Magnetic-field density-functional theory (BDFT): lessons from the adiabatic connection

We study the effects of magnetic fields in the context of magnetic field density-functional theory (BDFT), where the energy is a functional of the electron density p and the magnetic field B. We show that this approach is a worthwhile alternative to current-density functional theory (CDFT) and may p...

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Main Authors:	Reimann, Sarah, Borgoo, Alex, Tellgren, Erik I., Teale, Andrew M., Helgaker, Trygve
Format:	Article
Language:	English
Published:	American Chemical Society 2017
Online Access:	http://eprints.nottingham.ac.uk/44648/ http://eprints.nottingham.ac.uk/44648/ http://eprints.nottingham.ac.uk/44648/ http://eprints.nottingham.ac.uk/44648/1/mag_acpaper.pdf

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spelling	nottingham-446482018-08-02T04:30:33Z http://eprints.nottingham.ac.uk/44648/ Magnetic-field density-functional theory (BDFT): lessons from the adiabatic connection Reimann, Sarah Borgoo, Alex Tellgren, Erik I. Teale, Andrew M. Helgaker, Trygve We study the effects of magnetic fields in the context of magnetic field density-functional theory (BDFT), where the energy is a functional of the electron density p and the magnetic field B. We show that this approach is a worthwhile alternative to current-density functional theory (CDFT) and may provide a viable route to the study of many magnetic phenomena using density-functional theory (DFT). The relationship between BDFT and CDFT is developed and clarified within the framework of the four-way correspondence of saddle functions and their convex and concave parents in convex analysis. By decomposing the energy into its Kohn–Sham components, we demonstrate that the magnetizability is mainly determined by those energy components that are related to the density. For existing density functional approximations, this implies that, for the magnetizability, improvements of the density will be more beneficial than introducing a magnetic-field dependence in the correlation functional. However, once a good charge density is achieved, we show that high accuracy is likely only obtainable by including magnetic-field dependence. We demonstrate that adiabatic-connection (AC) curves at different field strengths resemble one another closely provided each curve is calculated at the equilibrium geometry of that field strength. In contrast, if all AC curves are calculated at the equilibrium geometry of the field-free system, then the curves change strongly with increasing field strength due to the increasing importance of static correlation. This holds also for density functional approximations, for which we demonstrate that the main error encountered in the presence of a field is already present at zero field strength, indicating that density-functional approximations may be applied to systems in strong fields, without the need to treat additional static correlation. American Chemical Society 2017-08-02 Article PeerReviewed application/pdf en http://eprints.nottingham.ac.uk/44648/1/mag_acpaper.pdf Reimann, Sarah and Borgoo, Alex and Tellgren, Erik I. and Teale, Andrew M. and Helgaker, Trygve (2017) Magnetic-field density-functional theory (BDFT): lessons from the adiabatic connection. Journal of Chemical Theory and Computation . ISSN 1549-9626 (In Press) http://pubs.acs.org/doi/abs/10.1021/acs.jctc.7b00295 doi:10.1021/acs.jctc.7b00295 doi:10.1021/acs.jctc.7b00295
repository_type	Digital Repository
institution_category	Local University
institution	University of Nottingham Malaysia Campus
building	Nottingham Research Data Repository
collection	Online Access
language	English
description	We study the effects of magnetic fields in the context of magnetic field density-functional theory (BDFT), where the energy is a functional of the electron density p and the magnetic field B. We show that this approach is a worthwhile alternative to current-density functional theory (CDFT) and may provide a viable route to the study of many magnetic phenomena using density-functional theory (DFT). The relationship between BDFT and CDFT is developed and clarified within the framework of the four-way correspondence of saddle functions and their convex and concave parents in convex analysis. By decomposing the energy into its Kohn–Sham components, we demonstrate that the magnetizability is mainly determined by those energy components that are related to the density. For existing density functional approximations, this implies that, for the magnetizability, improvements of the density will be more beneficial than introducing a magnetic-field dependence in the correlation functional. However, once a good charge density is achieved, we show that high accuracy is likely only obtainable by including magnetic-field dependence. We demonstrate that adiabatic-connection (AC) curves at different field strengths resemble one another closely provided each curve is calculated at the equilibrium geometry of that field strength. In contrast, if all AC curves are calculated at the equilibrium geometry of the field-free system, then the curves change strongly with increasing field strength due to the increasing importance of static correlation. This holds also for density functional approximations, for which we demonstrate that the main error encountered in the presence of a field is already present at zero field strength, indicating that density-functional approximations may be applied to systems in strong fields, without the need to treat additional static correlation.
format	Article
author	Reimann, Sarah Borgoo, Alex Tellgren, Erik I. Teale, Andrew M. Helgaker, Trygve
spellingShingle	Reimann, Sarah Borgoo, Alex Tellgren, Erik I. Teale, Andrew M. Helgaker, Trygve Magnetic-field density-functional theory (BDFT): lessons from the adiabatic connection
author_facet	Reimann, Sarah Borgoo, Alex Tellgren, Erik I. Teale, Andrew M. Helgaker, Trygve
author_sort	Reimann, Sarah
title	Magnetic-field density-functional theory (BDFT): lessons from the adiabatic connection
title_short	Magnetic-field density-functional theory (BDFT): lessons from the adiabatic connection
title_full	Magnetic-field density-functional theory (BDFT): lessons from the adiabatic connection
title_fullStr	Magnetic-field density-functional theory (BDFT): lessons from the adiabatic connection
title_full_unstemmed	Magnetic-field density-functional theory (BDFT): lessons from the adiabatic connection
title_sort	magnetic-field density-functional theory (bdft): lessons from the adiabatic connection
publisher	American Chemical Society
publishDate	2017
url	http://eprints.nottingham.ac.uk/44648/ http://eprints.nottingham.ac.uk/44648/ http://eprints.nottingham.ac.uk/44648/ http://eprints.nottingham.ac.uk/44648/1/mag_acpaper.pdf
first_indexed	2018-09-06T13:35:09Z
last_indexed	2018-09-06T13:35:09Z
_version_	1610865348104421376

Magnetic-field density-functional theory (BDFT): lessons from the adiabatic connection

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