Related papers: Approximate normalizations for approximate density…
Finite temperature density functional theory provides, in principle, an exact description of the thermodynamical equilibrium of many-electron systems. In practical applications, however, the functionals must be approximated. Efficient and…
In a previous paper, I demonstrated the accuracy of simple, precessing, power ellipse (p-ellipse) approximations to orbits of low-to-moderate eccentricity in power-law potentials. Here I explore several extensions of these approximations to…
We argue that any general mathematical measure of density error, no matter how reasonable, is too arbitrary to be of universal use. However the energy functional itself provides a universal relevant measure of density errors. For the…
The non-relativistic interacting electron gas in an external field of positively charged massive cores is dealt with in the scheme of second quantization. Ladder operators that change between stationary states of contiguous energy…
The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, and, in particular, to derive relativistic Scott correction term and also Dirac, Schwinger…
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…
The self-screening error in electronic structure theory is the part of the self-interaction error that would remain within the $GW$ approximation if the exact dynamically screened Coulomb interaction, $W$, were used, causing each electron…
In this manuscript we provide a family of lower bounds on the indirect Coulomb energy for atomic and molecular systems in two dimensions in terms of a functional of the single particle density with gradient correction terms.
The numerical implementation of an exchange-correlation functional is not always an accurate reproduction of its theoretical specification. For example, density functionals for exchange and correlation can be defined by an exchange or…
A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and…
Standard flavors of density-functional theory (DFT) calculations are known to fail in describing anions, due to large self-interaction errors. The problem may be circumvented by using localized basis sets of reduced size, leaving no…
The energy density functional (EDF) method is very widely used in nuclear physics, and among the various existing functionals those based on the relativistic Hartree (RH) approximation are very popular because the exchange contributions…
DFT calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation…
General theorem describing a relation between diagonal of one-electron density matrix and a certain class of many-electron ensembles of determinant states is proved. As a corollary to this theorem a constructive proof of sufficiency of…
In this paper, we extend several approximation theorems, originally formulated in the context of the standard $L^p$ norm, to the more general framework of variable exponent spaces. Our study is motivated by applications in neural networks,…
The Thomas-Fermi (TF) approximation for the static dielectric constant of a three-dimensional electron liquid can be derived from minimizing the TF local-density approximation for the kinetic-energy functional. Here we show that this…
A sufficiently damped iteration of the Kohn-Sham equations with the exact functional is proven to always converge to the true ground-state density, regardless of the initial density or the strength of electron correlation, for finite…
Experimental values of Coulomb sums for q > 2 fm^(-1) are considered. Assuming that a part of nucleons is modified in the nucleus, an approach is offered, in the framework of which the calculation is in agreement with the experimental data.…
We construct a generalized-gradient approximation for the exchange-energy density of finite two-dimensional systems. Guided by non-empirical principles, we include the proper small-gradient limit and the proper tail for the exchange-hole…
In principle, many-electron correlation energy can be precisely computed from a reduced Wigner distribution function ($\mathcal{W}$) thanks to a universal functional transformation ($\mathcal{F}$), whose formal existence is akin to that of…