Density functional theory for strongly-interacting electrons: Perspectives for Physics and Chemistry

Abstract

Improving the accuracy and thus broadening the applicability of electronic density functional theory (DFT) is crucial to many research areas, from material science, to theoretical chemistry, biophysics and biochemistry. In the last three years, the mathematical structure of the strong-interaction limit of density functional theory has been uncovered, and exact information on this limit has started to become available. The aim of this paper is to give a perspective on how this new piece of exact information can be used to treat situations that are problematic for standard Kohn-Sham DFT. One way to use the strong-interaction limit, more relevant for solid-state physical devices, is to define a new framework to do practical, non-conventional, DFT calculations in which a strong-interacting reference system is used instead of the traditional non-interacting one of Kohn and Sham. Another way to proceed, more related to chemical applications, is to include the exact treatment of the strong-interaction limit into approximate exchange-correlation energy density functionals in order to describe difficult situations such as the breaking of the chemical bond.

38 pages; invited perspective article for Phys. Chem. Chem. Phys

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• The Hubbard Dimer: A density functional case study of a many-body problem
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• Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes
• Wigner localization in quantum dots from Kohn-Sham density functional theory without symmetry breaking
• Improved Lieb-Oxford exchange-correlation inequality with gradient correction
• Floating Wigner crystal with no boundary charge fluctuations
• A weight-dependent local correlation density-functional approximation for ensembles
• Statistical Mechanics of the Uniform Electron Gas
• Strictly correlated uniform electron droplets
• The derivative discontinuity in the strong-interaction limit of density functional theory
• Exchange-correlation functionals from the strongly-interacting limit of DFT: Applications to model chemical systems
• Numerical methods for a Kohn-Sham density functional model based on optimal transport
• Electronic excited states in extreme limits via ensemble density functionals
• Augmented potential, energy densities, and virial relations in the weak- and strong-interaction limits of DFT
• Large coupling-strength expansion of the Møller-Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms
• No-go theorem for the description of Mott phenomena with conventional Density Functional Theory methods
• Universal Functionals in Density Functional Theory
• Density functional theory for strongly-correlated bosonic and fermionic ultracold dipolar and ionic gases
• Functional Derivative of the Zero Point Energy Functional from the Strong Interaction Limit of Density Functional Theory
• Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model
• Excited-State Wigner Crystals in One Dimension
• Optimal transport with Coulomb cost and the semiclassical limit of Density Functional Theory
• INQ, a modern GPU-accelerated computational framework for (time-dependent) density functional theory
• Grand-Canonical Optimal Transport
• Restoring the Point-and-Charge Gradient Expansion for the Strong Interaction Density Functionals
• Marginals with finite repulsive cost
• Relativistic density-functional theory based on effective quantum electrodynamics