Exact-exchange density-functional theory applied to a strongly inhomogeneous electron gas (original) (raw)
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Exact-exchange density functional theory for quasi-two-dimensional electron gases
Physical Review B, 2003
A simple exact-exchange density-functional method for a quasi-twodimensional electron gas with variable density is presented. An analytical expression for the exact-exchange potential with only one occupied subband is provided, without approximations. When more subbands are occupied the exact-exchange potential is obtained numerically. The theory shows that, in contradiction with LDA, the exact-exchange potential exhibits discontinuities and the system suffers a zero-temperature first-order transition each time a subband is occupied. Results suggesting that the translational symmetry might be spontaneously broken at zero temperature are presented. An extension of the theory to finite temperatures allows to describe a drop in the intersubband spacing in good quantitative agreement with recent experiments.
Descriptions of exchange and correlation effects in inhomogeneous electron systems
Physical Review B, 1979
Starting from a formula relating the exchange-correlation (XC) energy of the Kohn-Sham densityfunctional formalism to the XC hole, we discuss some general but approximate descriptions of XC effects in inhomogeneous electron systems, in particular valence electrons, using homogeneous-electron-gas data as input. The new descriptions have all the virtues of the local-density (LD) approximation, including the computational simplicity of a local XC potential, and it reduces to the latter in the proper limit. In addition, they have a physically motivated nonloca1 dependence on the electron density, which results in such desirable features as an asymptotical r ' behavior far away from, e.g. , atoms and a z ' behavior of the potential outside solid surfaces. %'e present two explicit forms of the XC energy functional, one which is exact for a system with almost constant density but with possibly spatially rapid variations, and another which is exact in some simple limits. Illustrations on atoms show them to reduce the error in the total energy by about one order of magnitude compared with the LD approximation. Applications to surfaces show a reasonable modeling of the image-potential effect but also illustrate shortcomings of the approximations. %e also point out shortcomings of two earlier methods to extend the LD approximation, the gradient expansion, and the expansion to second order in the density variations, when they are applied to inhomogeneous systems.
Physical Review B, 2016
The exchange-correlation potential experienced by an electron in the free space adjacent to a solid surface or to a low-dimensional system defines the fundamental image states and is generally important in surface-and nano-science. Here we determine the potential near the two-and onedimensional electron gases (EG), doing this analytically at the level of the exact exchange of the density-functional theory (DFT). We find that, at r ⊥ ≫ k −1 F , where r ⊥ is the distance from the EG and kF is the Fermi radius, the potential obeys the already known asymptotic −e 2 /r ⊥ , while at r ⊥ k −1 F , but still in vacuum, qualitative and quantitative deviations of the exchange potential from the asymptotic law occur. The playground of the excitations to the low-lying image states falls into the latter regime, causing significant departure from the Rydberg series. In general, our analytical exchange potentials establish benchmarks for numerical approaches in the low-dimensional science, where DFT is by far the most common tool.
Physical Review B, 2003
We use a variational quantum Monte Carlo realization of the adiabatic connection technique to calculate the most relevant quantities in Hohenberg-Kohn-Sham density functional theory for several strongly inhomogeneous electron-gas systems. Results for the coupling-constant dependence of the exchange-correlation energy, the pair-correlation function, the exchange-correlation hole, and the exchange and correlation energy densities are presented. Comparisons are made with the interaction strength interpolation ͑ISI͒ approximation, the local density approximation ͑LDA͒, the gradient expansion approximation ͑GEA͒, the generalized gradient approximation ͑GGA͒, and the weighted density approximation ͑WDA͒. The coupling-constant dependence of the exchange-correlation energy is accurately described by an ISI model that incorporates information on the strong-interaction limit. Unlike either the LDA or GEA, the WDA is successful in describing the nonlocal structure of the exchange-correlation hole. The LDA errors in the exchange-correlation energy density show a remarkable correlation with the Laplacian of the density. The GGA worsens the error in the integrated exchange-correlation energy as the inhomogeneity of the systems increases. This failure is shared by current meta-GGA functionals and is shown to be caused by the inability of these functionals to describe the LDA overestimation ͑in absolute value͒ of the exchange energy density around density maxima. It is suggested that this effect could be taken into account by including Laplacian terms in semilocal density functionals.
