Interpolated energy densities, correlation indicators and lower bounds from approximations to the strong coupling limit of DFT

Abstract

We investigate the construction of approximated exchange-correlation functionals by interpolating locally along the adiabatic connection between the weak- and the strong-coupling regimes, focussing on the effect of using approximate functionals for the strong-coupling energy densities. The gauge problem is avoided by dealing with quantities that are all locally defined in the same way. Using exact ingredients at weak coupling we are able to isolate the error coming from the approximations at strong coupling only. We find that the nonlocal radius model, which retains some of the non-locality of the exact strong-coupling regime, yields very satisfactory results. We also use interpolation models and quantities from the weak- and strong-coupling regimes to define a correlation-type indicator and a lower bound to the exact exchange-correlation energy. Open problems, related to the nature of the local and global slope of the adiabatic connection at weak coupling, are also discussed.

arXiv comment16 pages, 12 figures

References in corpus (16)

• Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction
• The discontinuous nature of the exchange-correlation functional -- critical for strongly correlated systems
• Describing static correlation in bond dissociation by Kohn-Sham density functional theory
• Optimal-transport formulation of electronic density-functional theory
• Strong correlation in Kohn-Sham density functional theory
• Density Functional Model for Nondynamic and Strong Correlation
• Wigner localization in quantum dots from Kohn-Sham density functional theory without symmetry breaking
• The interaction-strength interpolation method for main-group chemistry: benchmarking, limitations, and perspectives
• Improved Lieb-Oxford exchange-correlation inequality with gradient correction
• Towards the Kantorovich dual solution for strictly correlated electrons in atoms and molecules
• Adiabatic Connection in the Low-Density Limit
• Towards efficient orbital-dependent density functionals for weak and strong correlation
• 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
• Challenging the Lieb-Oxford Bound in a systematic way
• Energy Density Functionals From the Strong-Coupling Limit Applied to the Anions of the He Isoelectronic Series

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• Large coupling-strength expansion of the Møller-Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms
• Local and global interpolations along the adiabatic connection of DFT: A study at different correlation regimes
• Range separation of the Coulomb hole
• Kinetic correlation functionals from the entropic regularisation of the strictly-correlated electrons problem
• Restoring the Point-and-Charge Gradient Expansion for the Strong Interaction Density Functionals