Abstract
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 ρ 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.
Highlights
Magnetic fields and their effects on atoms and molecules have for many years been an active area of research in physics and chemistry
We investigate to what extent a field dependence in the density functional may improve the computation of the magnetizability, which is proportional to the second derivative of the energy with respect to the magnetic field strength
In Sec. , we study the adiabatic connection (AC) at different field strengths for H2 and LiH, yielding insight into the magnetic-field dependence of the correlation energy up to a field strength of one atomic unit, B0 = 2.35 × 105 T
Summary
Magnetic fields and their effects on atoms and molecules have for many years been an active area of research in physics and chemistry. We discuss DFT in the presence of a magnetic field—in particular, we develop CDFT and BDFT within the framework of convex conjugation, setting up and relating the Hohenberg–Kohn and Lieb variation principles for these theories. As an alternative to CDFT, we describe in magnetic-field density-functional theory (BDFT) 10 the atomic or molecular system in terms of the semi-universal density functional Gλ(ρ, A) rather than in terms of the universal CDFT density functional Fλ(ρ, jp), using the partial conjugations in Eq (14), yielding the following Hohenberg–Kohn and Lieb variation principles: Eλ(u, A)
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