Quantum Monte Carlo analysis of exchange and correlation in the strongly inhomogeneous electron gas
Physical review letters, 2001
We use the variational quantum Monte Carlo method to calculate the density-functional exchange-correlation hole n(xc), the exchange-correlation energy density e(xc), and the total exchange-correlation energy E(xc) of several strongly inhomogeneous electron gas systems. We compare our results with the local density approximation and the generalized gradient approximation. It is found that the nonlocal contributions to e(xc) contain an energetically significant component, the magnitude, shape, and sign of which are controlled by the Laplacian of the electron density.
An exchange-correlation energy for a twodimensional electron gas
1995
We present the results of a variational Monte Carlo calculation of the exchange-correlation energy for a spin-polarized two-dimensional electron gas in a perpendicular magnetic field. These energies are a necessary input to the recently developed current-density functional theory. Landau-level mixing is included in a variational manner, which gives the energy at finite density at finite field, in contrast to previous approaches. Results are presented for the exchange-correlation energy and excited-state gap at ν = 1/7, 1/5, 1/3, 1, and 2. We parameterize the results as a function of r s and ν in a form convenient for current-density functional calculations.
Physical Review B
In a recent paper [Horowitz et al., Phys. Rev. B 107, 195120 (2023)], an alternative route has been proposed to construct the so-called exchange-correlation (xc) enhancement factor F xc of density-functional theory, defined as the enhancement of a realistic xc energy density over its local exchange-only counterpart. This new route, based on the ab initio calculation of the exact exchange energy density of a family of electron-density profiles, was implemented on the basis of jellium-slab exact-exchange self-consistent calculations. Here, we follow this route to construct a meta-generalized-gradient approximation (MGGA) for exchange from a nonuniform onedimensional coordinate scaling, which we implement on the basis of a number of calculations performed for model densities of electrons confined by infinite-barrier walls, as the electron system is shrunk from three to two dimensions. Our MGGA yields exchange energies that approach in the two-dimensional (2D) limit the exact exchange energy of a 2D electron gas, by appealing to a scaling of the MGGA exchange enhancement factor.
Exchange instability of the two-dimensional electron gas in semiconductor quantum wells
Physical Review B, 2002
A two-dimensional ͑2D͒ electron gas formed in a modulation-doped GaAs/Al x Ga 1Ϫx As single quantum well undergoes a first-order transition when the first excited subband is occupied with electrons, as the Fermi level is tuned into resonance with the excited subband by applying a dc voltage. Direct evidence for this effect is obtained from low-temperature photoluminescence spectra that display the sudden renormalization of the intersubband energy E 01 upon the abrupt occupation of the first excited subband. Calculations within densityfunctional theory, which treat the 2D exchange potential exactly, show that this thermodynamical instability of the electron system is mainly driven by intersubband terms of the exchange Coulomb interaction, thus being a unique but fundamental property of an electron system with more than one occupied subband.
Exchange and correlation in the quasi-one-dimensional electron gas: The local-field correction
Physical Review B, 1995
The local-field correction for the quasi-one-dimensional electron gas in cylindrical quantum wires with wire radius Ro is calculated within the sum-rule approach of the self-consistent theory of Singwi, Tosi, Land, and Sjolander. The local-Geld correction is expressed by a generalized Hubbard form with two coefficients, which are determined self-consistently. Numerical results for the exchange energy and the correlation energy are presented for 0(r, & 20, where r, is the random-phase-approximation parameter. We find that the exchange energy in the low-density regime is strongly enhanced compared to two and three dimensions: c"(r,~0 0)~-ln(r,)/r,. For high density we find c"(r,~O)~a /Ro, where a* is the Bohr radius. For the correlation energy we get c", (r,~O)~r, /Ro. The local-field correction strongly reduces the correlation energy for small carrier density if compared with the random-phase approximation. We study the pair-correlation function, the plasmon dispersion, and the compressibility, and we describe the effects of exchange and correlation on these quantities. The parameter for weak coupling in wire systems is described by R, =4r, a */mR0 & 1 and strong coupling corresponds to R,)1.