Exact exchange-correlation potentials of singlet two-electron systems

2017 ◽  
Vol 147 (16) ◽  
pp. 164117 ◽  
Author(s):  
Ilya G. Ryabinkin ◽  
Egor Ospadov ◽  
Viktor N. Staroverov
Keyword(s):  
Electron Systems ◽  
Exchange Correlation ◽  
Exact Exchange

scholarly journals Asymptotic Behavior of the Exchange-Correlation Energy Density and the Kohn-Sham Potential in Density Functional Theory: Exact Results and Strategy for Approximations

2019 ◽  
Author(s):  
Eli Kraisler
Keyword(s):  
Density Functional Theory ◽  
Asymptotic Behavior ◽  
Energy Density ◽  
Density Functional ◽  
Correlation Energy ◽  
Electron Systems ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Exact Exchange ◽  
Exact Factorization

The present work is a review of two analytical properties of the exact exchange-correlation (xc) functional in density-functional theory. These properties are the asymptotic behavior of the xc energy density per particle and the asymptotic behavior of the Kohn-Sham potential, in finite many-electron systems. The derivation of the asymptotic forms for both quantities is reviewed, employing the concepts of the adiabatic connection and of the xc hole with relation to the first quantity and the electron exact factorization approach for the second one. Furthermore, it is shown that the correct asymptotic behavior of one of the aforementioned quantities does not guarantee a correct behavior of the other. In this process, a new quantity, the xc hole response function, is defined and its exact exchange part is analytically derived. The extent to which existing xc approximations satisfy the named exact properties is reviewed and the relationship between correct asymptotics and freedom from one-electron self-interaction in DFT is discussed. Finally, a strategy for development of advanced approximations for exchange and correlation with a correct asymptotic behavior is suggested.<br>

scholarly journals Asymptotic Behavior of the Exchange-Correlation Energy Density and the Kohn-Sham Potential in Density Functional Theory: Exact Results and Strategy for Approximations

2019 ◽  
Author(s):  
Eli Kraisler
Keyword(s):  
Density Functional Theory ◽  
Asymptotic Behavior ◽  
Energy Density ◽  
Density Functional ◽  
Correlation Energy ◽  
Electron Systems ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Exact Exchange ◽  
Exact Factorization

The present work is a review of two analytical properties of the exact exchange-correlation (xc) functional in density-functional theory. These properties are the asymptotic behavior of the xc energy density per particle and the asymptotic behavior of the Kohn-Sham potential, in finite many-electron systems. The derivation of the asymptotic forms for both quantities is reviewed, employing the concepts of the adiabatic connection and of the xc hole with relation to the first quantity and the electron exact factorization approach for the second one. Furthermore, it is shown that the correct asymptotic behavior of one of the aforementioned quantities does not guarantee a correct behavior of the other. In this process, a new quantity, the xc hole response function, is defined and its exact exchange part is analytically derived. The extent to which existing xc approximations satisfy the named exact properties is reviewed and the relationship between correct asymptotics and freedom from one-electron self-interaction in DFT is discussed. Finally, a strategy for development of advanced approximations for exchange and correlation with a correct asymptotic behavior is suggested.<br>

Developing new and understanding old approximations in TDDFT

2020 ◽  
Vol 224 ◽  
pp. 382-401
Author(s):  
Lionel Lacombe ◽  
Neepa T. Maitra
Keyword(s):  
Path Integration ◽  
Coupling Constant ◽  
Exchange Correlation ◽  
Exchange Correlation Potential ◽  
Correlation Potential ◽  
Exact Exchange

In this paper we derive a new expression for the exact exchange–correlation potential from a coupling-constant path integration.

Exact exchange-correlation potentials in spin-density functional theory and their discontinuities at unit electron number

2009 ◽  
Vol 87 (10) ◽  
pp. 1268-1272 ◽  
Author(s):  
John P. Perdew ◽  
Espen Sagvolden
Keyword(s):  
Density Functional Theory ◽  
Spin Density ◽  
Density Functional ◽  
Electron Number ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Exchange Correlation Potential ◽  
Correlation Potential ◽  
Exact Exchange ◽  
Physical Consequences

The exact exchange-correlation potential of Kohn–Sham density functional theory is known to jump discontinuously by a spatial constant as the average electron number, N, crosses an integer in an open system of fluctuating electron number, with important physical consequences for charge transfers and band gaps. We have recently constructed an essentially exact exchange-correlation potential vxc for N electrons (0 ≤ N ≤ 2) in the presence of a –1/r external potential, i.e., for a ground ensemble of H+ ion, H atom, and H– ion densities. That construction illustrates the discontinuity at N = 1, where it equals IH – AH, the positive difference between the ionization energy and the electron affinity of the hydrogen atom. Here we construct the corresponding essentially exact spin-up and spin-down exchange-correlation potentials vxc,↑ and vxc,↓ of the Kohn–Sham spin-density functional theory, more commonly used for electronic structure calculations, for the ground ensemble with most-negative z-component of spin (or equivalently in the presence of a uniform magnetic field of infinitesimal strength). The potentials vxc, vxc,↑, and vxc,↓, which vanish as r → ∞ (except when N approaches an integer from above), are identical for 0 ≤ N ≤ 1 and for N = 2 but not for 1 < N < 2. We find that the majority or spin-down potential has a spatially constant discontinuity at N = 1 equal to IH – AH. The minority or spin-up potential has a discontinuity which is this constant in one order of limits, but is a spatially varying function in a different order of limits. This order-of-limits problem is a consequence of a special circumstance: the vanishing of the spin-up density at N = 1.

scholarly journals Accurate Prediction of the S1 Excitation Energy in Solvated Azobenzene Derivatives via Embedded Orbital-Tuned Bethe-Salpeter Calculations

2019 ◽  
Author(s):  
Aseem Rajan Kshirsagar ◽  
Gabriele D'Avino ◽  
Xavier Blase ◽  
Jing Li ◽  
Roberta Poloni
Keyword(s):  
Excitation Energy ◽  
Absolute Error ◽  
Hybrid Functional ◽  
Vertical Excitation ◽  
Exchange Correlation ◽  
Vertical Excitation Energy ◽  
Exact Exchange ◽  
Cis And Trans ◽  
Azobenzene Derivatives ◽  
Band Separation

By employing the Bethe-Salpeter formalism with a non-equilibrium embedding scheme, we demonstrate that the paradigmatic case of S<sub>1</sub> band separation between cis and trans in azobenzene derivatives can be computed with excellent accuracy compared to experimental optical spectra. Besides embedding, we show that the choice of the Kohn-Sham exchange correlation functional for DFT is critical, despite the iterative convergence of GW quasiparticle energies. We address this by using a global hybrid functional, PBEh, with the amount of exact exchange fulfilling the Koopman’s theorem for DFT hence yielding an environment-consistent ionization potential.<br>This method yields the first vertical excitation energy of 20 azo molecules with a mean absolute error as low as 0.06 eV, up to three times smaller compared to standard functionals such as M06-2X and PBE0, and five times smaller compared to recent TDDFT results.<br><br>

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