COMPLEX-ROTATION CALCULATIONS FOR DOUBLY EXCITED STATES (Nℓ N’ℓ’) 2S+1L ᴨ [(2≤N≤ 3 ) ; ( 3 ≤N’≤4); (0 ≤ ℓ ≤ 2 ) AND ( 0 ≤ ℓ’ ≤ 2)] OF HELIUM ISOELECTRONIC SERIES

In this paper, we report the energies and resonant widths of the [(2s3s 1Se and 2s3s 3Se) (2s4s 1Se and 2s4s 3Se) (2s3p 1P0 and 2s3p 3P0) (2s4p 1P0 and 2s4p 3P0) (2p3p 1De and 2p3p 3De) (2p4p 1De and 2p4p 3De) (3s4s 1Se and 3s4s 3Se) (3s4p 1P0 and 3s4p 3P0) (3p4p 1De and 3p4p 3De) (3d4d 1Ge and 3d4d 1Ge)] Doubly Excited States of Helium isoelectronic series with nuclear charge Z (2 ≤ Z ≤ 10).Calculations are performedusing the Complex Rotation Method (CRM) in the framework of a variational procedure. The purpose of this study required a new correlated hydrogenic radial wave function combined with a Hylleraas wave function. The study leads to analytical expressions which are carried out under special MAXIMA computational program. This proposed variational procedure, leads to accurate results in good agreement with available other theoretical results.The present accurate data may be a useful guideline for future experimental and theoretical studies in the (Nℓ Nℓ) 2S+1Lᴨsystems.

Shannon, R\’enyi, Tsallis entropies of 1s$^2$-State Atomic System

The Shannon, R\’enyi, and Tsallis entropies of normalized electron density in position and momentum spaces are studied for the 1s${}^{2}$ state of Helium-isoelectronic series. Within single-zeta $\beta$-type orbitals ($\beta$TOs), the Hartree-Fock-Roothaan (HFR) calculations are considered and condensed on the most features of the physical results. The information quantities with atomic number deal with the interactions between the core and valence regions of the atom and thus enhance a geometrical understanding for the difference. It is assumed that the presented result might be a significant reference for further research topic on theoretical information quantities of atomic and molecular. Indeed, Our results have a good agreement in comparison with the previous published results.

Towards Density Functional Approximations from Coupled Cluster Correlation Energy Densities

<div> <div> <div> <p>(Semi-)local density functional approximations (DFAs) are the workhorse electronic structure methods in condensed matter theory and surface science. The correlation energy density εc(r) (a spatial function that yields the correlation energy Ec upon integration) is central to defining such DFAs. Unlike Ec, εc(r) is not uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct Ec for a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection between εc(r) and ρ. Herein, we present a new such approach by deriving εc(r) directly from the coupled- cluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron systems. To explore their usefulness for designing DFAs, we construct a semilocal functional to approximate the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as reference data, but guide the choice of the functional form, leading to a remarkably simple and accurate correlation functional for the Helium isoelectronic series. </p> </div> </div> </div>

Towards Density Functional Approximations from Coupled Cluster Correlation Energy Densities

<div> <div> <div> <p>(Semi-)local density functional approximations (DFAs) are the workhorse electronic structure methods in condensed matter theory and surface science. The correlation energy density εc(r) (a spatial function that yields the correlation energy Ec upon integration) is central to defining such DFAs. Unlike Ec, εc(r) is not uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct Ec for a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection between εc(r) and ρ. Herein, we present a new such approach by deriving εc(r) directly from the coupled- cluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron systems. To explore their usefulness for designing DFAs, we construct a semilocal functional to approximate the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as reference data, but guide the choice of the functional form, leading to a remarkably simple and accurate correlation functional for the Helium isoelectronic series. </p> </div> </div> </div>

Towards Density Functional Approximations from Coupled Cluster Correlation Energy Densities

<div> <div> <div> <p>(Semi-)local density functional approximations (DFAs) are the workhorse electronic structure methods in condensed matter theory and surface science. The correlation energy density εc(r) (a spatial function that yields the correlation energy Ec upon integration) is central to defining such DFAs. Unlike Ec, εc(r) is not uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct Ec for a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection between εc(r) and ρ. Herein, we present a new such approach by deriving εc(r) directly from the coupled- cluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron systems. To explore their usefulness for designing DFAs, we construct a semilocal functional to approximate the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as reference data, but guide the choice of the functional form, leading to a remarkably simple and accurate correlation functional for the Helium isoelectronic series. </p> </div> </div> </div>