Related papers: Atomic correlation energies and the generalized gr…
The large-$Z$ asymptotic expansion of atomic energies has been useful in determining exact conditions for corrections to the local density approximation in density functional theory. The correction for exchange is fit well with a leading $Z…
The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi approximation in the non-relativistic semiclassical (or large-$Z$) limit for all matter, i.e, the kinetic energy becomes local. Exchange also becomes…
A curious behavior of electron correlation energy is explored. Namely, the correlation energy is the energy that tends to drive the system toward that of the uniform electron gas. As such, the energy assumes its maximum value when a…
A simple, approximate relation is found between the total energy of a free atom and its atomic number: E ~= -Z^{2.411}. The existence of this index is inherent in the Coulomb and many-body nature of the electron-electron interaction in the…
Under a certain scaling, the electron densities of finite systems become both large and slowly-varying, so that the gradient expansions of the density functionals for the Kohn-Sham kinetic and exchange energies become asymptotically exact…
Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of…
The correlation energies of various atoms in their excited-states are estimated by modelling the Coulomb hole following the previous work by Chakravorty and Clementi. The parameter in the model is fixed by making the corresponding Coulomb…
We consider non-relativistic electron correlation energies of heavy noble gas atoms including the superheavy element Og. The corresponding data enables us to quantify fixed-node errors in real space quantum Monte Carlo methods as a function…
Methods for estimating the correlation energy of molecules and other electronic systems are discussed based on the assumption that the correlation energy can be partitioned between atomic regions. In one method, the electron density is…
The flexibility of common generalized gradient approximation for the exchange-correlation energy is investigated by monitoring the equilibrium volume of transition metals. It is shown that no universal gradient-level approximation yielding…
Radial, angular and total correlation energies are calculated for four two-electron systems with atomic numbers Z=0-3 confined within an impenetrable sphere of radius R. We report accurate results for the non-relativistic, restricted…
The correlation energy per electron in the high-density uniform electron gas can be written as $\Ec(r_s,\zeta) = \lam_0(\zeta) \ln r_s + \eps_0(\zeta) + \lam_1(\zeta) \,r_s \ln r_s + O(r_s)$, where $r_s$ is the Seitz radius and $\zeta$ is…
We show in this note how many electron irreducible representations of the Lorentz group L can be expressed in terms of the sums of Slater determinants and principal minors. In this way the full configuration wave function of quantum…
In order to assess the accuracy of commonly used approximate exchange-correlation density functionals, we present a comparison of accurate exchange and correlation potentials, exchange energy densities and energy components with the…
The non-relativistic large-$Z$ expansion of the exchange energy of neutral atoms provides an important input to modern non-empirical density functional approximations. Recent works report results of fitting the terms beyond the dominant…
The all-order correlation potential method of accurate atomic structure calculations for atoms with one external electron is extended to include one more class of correlation diagrams to all orders. These are the so-called ladder diagrams…
We find an unexpected scaling in the correlation energy of artificial atoms, i.e., harmonically confined two-dimensional quantum dots. The scaling relation is found through extensive numerical examinations including Hartree-Fock,…
We study the $D$-dimensional high-density correlation energy $\Ec$ of the singlet ground state of two electrons confined by a harmonic potential with Coulombic repulsion. We allow the harmonic potential to be anisotropic, and examine the…
The components of the radial correlation energy density are calculated and analyzed for the atoms from He to Ar. The components include the nucleus-electron potential correlation energy density, the kinetic correlation energy density and…
We present an intuitive and general analytical approximation estimating the energy of covalent single and double bonds between participating atoms in terms of their respective nuclear charges with just three parameters, $[{E_\text{AB}…