Models and corrections: range separation for electronic interaction -- lessons from density functional theory

Abstract

Model Hamiltonians with long-range interaction yield energies that are corrected taking into account the universal behavior of the electron-electron interaction at short range. Although the intention of the paper is to explore the foundations of using density functionals combined with range separation, the approximations presented can be used without them, as illustrated by a calculation on Harmonium. In the regime when the model system approaches the Coulomb system, they allow the calculation of ground states, excited states, and properties, without making use of the Hohenberg-Kohn theorem. Asymptotically, the technique is improvable, allows for error estimates that can validate the results. Some considerations for correcting the errors of finite basis sets in this spirit are also presented. Being related to the present understanding of density functional approximations, the results are comparable to those obtained with the latter, as long as these are accurate.

References in corpus (16)

• Van der Waals Energies in Density Functional Theory
• Long-range/short-range separation of the electron-electron interaction in density functional theory
• Van der Waals forces in density functional theory: perturbational long-range electron interaction corrections
• Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation
• Local-spin-density functional for multideterminant density functional theory
• Density Matrix Renormalization Group with Efficient Dynamical Electron Correlation Through Range Separation
• Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories
• Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence
• Curing basis-set convergence of wave-function theory using density-functional theory: a systematically improvable approach
• Analytic structure of many-body Coulombic wave functions
• Ghost interaction correction in ensemble density-functional theory for excited states with and without range separation
• Excitation energies along a range-separated adiabatic connection
• Combining linear interpolation with extrapolation methods in range-separated ensemble density-functional theory
• Exchange-correlation potentials and local energies per particle along non-linear adiabatic connections
• Pseudopotential for the electron-electron interaction
• Plane wave basis set correction methods for RPA correlation energies

Cited by in corpus (7)

• Projected Hybrid Density Functionals: Method and Application to Core Electron Ionization
• Correcting models with long-range electron interaction using generalized cusp conditions
• Second-order adiabatic connection: The theory and application to two electrons in a parabolic confinement
• Two-particle coalescence conditions revisited
• Exploring the role of mean-field potentials and short-range wave function behavior in the adiabatic connection
• Erfonium: A Hooke Atom with Soft Interaction Potential
• A modified expression for the Hamiltonian expectation value exploiting the short-range behavior of the wave function