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Localization via Density Functionals
1999After a discussion of the form of low-order density matrices built from strongly orthogonal geminals, density functional theory is utilized to deal with the phenomenon of Wigner electron crystallization. This is followed by a brief treatment of localized versus molecular orbital theories of electrons, illustrated by the stretched H2 molecule.
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The Journal of Chemical Physics, 2010
This work proposes a new term on the “Jacob’s ladder” of approximate exchange-correlation functionals in Kohn–Sham density functional theory. In these Rung 3.5 functionals, the exchange-correlation energy density at a point depends linearly (rather than quadratically) on the nonlocal Kohn–Sham one-particle density matrix in a finite neighborhood around
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This work proposes a new term on the “Jacob’s ladder” of approximate exchange-correlation functionals in Kohn–Sham density functional theory. In these Rung 3.5 functionals, the exchange-correlation energy density at a point depends linearly (rather than quadratically) on the nonlocal Kohn–Sham one-particle density matrix in a finite neighborhood around
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THE MARGINAL PROBABILITY DENSITY FUNCTIONS OF WISHART PROBABILITY DENSITY FUNCTION
Far East Journal of Theoretical Statistics, 2018Summary: Here we directly evaluate an \(\begin{pmatrix}{m+1}\\{2}\end{pmatrix}\)-dimensional integral \[ \int_{\mathbf{S}_{m}>0}|\mathbf{S}_m|^{\frac{n-m}{2}-1}\exp(-\mathrm{tr}(\mathbf{S}_{\mathbf{m}}))\mathrm{d}\mathbf{S}_m \] as an integral representation of Wishart multivariate gamma function \(\Gamma_m\left(\frac{n-1}{2}\right)\), by deriving the ...
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Density functional theory of complex transition densities
The Journal of Chemical Physics, 2006We present an extension of Hohenberg-Kohn-Sham density functional theory to the domain of complex local potentials and complex electron densities. The approach is applicable to resonance (Siegert) [Phys. Rev. 56, 750 (1939)] states and other scattering and transport problems that can be described by a normalized state of a Hamiltonian containing a ...
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Electroceramics for High-Energy Density Capacitors: Current Status and Future Perspectives
Chemical Reviews, 2021, Zhilun Lu, Linhao Li
exaly
Formulating energy density for designing practical lithium–sulfur batteries
Nature Energy, 2022Guangmin Zhou, Hao Chen
exaly
Interfacial engineering to achieve an energy density of over 200 Wh kg−1 in sodium batteries
Nature Energy, 2022Yuqi Li, Feixiang Ding, Xingguo Qi
exaly