scholarly journals Excitation energies from ground-state density-functionals by means of generator coordinates

2009 ◽  
Vol 11 (22) ◽  
pp. 4564 ◽  
Author(s):  
E. Orestes ◽  
A. B. F. da Silva ◽  
K. Capelle
Keyword(s):  
Ground State ◽  
State Density ◽  
Density Functionals ◽  
Excitation Energies ◽  
Ground State Density

scholarly journals Moments of the ground state density for the d-dimensional Fermi gas in an harmonic trap

2020 ◽  
pp. 2150018
Author(s):  
Peter J. Forrester
Keyword(s):  
Ground State ◽  
Matrix Theory ◽  
Fermi Gas ◽  
State Density ◽  
Harmonic Trap ◽  
Second Order ◽  
Closed Form Expression ◽  
Gaussian Unitary Ensemble ◽  
Linear Differential ◽  
Ground State Density

We consider properties of the ground state density for the [Formula: see text]-dimensional Fermi gas in an harmonic trap. Previous work has shown that the [Formula: see text]-dimensional Fourier transform has a very simple functional form. It is shown that this fact can be used to deduce that the density itself satisfies a third-order linear differential equation, previously known in the literature but from other considerations. It is shown too how this implies a closed form expression for the [Formula: see text]th non-negative integer moments of the density, and a second-order recurrence. Both can be extended to general Re[Formula: see text]. The moments, and the smoothed density, permit expansions in [Formula: see text], where [Formula: see text], with [Formula: see text] denoting the shell label. The moment expansion substituted in the second-order recurrence gives a generalization of the Harer–Zagier recurrence, satisfied by the coefficients of the [Formula: see text] expansion of the moments of the spectral density for the Gaussian unitary ensemble in random matrix theory.

Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed

2009 ◽  
Vol 5 (4) ◽  
pp. 902-908 ◽  
Author(s):  
John P. Perdew ◽  
Adrienn Ruzsinszky ◽  
Lucian A. Constantin ◽  
Jianwei Sun ◽  
Gábor I. Csonka
Keyword(s):  
Density Functional Theory ◽  
Ground State ◽  
Density Functional ◽  
State Density ◽  
Functional Theory ◽  
Ground State Density

scholarly journals An Analysis of Recent BLYP and PBE-Based Range-Separated Double-Hybrid Density Functional Approximations for Main-Group Thermochemistry, Kinetics and Noncovalent Interactions

2021 ◽  
Author(s):  
Asim Najibi ◽  
Marcos Casanova Paez ◽  
Lars Goerigk
Keyword(s):  
Ground State ◽  
Density Functional ◽  
Noncovalent Interactions ◽  
Main Group ◽  
Density Functionals ◽  
Excitation Energies ◽  
Third Order ◽  
Semi Empirical ◽  
Hybrid Density Functional ◽  
Electronic Ground

<div> <div> <div> <p>We investigate the effects of range separation of the exchange energy on electronic ground-state properties for recently published double-hybrid density functionals (DHDFs) with the extensive GMTKN55 database for general main-group thermochemistry, kinetics and noncovalent interactions. We include the semi-empirical range-separated DHDFs ωB2PLYP and ωB2GP-PLYP developed by our group for excitation energies, together with their ground-state-parametrized variants, which we denote herein as ωB2PLYP18 and ωB2GP-PLYP18. We also include the non-empirical range-separated DHDFs RSX-0DH and RSX-QIDH. For all six DHDFs, damping parameters for the DFT-D3 dispersion correction (and for its DFT-D4 variant) are presented. We comment on when the range-separated functionals can be more beneficial than their global counterparts, and conclude that range separation alone is no guarantee for overall improved results. We observe that the BLYP-based functionals generally outperform the PBE-based functionals. We finally note that the best-performing double-hybrid density functionals for GMTKN55 are still the semi-empirical range-separated double hybrids ωDSD3-PBEP86-D4 and ωDSD72-PBEP86-D4, the former of which includes a third-order perturbative correlation term in addition to the more conventional second- order perturbation that DHDFs are based upon.</p> </div> </div> </div>

Local ground state density in metal-dielectric-semiconductor structures

1983 ◽  
Vol 26 (3) ◽  
pp. 288-292
Author(s):  
D. I. Sheka ◽  
A. M. Voskoboinikov ◽  
V. I. Strikha
Keyword(s):  
Ground State ◽  
State Density ◽  
Semiconductor Structures ◽  
Ground State Density
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