scholarly journals Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory

2018 ◽  
Author(s):  
Tim Gould ◽  
Stefano Pittalis ◽  
Leeor Kronik
Keyword(s):  
Charge Transfer ◽  
Ground State ◽  
Molecular Model ◽  
Exchange Theory ◽  
Exact Results ◽  
Dissociation Curve ◽  
Excitation Energies ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Ground State Energies

By studying the lowest excitations of an exactly solvable one-dimensional \SP{}{soft-Coulomb} molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfers. Furthermore, we compute the approximate excitation energies obtained by using the exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [Gould and Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.<br><br>

scholarly journals Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory

2018 ◽  
Author(s):  
Tim Gould ◽  
Stefano Pittalis ◽  
Leeor Kronik
Keyword(s):  
Charge Transfer ◽  
Ground State ◽  
Molecular Model ◽  
Exchange Theory ◽  
Exact Results ◽  
Dissociation Curve ◽  
Excitation Energies ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Ground State Energies

By studying the lowest excitations of an exactly solvable one-dimensional \SP{}{soft-Coulomb} molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfers. Furthermore, we compute the approximate excitation energies obtained by using the exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [Gould and Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.<br><br>

scholarly journals Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory

2018 ◽  
Author(s):  
Tim Gould ◽  
Stefano Pittalis ◽  
Leeor Kronik
Keyword(s):  
Charge Transfer ◽  
Ground State ◽  
Molecular Model ◽  
Exchange Theory ◽  
Dissociation Curve ◽  
Excitation Energies ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Ground State Energies ◽  
Proof Of Principle

Paper providing a proof-of-principle that ensemble DFT can reproduce difficult charge transfer physics.<br><br> By studying the lowest excitations of an exactly solvable one-dimensional molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfers. Furthermore, we compute the approximate excitation energies obtained by using thee exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [Gould and Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.<br><br>

AN EXACTLY SOLVABLE ONE-DIMENSIONAL MODEL OF FERMIONS WITH CORRELATED HOPPING

1996 ◽  
Vol 10 (27) ◽  
pp. 3673-3683 ◽  
Author(s):  
IGOR N. KARNAUKHOV
Keyword(s):  
Critical Exponents ◽  
Ground State ◽  
Correlation Functions ◽  
State Energy ◽  
One Dimension ◽  
Supersymmetric Model ◽  
Dimensional Model ◽  
Long Distance ◽  
One Dimensional ◽  
Exactly Solvable

A new solution of supersymmetric model of electrons with correlated hopping which generalizes those obtained earlier is formulated. The model is solved in one dimension by the Bethe ansatz. The ground state energy is calculated, and the critical exponents describing the decrease of the correlation functions on long distance are derived.

All-Temperature Partition Function from Variationally Optimized Canonical Density Matrix

1983 ◽  
Vol 38 (12) ◽  
pp. 1373-1382
Author(s):  
R. Baltin
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Order Differential Equation ◽  
Bloch Equation ◽  
Mean Square ◽  
Spatial Variables ◽  
One Dimensional ◽  
Exactly Solvable ◽  
The Mean ◽  
The One

Abstract For the canonical density matrix C(r, r0,β) a variational ansatz C̄̄f = (1 - f̄) Ccl + f̄ Cgr is made where Ccl and Cgr are the classical and the ground state expressions which are exact in the high temperature (β → 0) and in the low-temperature limits (β → + ∞), respectively, and f̄ is a trial function subject to the restriction that f̄ → 0 for β → 0 and f̄ → 1 for β → ∞. With the approximation that f̄ be dependent only upon β, not upon spatial variables, the mean square error arising when Cf is inserted into the Bloch equation is made a minimum. The Euler equation for this variational problem is an ordinary second order differential equation for f̄=f(β) to be solved numerically. The method is tested for the exactly solvable case of the one dimensional harmonic oscillator.

Finite Temperature SU(2) LMG Model: Mean-Field Versus Exact Calculation

1997 ◽  
Vol 12 (38) ◽  
pp. 2985-2992 ◽  
Author(s):  
L. Brito ◽  
C. Da Providência ◽  
J. Da Providência
Keyword(s):  
Ground State ◽  
Temperature Effects ◽  
Variational Approach ◽  
State Energy ◽  
Mean Field ◽  
Strength Distribution ◽  
Schematic Model ◽  
Exact Results ◽  
Field Versus ◽  
Exactly Solvable

A variational approach is applied to the description of temperature effects in an N-particle exactly solvable schematic model, with SU(2) symmetry. The ground-state energy and the strength distribution for different couplings and temperatures are compared with the exact results.

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