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 and the first-order correction −1 /2r of (4.25), including the Hartree contribution 1 /2v H (r), for Hooke's atom with ω = 0.5. The energy densities are in the definition of the electrostatic potential of the exchange-correlation hole and are computed from the KS, physical and SCE pair density. Comparison is undertaken with the second-order correction from the asymptotic expansion of the physical pair density (4.25).](profile/Andre-Mirtschink/publication/270582389/figure/fig3/AS:669094890188814@1536536061754/Difference-between-the-energy-density-w-l-rr-and-the-first-order-correction-1-2r.png)
4: Difference between the energy density w λ [ρ](r) and the first-order correction −1 /2r of (4.25), including the Hartree contribution 1 /2v H (r), for Hooke's atom with ω = 0.5. The energy densities are in the definition of the electrostatic potential of the exchange-correlation hole and are computed from the KS, physical and SCE pair density. Comparison is undertaken with the second-order correction from the asymptotic expansion of the physical pair density (4.25).
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 in the definition of the...](profile/Andre-Mirtschink/publication/270582389/figure/fig2/AS:669094890184714@1536536061719/Energy-densities-w-l-rr-in-the-definition-of-the-electrostatic-potential-of-the_Q320.jpg)
 and the...](profile/Andre-Mirtschink/publication/270582389/figure/fig3/AS:669094890188814@1536536061754/Difference-between-the-energy-density-w-l-rr-and-the-first-order-correction-1-2r_Q320.jpg)
![Figure 5.2: Schematic representation of the functional W λ [ρ] as a...](profile/Andre-Mirtschink/publication/270582389/figure/fig5/AS:669094890197002@1536536061801/Schematic-representation-of-the-functional-W-l-r-as-a-function-of-l-for-the-SCE_Q320.jpg)
Dissertation thesis, Devision of Theoretical Chemistry, VU University Amsterdam, 2014
Monograph on:
- electronic structure problem, focus DFT
- strictly correlated electrons concept
- functional approximations by interpolations on the local energy density
- KS-SCE method with pilot applications
- the derivative discontinuity of the SCE functi...
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By making use of Janak's interpolation in the Kohn-Sham method, together with an explicit and differentiable functional of the density for the exchange-correlation energy, like LDA or GGA, the second derivative of the energy with respect to the number of electrons, N, is evaluated from the derivative of the highest occupied molecular orbital (HOMO)...
Citations
... While a considerable amount of work on the strictly-correlatedelectrons (SCE) formalism 1-3 within the framework of ground state Kohn-Sham (KS) density functional theory (DFT) has been carried out, 4-8 the study of its performances in the time domain is just starting. 9,10 The aim of this work is to begin a systematic investigation of the SCE functional in the context of time dependent problems, in order to understand its fundamental aspects and its potential in tackling challenging problems for the standard approximations employed in time-dependent (TD) DFT. ...
... In particular, the SCE state (6) has been proven to be the true minimizer for any number of particles N in one dimensional (1D) systems 43 and in any dimension for N = 2. 41 For more general cases, it has been shown that the minimizer might not be always of the SCE form. 44 Even in those cases, however, SCE-like solutions seem to be able to go very close to the true minimum, 45 and in several cases it is still possible to prove eqn (9). 45 In the low-density limit (or strong-coupling limit) the exact Hartree and exchange-correlation (Hxc) energy functional of KS DFT tends asymptotically to V SCE ee [n], 42,46 thus, in the following we denote v SCE ([n];r) of eqn (9) as v SCE Hxc ([n];r), to stress that this potential is the strong-coupling approximation to the standard Hxc potential of KS DFT. ...
... 44 Even in those cases, however, SCE-like solutions seem to be able to go very close to the true minimum, 45 and in several cases it is still possible to prove eqn (9). 45 In the low-density limit (or strong-coupling limit) the exact Hartree and exchange-correlation (Hxc) energy functional of KS DFT tends asymptotically to V SCE ee [n], 42,46 thus, in the following we denote v SCE ([n];r) of eqn (9) as v SCE Hxc ([n];r), to stress that this potential is the strong-coupling approximation to the standard Hxc potential of KS DFT. 4,46 Now that the basics of the SCE formalism at the ground state level have been reviewed, we can move to the time-dependent domain. ...
We investigate a number of formal properties of the adiabatic
strictly-correlated electrons (SCE) functional, relevant for time-dependent
potentials and for kernels in linear response time-dependent density functional
theory. Among the former, we focus on the compliance to constraints of exact
many-body theories, such as the generalised translational invariance and the
zero-force theorem. Within the latter, we derive an analytical expression for
the adiabatic SCE Hartree exchange-correlation kernel in one dimensional
systems, and we compute it numerically for a variety of model densities. We
analyse the non-local features of this kernel, particularly the ones that are
relevant in tackling problems where kernels derived from local or semi-local
functionals are known to fail.
