Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence

Abstract

The combination of density functional theory with other approaches to the many-electron problem through the separation of the electron-electron interaction into a short-range and a long-range contribution is a promising method, which is raising more and more interest in recent years. In this work some properties of the corresponding correlation energy functionals are derived by studying the electron-electron coalescence condition for a modified (long-range-only) interaction. A general relation for the on-top (zero electron-electron distance) pair density is derived, and its usefulness is discussed with some examples. For the special case of the uniform electron gas, a simple parameterization of the on-top pair density for a long-range only interaction is presented and supported by calculations within the ``extended Overhauser model''. The results of this work can be used to build self-interaction corrected short-range correlation energy functionals.

revised version, to appear in Phys. Rev. A

References in corpus (12)

• Van der Waals Energies in Density Functional Theory
• Long-range/short-range separation of the electron-electron interaction in density functional theory
• A density functional theory with correct long-range asymptotic behavior
• Van der Waals forces in density functional theory: perturbational long-range electron interaction corrections
• Short-range exchange and correlation energy density functionals: beyond the local density approximation
• Pair distribution function of the spin-polarized electron gas: A first-principles analytic model for all uniform densities
• Short-range correlation in the uniform electron gas: Extended Overhauser model
• Integral Coalescence Conditions In $D\ge 2$ Dimension Space
• Simple model for the spherically- and system-averaged pair density: Results for two-electron atoms
• Self-consistent Overhauser model for the pair distribution function of an electron gas in dimensionalities D=3 and D=2
• The on-top pair-correlation density in the homogeneous electron liquid
• Pair densities at contact in the quantum electron gas

Cited by in corpus (30)

• Local-spin-density functional for multideterminant density functional theory
• Computing Counterion Densities at Intermediate Coupling
• Simple dynamic exchange-correlation kernel of the uniform electron gas
• A Density-Based Basis-Set Correction For Wave Function Theory
• Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density
• Basis convergence of range-separated density-functional theory
• Chemically Accurate Excitation Energies With Small Basis Sets
• A Density-Based Basis-Set Incompleteness Correction for GW Methods
• Double hybrid density-functional theory using the Coulomb-attenuating method
• A basis-set error correction based on density-functional theory for strongly correlated molecular systems
• Electronic excitations from a linear-response range-separated hybrid scheme
• Short-distance properties of Coulomb systems
• Models and corrections: range separation for electronic interaction -- lessons from density functional theory
• A new form of transcorrelated Hamiltonian inspired by range-separated DFT
• Excitation energies along a range-separated adiabatic connection
• Alternative separation of exchange and correlation energies in range-separated density-functional perturbation theory
• Combining linear interpolation with extrapolation methods in range-separated ensemble density-functional theory
• Self-consistent density-based basis-set correction: How much do we lower total energies and improve dipole moments?
• Accurate energies of transition metal atoms, ions, and monoxides using selected configuration interaction and density-based basis-set corrections
• Range separation combined with the Overhauser model: Application to the H${}_2$ molecule along the dissociation curve
• Radial distribution function in a diffusion Monte Carlo simulation of a Fermion fluid between the ideal gas and the Jellium model
• Combining Density Functional Theory and Green's Function Theory: Range-Separated, Non-local, Dynamic, and Orbital-Dependent Hybrid Functional
• A density-fitting implementation of the density-based basis-set correction method
• Combining density based dynamical correlation with a reduced density matrix strong correlation description
• 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
• Short-range correlation energy of the relativistic homogeneous electron gas
• 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