Seven Useful Questions in Density Functional Theory

Abstract

We explore a variety of unsolved problems in density functional theory, where mathematicians might prove useful. We give the background and context of the different problems, and why progress toward resolving them would help those doing computations using density functional theory. Subjects covered include the magnitude of the kinetic energy in Hartree-Fock calculations, the shape of adiabatic connection curves, using the constrained search with input densities, densities of states, the semiclassical expansion of energies, the tightness of Lieb-Oxford bounds, and how we decide the accuracy of an approximate density.

arXiv comment21 pages, 6 figures

References in corpus (61)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Variational Quantum Algorithms
• Quantum computational advantage using photons
• PaLM: Scaling Language Modeling with Pathways
• Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding
• Growth Model Interpretation of Planet Size Distribution
• The Hubbard Model
• Understanding and reducing errors in density functional calculations
• Superconducting hydrides under pressure
• Computational Complexity of interacting electrons and fundamental limitations of Density Functional Theory
• FAIR data enabling new horizons for materials research
• Describing static correlation in bond dissociation by Kohn-Sham density functional theory
• DFT: A Theory Full of Holes?
• The Importance of being consistent
• Gedanken Densities and Exact Constraints in Density Functional Theory
• Relevance of the slowly-varying electron gas to atoms, molecules, and solids
• Does Simple Two-Dimensional Hubbard Model Account for High-Tc Superconductivity in Copper Oxides?
• The Hubbard Dimer: A density functional case study of a many-body problem
• Metal-insulator transition in the one-dimensional SU(N) Hubbard model
• Predictive Power of the Exact Constraints and Appropriate Norms in Density Functional Theory
• There are No Unfilled Shells in Hartree-Fock Theory
• Mott Transition in the Two-Dimensional Hubbard Model
• Exact ensemble density functional theory for excited states in a model system: investigating the weight dependence of the correlation energy
• Kohn-Sham calculations with the exact functional
• Challenging Adiabatic Time-dependent Density Functional Theory with a Hubbard Dimer: The Case of Time-Resolved Long-Range Charge Transfer
• Guaranteed convergence of the Kohn-Sham equations
• Adiabatic connection from accurate wavefunction calculations
• Energy surface, chemical potentials, Kohn-Sham energies in spin-polarized density functional theory
• Frank Discussion of the Status of Ground-state Orbital-free DFT
• Ionization potentials in the limit of large atomic number
• Locality of correlation in density functional theory
• Floating Wigner crystal with no boundary charge fluctuations
• Landscape of an exact energy functional
• Understanding density driven errors for reaction barrier heights
• Linear response time-dependent density functional theory of the Hubbard dimer
• The time-dependent exchange-correlation functional for a Hubbard dimer: quantifying non-adiabatic effect
• Quantum mechanics in metric space: wave functions and their densities
• Challenging the Lieb-Oxford Bound in a systematic way
• Embedding via the Exact Factorization Approach
• KS-pies: Kohn-Sham Inversion Toolkit
• Lower Bound on the Hartree-Fock Energy of the Electron Gas
• The Lieb-Thirring inequality revisited
• Building Kohn-Sham potentials for ground and excited states
• Fock space embedding theory for strongly correlated topological phases
• Atoms and Quantum Dots With a Large Number of Electrons: the Ground State Energy
• Leading correction to the local density approximation for exchange in large-$Z$ atoms
• Some properties of the potential-to-ground state map in quantum mechanics
• Metric space analysis of systems immersed in a magnetic field
• Metric space approach to potentials and its relevance to density functional theory
• Mott Transition in the Hubbard model
• Levy-Lieb principle: The bridge between the electron density of Density Functional Theory and the wavefunction of Quantum Monte Carlo
• The Scott conjecture for large Coulomb systems: a review
• Semiclassics: The hidden theory behind the success of DFT
• Can the Hartree-Fock kinetic energy exceed the exact kinetic energy?
• On Some Open Problems in Many-Electron Theory
• The Atomic Density on the Thomas--Fermi Length Scale for the Chandrasekhar Hamiltonian
• The Levy-Lieb embedding of density functional theory and its Quantum Kernel: Illustration for the Hubbard Dimer using near-term quantum algorithms
• The Lieb-Thirring inequalities: Recent results and open problems
• Generalized gradient approximations to density functional theory: comparison with exact results
• The Lieb-Oxford bound and the optimal transport limit of DFT

Cited by in corpus (8)

• Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
• Exchange Correlation Potentials from Full Configuration Interaction in a Slater Orbital Basis
• A simple and efficient route towards improved energetics within the framework of density-corrected density functional theory
• Kohn-Sham inversion with mathematical guarantees
• Quantum-Electrodynamical Density-Functional Theory Exemplified by the Quantum Rabi Model
• Exchange-only virial relation from the adiabatic connection
• Regularised density-potential inversion for periodic systems: application to exact exchange in one dimension
• Preserving the Hermiticity of the One-Body Density Matrix for a Non-Interacting Fermi Gas