Related papers: Non-empirical hyper-generalized-gradient functiona…
In the framework of density-functional theory, several popular density functionals for exchange and correlation have been constructed to satisfy a local form of the Lieb-Oxford bound. In its original global expression, the bound represents…
Lieb and Oxford (1981) derived rigorous lower bounds, in the form of local functionals of the electron density, on the indirect part of the Coulomb repulsion energy. The greatest lower bound for a given electron number N depends…
The Lieb-Oxford bound, a nontrivial inequality for the indirect part of the many-body Coulomb repulsion in an electronic system, plays an important role in the construction of approximations in density functional theory. Using the…
Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, inparticular, are important for the construction of improved density functionals. Here we investigate one…
Lewin and Lieb have recently proven several new bounds on the exchange-correlation energy that complement the Lieb-Oxford bound. We test these bounds for atoms, for slowly-varying gases, and for Hooke's atom, finding them usually less…
Density-functional theory requires ever better exchange-correlation (xc) functionals for the ever more precise description of many-body effects on electronic structure. Universal constraints on the xc energy are important ingredients in the…
We propose a simple gradient-dependent bound for the exchange-correlation energy (sLL), based on the recent non-local bound derived by Lewin and Lieb. We show that sLL is equivalent to the original Lieb-Oxford bound in rapidly-varying…
A widely used approximation to the exchange-correlation functional in density functional theory is the local density approximation (LDA), typically derived from the properties of the homogeneous electron gas (HEG). We previously introduced…
The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation…
We study the energetic properties of finite but internally homogeneous D-dimensional electron droplets in the strict-correlation limit. The indirect Coulomb interaction is found to increase as a function of the electron number, approaching…
The local density approximation (LDA) constructed through quantum Monte Carlo calculations of the homogeneous electron gas (HEG) is the most common approximation to the exchange-correlation functional in density functional theory. We…
We show how one can construct \alert{a simple} exchange functional by extending the well-know local-density approximation (LDA) to finite uniform electron gases. This new generalized local-density approximation (GLDA) functional uses only…
We extend the previously proposed one-parameter double-hybrid density-functional theory [K. Sharkas, J. Toulouse, and A. Savin, J. Chem. Phys. 134, 064113 (2011)] to meta-generalized-gradient-approximation (meta-GGA) exchange-correlation…
Approximations to the exact density functional for the exchange-correlation energy of a many-electron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities…
The Lieb-Oxford bound is a constraint upon approximate exchange-correlation functionals. We explore a non-empirical tightening of that bound in both universal and electron-number-dependent form. The test functional is PBE. Regarding both…
We discuss energy densities in the strong-interaction limit of density functional theory, deriving an exact expression within the definition (gauge) of the electrostatic potential of the exchange-correlation hole. Exact results for small…
The central quantity of density functional theory is the so-called exchange-correlation functional. This quantity encompasses all non-trivial many-body effects of the ground-state and has to be approximated in any practical application of…
We present the self-consistent implementation of current-dependent (hybrid) meta generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is…
We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating…
We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the…