A New Method for the Atomic Ground-State Energy in the Screened Coulomb Potential

The new method proposed recently by Friedberg,Lee and Zhao is applied to the derivation of the atomic ground-state energy with the inclusion of the screening effect.The present results are compared with those obtained in the pure Coulomb potential and by the variational approach.The overall good results are obtained with this new method.     

Correlation functional in screened‐exchange density functional theory procedures

In the present study, we have explored several prospects for the further development of screened‐exchange density functional theory (SX‐DFT) procedures. Using the performance of HSE06 as our measure, we find that the use of alternative correlation functionals (as oppose to PBEc in HSE06) also yields adequate results for a diverse set of thermochemical properties. We have further examined the performance of new SX‐DFT procedures (termed HSEB‐type methods) that comprise the HSEx exchange and a (near‐optimal) reparametrized B97c (c _OS,0 = c _SS,0 = 1, c _OS,1 = −1.5, c _OS,2 = −0.644, c _SS,1 = −0.5, and c _SS,2 = 1.10) correlation functionals. The different variants of HSEB all perform comparably to or slightly better than the original HSE‐type procedures. These results, together with our fundamental analysis of correlation functionals, point toward various directions for advancing SX‐DFT methods. © 2017 Wiley Periodicals, Inc.     

Shannon entropy and Fisher information for screened Kratzer potential

In this paper, Shannon entropy and Fisher information is studied for the screened Kratzer potential model and compared with the screened Coulomb in three dimensions. Our results showed similar higher-order characteristic behavior for position and momentum space. Our numerical results showed that increases in the accuracy of predicting particle location occurred in the position space. Our result shows that the sum of the position and momentum entropies satisfies the lower-bound Berkner, Bialynicki-Birula, and Mycieslki inequality. The Stam-Cramer-Rao inequalities relation for Fisher information and the expectation values were also satisfied for the different eigenstates.     

Mass of a lattice polaron from an extended Holstein model using the Yukawa potential

Renormalization of the mass of an electron is studied within the framework of the Extended Holstein model at strong coupling regime and nonadiabatic limit. In order to take into account an effect of screening of an electron-phonon interaction on a polaron it is assumed that the electron-phonon interaction potential has the Yukawa form and screening of the electron-phonon interaction is due to the presence of other electrons in a lattice. The forces are derived from the Yukawa type electron-phonon interaction potential. It is emphasized that the early considered screened force of (Kornilovitch (1998), Spencer et al. (2005), Hague et al. (2006), Hague and Kornilovitch (2009)) Refs. [7], [18], [19] and [22] is a particular case of the force deduced from the Yukawa potential and is approximately valid at large screening radiuses compared to the distances under consideration. The Extended Holstein polaron with the Yukawa type potential is found to be a more mobile than polaron studied in early works at the same screening regime.     

A New Method for the Atomic Ground-State Energy in the Screened Coulomb Potential

The new method proposed recently by Friedberg,Lee and Zhao is applied to the derivation of the atomic ground-state energy with the inclusion of the screening effect.The present results are compared with those obtained in the pure Coulomb potential and by the variational approach.The overall good results are obtained with this new method.``     

Supersymmetric solutions of <Emphasis Type="Italic">PT</Emphasis>-/non-<Emphasis Type="Italic">PT</Emphasis>-symmetric and non-Hermitian screened Coulomb potential via Hamiltonian hierarchy inspired variational method

The supersymmetric solutions of PT -symmetric and Hermitian/non-Hermitian forms of quantum systems are obtained by solving the Schr?dinger equation for the Exponential-Cosine Screened Coulomb potential. The Hamiltonian hierarchy inspired variational method is used to obtain the approximate energy eigenvalues and corresponding wave functions.      

Bound states of a more general exponential screened Coulomb potential

An alternative approximation scheme has been used in solving the Schr?dinger equation to the more general case of exponential screened Coulomb potential, V(r) = −(a/r)[1 + (1 + br)e ^−2br ]. The bound state energies of the 1s, 2s and 3s-states, together with the ground state wave function are obtained analytically upto the second perturbation term.      

Unnatural parity states of helium with screened Coulomb potentials

Effect of screened Coulomb (Yukawa) potentials on the doubly excited meta‐stable bound states and the resonance states with unnatural parities of the helium atom have been investigated in the framework of stabilization method using CI‐type basis functions. A total of 54 resonances (6 each of ¹D^o and ³D^o states, 12 each of ¹F^e and ³F^e states, 9 each of ¹G^o and ³G^o states) below the He⁺(3P) thresholds have been estimated by calculating the density of resonance states using a stabilization method. The resonances belong to the different 3lnl′ (n ≥ 3) series. We have also calculated the doubly excited ^1,3F^e and ^1,3G^o meta‐stable bound states of He atom below the He⁺ (2P) thresholds. The resonance energies and widths along with the meta‐stable bound states energies are reported for various screening parameters. In free atom case, some of the F‐wave resonance states and most of the cases, F‐ and G‐wave resonance widths are reported for the first time. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Dispersion coefficients for Li+–H and Li+–He systems with coulomb and screened coulomb potentials

Exploiting powerful computational aspects and highly correlated exponential wave functions for two‐electron atoms, we have investigated the effects of screened Coulomb interaction on the hexadecapole polarizability of Li⁺(1¹S), and the dispersion coefficients C₆, C₈, C₁₀, and C₁₂ for interaction of Li⁺ with H and He atoms in their ground states. The dispersion coefficients and hexadecapole polarizability for different screening parameters ranging from 0 to 1.0 a are reported. In the unscreened case, the hexadecapole polarizability of Li⁺, and the dispersion C₁₂ coefficients for Li⁺–H and Li⁺–He system are reported for the first time in the literature. The C₆, C₈, and C₁₀ coefficients for the unscreened cases are comparable with the reported results. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

A New Version of the Fast Multipole Method for Screened Coulomb Interactions in Three Dimensions

We present a new version of the fast multipole method (FMM) for screened Coulomb interactions in three dimensions. Existing schemes can compute such interactions in O(N) time, where N denotes the number of particles. The constant implicit in the O(N) notation, however, is dominated by the expense of translating far-field spherical harmonic expansions to local ones. For each box in the FMM data structure, this requires 189p⁴ operations per box, where p is the order of the expansions used. The new formulation relies on an expansion in evanescent plane waves, with which the amount of work can be reduced to 40p²+6p³ operations per box.