Exact Kohn–Sham potential of strongly correlated finite systems

We study model one-dimensional chemical systems (representative of their three-dimensional counterparts) using the strictly-correlated electrons (SCE) functional, which, by construction, becomes asymptotically exact in the limit of infinite coupling strength. The SCE functional has a highly non-local dependence on the density and is able to capture strong correlation within KohnSham theory without introducing any symmetry breaking. Chemical systems, however, are not close enough to the strong-interaction limit so that, while ionization energies and the stretched H2 molecule are accurately described, total energies are in general way too low. A correction based on the exact next leading order in the expansion at infinite coupling strength of the Hohenberg-Kohn functional largely improves the results.

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“…The diagonal contributions to the Hessian are readily evaluated to be (35) and the off-diagonal elements become (i = j)…”

Section: B Calculation Of the Zero-point Energies (Zpe) In 1dmentioning

confidence: 99%

Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

Malet

Mirtschink

Giesbertz

et al. 2014

Phys. Chem. Chem. Phys.

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“…Steps in the xc potential (a jump in the level of the xc potential over a relatively short distance) have been shown to be crucial for an accurate description of the electron density for a variety of ground-state and timedependent systems [5][6][7][8][9][10][11][12][13][14][15] , such as tunneling electrons and charge transfer/excitations. Atomic structure calculations by van Leeuwen et al 6 demonstrated that steps arise at the boundaries between atomic shells.…”

Section: Introductionmentioning

confidence: 99%

Origin of static and dynamic steps in exact Kohn-Sham potentials

2016

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Knowledge of exact properties of the exchange-correlation (xc) functional is important for improving the approximations made within density functional theory. Features such as steps in the exact xc potential are known to be necessary for yielding accurate densities, yet little is understood regarding their shape, magnitude and location. We use systems of a few electrons, where the exact electron density is known, to demonstrate general properties of steps. We find that steps occur at points in the electron density where there is a change in the 'local effective ionization energy' of the electrons. We provide practical arguments, based on the electron density, for determining the position, shape and height of steps for ground-state systems, and extend the concepts to time-dependent systems. These arguments are intended to inform the development of approximate functionals, such as the mixed localization potential (MLP), which already demonstrate their capability to produce steps in the Kohn-Sham potential.PACS numbers: 31.15. 71.15.Mb, 31.15.A,

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“…This model has two nice features: first the bonding and antibonding eigenstates are exactly known and they can be calculated by means of a superpotential, as it is done in supersymmetric quantum mechanics 43 ; second, in the limit of large inter-well distances, it reduces to a superposition of two Eckart wells 44 allowing to recover a model often used in molecular physics 45 .…”

Section: Numerical Solution For a Simple Two-atom Moleculementioning

confidence: 99%

Strong parameter renormalization from optimum lattice model orbitals

2017

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We revisit the old problem of which is the best single particle basis to express a Hubbard-like lattice model. A rigorous variational solution of this problem leads to equations in which the answer depends in a self-consistent manner on the solution of the lattice model itself. Contrary to naive expectations, for arbitrary small interactions, the optimized orbitals differ from the noninteracting ones, leading also to substantial changes in the model parameters as shown analytically and in an explicit numerical solution for a simple double-well one-dimensional case. At strong coupling, we obtain the direct exchange interaction with a very large renormalization with important consequences for the explanation of ferromagnetism with model hamiltonians. Moreover, in the case of two atoms and two fermions we show that the optimization equations are closely related to reduced density matrix functional theory thus establishing an unsuspected correspondence between continuum and lattice approaches.

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Exact Kohn–Sham potential of strongly correlated finite systems

Cited by 103 publications

References 28 publications

Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

Origin of static and dynamic steps in exact Kohn-Sham potentials

Strong parameter renormalization from optimum lattice model orbitals

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