Related papers: Understanding correlation between two bound state …
Electron-electron correlation forms the basis of difficulties encountered in many-body problems. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in this correlation. In an…
A new method to determine electron correlation energy is described. This method is based on a better representation of the potential due to interacting electrons that is obtained by specifying both the average and standard deviation. The…
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…
Dirac equation for the finite dipole potential is solved by the method of the join of the asymptotics. The formulas for the near continuum state energy term of a relativistic electron-dipole system are obtained analytically. Two cases are…
Solution of the Dirac equation predicts that when an electron with non-zero orbital angular momentum propagates in a cylindrically symmetric potential, its spin and orbital degrees of freedom interact, causing the electron's phase velocity…
We study the ground-state correlation energy $E_{\rm c}$ of two electrons of opposite spin confined within a $D$-dimensional ball ($D \ge 2$) of radius $R$. In the high-density regime, we report accurate results for the exact and restricted…
Two-electron correlated spectra of non-sequential double ionization below laser-intensity threshold are known to exhibit back-to-back scattering of the electrons, viz., the anticorrelation of the electrons. Currently, the widely accepted…
In this paper, we consider the one-dimensional semirelativistic Schr\"{o}dinger equation for a particle interacting with $N$ Dirac delta potentials. Using the heat kernel techniques, we establish a resolvent formula in terms of an $N \times…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…
We consider the two-band Hubbard model, where electrons from different bands interact through an on-site one- and two-particle hybridization. The proposed Hamiltonian makes it possible to construct an effective theory and answer the…
The many-body Coulomb repulsive energy of strictly correlated electrons provides direct information of the exact Hohenberg-Kohn exchange-correlation functional in the strong interaction limit. Until now the treatment of strictly correlated…
The relation between the Poisson and Schr\"odinger equation in one dimension is obtained through a simple transformation. It is pointed out that this analogy between both equations can be only applied for potentials that involve a…
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…
We study the two-body problem for two-dimensional electron systems in a symmetrized Bernevig-Hughes-Zhang model which is widely used to describe topological and conventional insulators. The main result is that two interacting electrons can…
In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schr\"odinger equation. Such an error in the different calculations is not…
The analysis of correlation energy of the simplest first approximation of a variational method for the intrashell states of two-electron atoms is the purpose of the present work. This method allows to divide energy of atom on Coulomb and…
Describing the Coulomb interactions between electrons in atomic or molecular systems is an important step to help us obtain accurate results for the different observables in the system. One convenient approach is to separate the dynamic…
Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize, thereby reducing the magnitude of the interaction. Exchange integrals of…
We present an efficient approach to the electron correlation problem that is well-suited for strongly interacting many-body systems, but requires only mean-field-like computational cost. %which is based on orbital optimization of electron…
Quantum entanglement is a concept commonly used with reference to the existence of certain correlations in quantum systems that have no classical interpretation. It is a useful resource to enhance the mutual information of memory channels…