Restoring the Point-and-Charge Gradient Expansion for the Strong Interaction Density Functionals

Abstract

The strong-interaction functionals $W_{\infty }[n]$ and ${W^{\prime }}_{\infty }[n]$ play an important role in the adiabatic-connection method of Density Functional Theory. The strictly-correlated electron approach can be used to exactly compute these functionals, yet calculations are computationally very expensive even for small electronic systems, and thus semilocal approximations have been proposed. In this work we develop a meta-generalized gradient approximation (meta-GGA) model for the strong-interaction functionals, enhanced point-and-charge (ePC), constructed from exact constraints. In particular, the ePC restores the second-order gradient expansion of the PC model, that is relevant for the equilibrium properties of Wigner crystals, and ensures the non-negativity of ${W^{\prime }}_{\infty }[n]$. We assess the ePC model for atoms and various model systems: Hooke's atoms, two-electron exponential densities, s- and p-hydrogenic shells, quasi-two-dimensional infinite barrier model, perturbed uniform electron gas and H${}_2$ dissociation. We prove a good overall accuracy of the ePC model, that achieves a broader applicability than any previous semilocal models.

17 pages, 14 figures

References in corpus (32)

• Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids
• Perspective on density functional theory
• Fractional spins and static correlation error in density functional theory
• The discontinuous nature of the exchange-correlation functional -- critical for strongly correlated systems
• Density Functionals that Recognize Covalent, Metallic, and Weak Bonds
• Accurate semilocal density functional for condensed matter physics and quantum chemistry
• Exact-exchange energy density in the gauge of a semilocal density functional approximation
• Strong correlation in Kohn-Sham density functional theory
• Density functional theory for strongly interacting electrons
• Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories
• Density functional theory for strongly-interacting electrons: Perspectives for Physics and Chemistry
• Kohn-Sham Kinetic Energy Density in the Nuclear and Asymptotic Regions: Deviations from the Von Weizsäcker Behavior and Applications to Density Functionals
• Enhancing the efficiency of density functionals with a novel iso-orbital indicator
• The interaction-strength interpolation method for main-group chemistry: benchmarking, limitations, and perspectives
• Adiabatic Connection in the Low-Density Limit
• Restoring size consistency of approximate functionals constructed from the adiabatic connection
• Interpolated energy densities, correlation indicators and lower bounds from approximations to the strong coupling limit of DFT
• Assessment of interaction-strength interpolation formulas for gold and silver clusters
• Nonempirical Density Functionals Investigated for Jellium: Spin-Polarized Surfaces, Spherical Clusters, and Bulk Linear Response
• Constraint-based Wavevector- and Frequency-dependent Exchange-Correlation Kernel of the Uniform Electron Gas
• Low-density Phase Diagram of the Three-Dimensional Electron Gas
• Adiabatic Connection for Strictly-Correlated Electrons
• Efficient and improved prediction of the band offsets at semiconductor heterojunctions from meta-GGA density functionals
• Augmented potential, energy densities, and virial relations in the weak- and strong-interaction limits of DFT
• Global hybrids from the semiclassical atom theory satisfying the local density linear response
• Accurate Adiabatic Connection Curve Beyond the Physical Interaction Strength
• Local and global interpolations along the adiabatic connection of DFT: A study at different correlation regimes
• Three- to two-dimensional crossover in time-dependent density-functional theory
• Adiabatic connection at negative coupling strengths
• Hartree potential dependent exchange functional
• Examining the order-of-limits problem and lattice constant performance of the Tao--Mo Functional
• Advancing excited-state properties of two-dimensional materials using a dielectric-dependent hybrid functional