (MBPT) owing to its low computational cost. However, the exact KS potential can be challenging to approximate, for example in the presence of localized subsystems where the exact potential is known to exhibit pathological featur...
We assess the accuracy of the electron density obtained from various flavours of the GW approximation for one-dimensional finite systems consisting of few electrons for which the many-electron Schrödinger equation can be solved exactly. We find that the density and ionisation potential is adversely effected by the self-screening error, which is the...
This talk was given at the Young Researchers' Meeting in Hamburg, Germany 2018. The talk presents our work on the self-screening error in GW and its correction. The self-screening error in electronic structure theory is the part of the self-interaction error that would remain within the GW approximation if the exact dynamically screened Coulomb int...
We evaluate the accuracy of electron densities and quasiparticle energy gaps given by hybrid functionals by directly comparing these to the exact quantities obtained from solving the many-electron Schrodinger equation. We determine the admixture of Hartree-Fock exchange to approximate exchange-correlation in our hybrid functional via one of several...
We evaluate the accuracy of electron densities and quasiparticle energy gaps given by hybrid functionals by directly comparing these to the exact quantities obtained from solving the many-electron Schrödinger equation. We determine the admixture of Hartree-Fock exchange to approximate exchange-correlation in our hybrid functional via one of several...
We evaluate the accuracy of electron densities and quasiparticle energy gaps given by hybrid functionals by directly comparing these to the exact quantities obtained from solving the many-electron Schrodinger equation. We determine the admixture of Hartree-Fock exchange to approximate exchange-correlation in our hybrid functional via one of several...
An accurate approximation to the exchange-correlation (xc) part of the Kohn-Sham (KS) potential is essential for any density-functional calculation. Density-functional theory (DFT) is widely used in condensed matter physics, quantum chemistry and many other fields. Therefore, understanding the behaviour of the exact xc potential and developing impr...
The self-screening error in electronic structure theory is the part of the self-interaction error that would remain within the GW approximation if the exact dynamically screened Coulomb interaction W were used, causing each electron to artificially screen its own presence. This introduces error into the electron density and ionization potential. We...
The self-screening error in electronic structure theory is the part of the self-interaction error that would remain within the GW approximation if the exact dynamically screened Coulomb interaction, W, were used, causing each electron to artificially screen its own presence. This introduces error into the electron density and ionization potential....
The self-screening error in electronic structure theory is the part of the self-interaction error that would remain within the $GW$ approximation if the exact dynamically screened Coulomb interaction, $W$, were used, causing each electron to artificially screen its own presence. This introduces error into the electron density and ionization potenti...
The most direct signature of electron localisation is the tendency of an electron in a many-body system to exclude other same-spin electrons from its vicinity. By applying this concept directly to the exact many-body wavefunction, we find that localisation can vary considerably between different ground-state systems, and can also be strongly disrup...
Accurate density-functional calculations hinge on reliable approximations to the unknown exchange-correlation (xc) potential. The most popular approximations usually lack features of the exact xc potential that are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. Two principal features i...
The major goal of time-dependent density-functional theory (TDDFT) is to predict the time-evolution of the density as a system responds to a perturbation. The objective is to create a family of systems that have a current density that is driven almost entirely by electron-electron interaction, allowing us to discriminate among different TDDFT appro...
The reliability of density-functional calculations hinges on accurately approximating the unknown exchange-correlation (xc) potential. Common (semi-)local xc approximations lack the jump experienced by the exact xc potential as the number of electrons infinitesimally surpasses an integer, and the spatial steps that form in the potential as a result...
The self-screening error in electronic structure theory is the part of the self-interaction error that would remain within the GW approximation if the exact dynamically screened Coulomb interaction W were used, causing each electron to artificially screen its own presence. This introduces error into the electron density and ionization potential. We...
One of the major goals of the GW method is to improve the accuracy
of charge densities produced by density functional theory (DFT). In
this work we test the applicability of one-shot GW from various DFT
starting Kohn-Sham orbitals. Also we implement and test the fully self-
consistent GW method. We test the applicability of these methods by
using t...
Accurate density functional calculations hinge on reliable approximations to the unknown exchange-correlation (xc) potential. The most popular approximations usually lack features of the exact xc potential that are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. Two principal features i...
The local density approximation (LDA) constructed through quantum Monte Carlo calculations of the homogeneous electron gas (HEG) is the most common approximation to the exchange-correlation functional in density functional theory. We introduce an alternative set of LDAs constructed from slablike systems of one, two and three electrons that resemble...
For calculating the properties of solids and molecules, density functional theory (DFT) has become extremely popular because of its inherent computational efficiency. However, despite being in principle exact, an approximation must be introduced into DFT in practice. The accuracy of DFT has been key to its popularity; however, even for some of the...
Knowledge of exact properties of the exchange-correlation (xc) functional is important for improving the approximations made within density functional theory. Features such as steps in the exact xc potential are known to be necessary for yielding accurate densities, yet little is understood regarding their shape, magnitude and location. We use syst...
Knowledge of exact properties of the exchange-correlation (xc) functional is important for improving the approximations made within density functional theory. Features such as steps in the exact xc potential are known to be necessary for yielding accurate densities, yet little is understood regarding their shape, magnitude, and location. We use sys...
Density functional theory, in the Kohn-Sham (KS) approach, is widely used in quantum chemistry and solid state physics. Nonlocal ‘steps’ in the KS potential are crucial in certain circumstances for accurate electron densities. However, the commonly used approximations cannot give step features in the KS potential, and little about steps is understo...
Electron localization is the tendency of an electron in a many-body system to exclude other electrons from its vicinity. Using a new natural measure of localization based on the exact many-electron wavefunction, we find that localization can vary considerably between different ground-state systems, and can also be strongly disrupted, as a function...
The focus of the talk was the search for more accurate approximations of the exchange-correlation (xc) functional, used within time-dependent density functional theory (TDDFT). Our group has developed a new approach to approximate density functionals which reproduces important features, present in the exact xc potential, which are currently missing...
We propose a new approach to developing approximate density functionals which mixes the known analytic form of the exact density functional for a completely localised electron with the xc potential which favours delocalised electrons based on the degree of actual localisation in the system at a given point in space and time – we term this the 'mixe...
