A topological approach to electron correlation in density-functional theories

Projektinformationen

topDFT

ID Finanzhilfevereinbarung: 772259

DOI

10.3030/772259

Projekt abgeschlossen

EK-Unterschriftsdatum 8 Februar 2018

Startdatum 1 Mai 2018

Enddatum 31 Juli 2024

Finanziert unter

• EXCELLENT SCIENCE - European Research Council (ERC)

Gesamtkosten

€ 1 998 649,00

EU-Beitrag

€ 1 998 649,00

Koordiniert durch

THE UNIVERSITY OF NOTTINGHAM
United Kingdom

Periodic Reporting for period 4 - topDFT (A topological approach to electron correlation in density-functional theories)

Berichtszeitraum: 2022-11-01 bis 2024-07-31

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

Density-functional theory (DFT) is the most widely used method to study the electronic structure of complex molecules, solids, and materials. Its use across chemistry, solid-state physics and materials science is a testament to its black-box nature and low cost. However, many important areas remain inaccessible to DFT simulations, including applications to strongly correlated materials and systems in electromagnetic fields. The topDFT project will deliver new conceptual approaches to design the next generation of density-functional methods. This will be achieved by pursuing three parallel strategies: i) Developing new strategies for the design of functionals ii) Implementing topological DFT, a new computational framework iii) Developing extended density-functional theories.

Techniques have been developed for learning about the behaviour of the exact density-functional from high level correlated calculations. These approaches have been significantly extended to treat open-shell systems and systems in the presence of external electromagnetic fields. A new framework for computation has been developed by combining techniques from topological electronic structure methods with DFT, allowing for the identification of correlation ‘hotspots’. This idea is chemically intuitive; electrons close together interact in a fundamentally different way to those far apart. The new computational approach is capable of recognising these hotspots, and adapting dynamically to them.

Extended-DFTs have been implemented and opened the way to routinely study systems in the presence of external electric and magnetic fields of arbitrary strength in a routine manner. These calculations have helped give insight into chemical reactivity in the presence of these fields, as well as their excited states and electron dynamics.

Arbeit, die ab Beginn des Projekts bis zum Ende des durch den Bericht erfassten Berichtszeitraums geleistet wurde, und die wichtigsten bis dahin erzielten Ergebnisse

A substantial effort has been placed on developing a new code to perform practical calculations at the standard DFT and current-dependent CDFT levels. The program uses complex algebra throughout and is readily applied in the presence of strong electromagnetic fields. Alongside this, implementations of high-level Moller-Plesset and Coupled-Cluster theories with access to the corresponding relaxed electron densities have been constructed. These have been implemented for both standard calculations and those in the presence of strong magnetic fields. These ab initio methods underpin a practical implementation of the Lieb optimization procedure that can now be used to study both the conventional universal density functional and its counterpart in current-density functional theory in a single framework. The latter enables calculation of the adiabatic connections, coupling constant averaged exchange correlation holes and energy densities that are central to the topDFT project. In particular, these methods are available for both closed and open-shell systems, with the latter being essential to study spin-polarised density-functionals.

In addition to this a number of key features have been added to provide access to molecular properties. This includes: electronic excitation spectra and circular dichroism spectra, and magnetic circular dichroism spectra at the CDFT level via real-time electronic structure methods, molecular structure under strong fields at the CDFT level with efficient evaluations of the required integral derivatives with London atomic orbitals, and the implementation of linear response calculations for excitation energies at the RPA level.

To enable the study of larger systems an embarrassingly parallel implementation of the embedded fragment method has been constructed, which is also able to treat systems in a strong magnetic field with any of the electronic structure methods (HF/DFT/MPn/CC) available in the program.

These advances have been disseminated to the scientific community via publications in a wide variety of peer-reviewed international journals, describing the implementations and applications.

Fortschritte, die über den aktuellen Stand der Technik hinausgehen und voraussichtliche potenzielle Auswirkungen (einschließlich der bis dato erzielten sozioökonomischen Auswirkungen und weiter gefassten gesellschaftlichen Auswirkungen des Projekts)

Progress beyond state of the art has been made in several areas and include:

- New tools for analysis of the exact density-functional using Lieb maximization with high-level ab inito methods. This includes extensions to treat open shells and describe local adiabatic connections and exchange-correlation holes.

- Efficient implementations bringing current-density-functional theory to routine use for molecular systems. This allows seamless description of molecular systems from zero field to arbitrary field strengths.

- Real-time CDFT approaches to access excited states and electron dynamics in the presence of external electric and/or magnetic fields.

- New fragment and semi-empirical methods to address very large systems in arbitrary magnetic fields.

Overview of the topDFT project