相关论文: Tightened Lieb-Oxford bound for systems of fixed p…
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…
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…
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…
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…
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…
Eleven density functionals are compared with regard to their performance for the lattice constants of solids. We consider standard functionals, such as the local-density approximation and the Perdew-Burke-Ernzerhof (PBE)…
We study numerically the strong-interaction limit of the exchange-correlation functional for neutral atoms and for Bohr atoms as the number of electrons increases. Using a compact representation, we analyse the second-order gradient…
We investigate and prove Lieb-Oxford bounds in one dimension by studying convex potentials that approximate the ill-defined Coulomb potential. A Lieb-Oxford inequality establishes a bound of the indirect interaction energy for electrons in…
The Lieb-Oxford inequality provides a lower bound on the Coulomb energy of a classical system of $N$ identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality.…
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…
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…
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 simple and completely general representation of the exact exchange-correlation functional of density-functional theory is derived from the universal Lieb-Oxford bound, which holds for any Coulomb-interacting system. This representation…
We prove a new lower bound on the indirect Coulomb energy in quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the classical Lieb--Oxford bound (with a smaller…
We revisit the two derivations of the PBE correlation functional: The real-space cut-off of the exchange-correlation hole and the imposition of exact conditions. These differ in the Lieb-Simon limit, exemplified by the scaling of neutral…
A new functional form for the exchange enhancement in the generalized gradient approximation within density functional theory is given. The functional form satisfies the constraints used to construct the Perdew-Burke-Ernzerhof (PBE)…
Lieb-Robinson bounds are powerful analytical tools for constraining the dynamic and static properties of non-relativistic quantum systems. Recently, a complete picture for closed systems that evolve unitarily in time has been achieved. In…
We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb energy of a general many-particle quantum state, with a lower constant than the original statement but involving an additional gradient correction. The result is…
The linear combination of atomic orbitals (LCAO) is a standard method for studying solids and molecules, it is also known as the tight$-$binding (TB) method. In most of the implementations only the basis set and the coupling constants are…
Lieb-Robinson-type bounds are reported for a large class of classical Hamiltonian lattice models. By a suitable rescaling of energy or time, such bounds can be constructed for interactions of arbitrarily long range. The bound quantifies the…