Density gradients for the exchange energy of electrons in two dimensions

Abstract

We derive a generalized gradient approximation to the exchange energy to be used in density functional theory calculations of two-dimensional systems. This class of approximations has a long and successful history, but it has not yet been fully investigated for electrons in two dimensions. We follow the approach originally proposed by Becke for three-dimensional systems [Int. J. Quantum Chem. 23, 1915 (1983), J. Chem. Phys. 85, 7184 (1986)]. The resulting functional depends on two parameters that are adjusted to a test set of parabolically confined quantum dots. Our exchange functional is then tested on a variety of systems with promising results, reducing the error in the exchange energy by a factor of 4 with respect to the simple local density approximation.

References in corpus (14)

• Correlation energy and spin polarization in the 2D electron gas
• Full configuration interaction approach to the few-electron problem in artificial atoms
• Two-dimensional limit of exchange-correlation energy functional approximations in density functional theory
• Electronic structure of rectangular quantum dots
• Simple Analytical Particle and Kinetic Energy Densities for a Dilute Fermionic Gas in a d-Dimensional Harmonic Trap
• Pair-distribution functions of the two-dimensional electron gas
• Testing of two-dimensional local approximations in the current-spin and spin-density-functional theories
• Exchange-energy functionals for finite two-dimensional systems
• Self-consistent calculation of the electron distribution near a Quantum-Point Contact in the integer Quantum Hall Effect
• Local correlation functional for electrons in two dimensions
• Exchange-correlation orbital functionals in current-density-functional theory: Application to a quantum dot in magnetic fields
• Electron localization function for two-dimensional systems
• Exact first-order density matrix for a d-dimensional harmonically confined Fermi gas at finite temperature
• Magnetoplasmon excitations in arrays of circular and noncircular quantum dots

Cited by in corpus (20)

• Libxc: a library of exchange and correlation functionals for density functional theory
• Becke-Johnson-type exchange potential for two-dimensional systems
• Gaussian approximations for the exchange-energy functional of current-carrying states: Applications to two-dimensional systems
• On the Kirzhnits gradient expansion in two dimensions
• Generalized gradient approximation correlation energy functionals based on the uniform electron gas with gap model
• Correlation energy of two-dimensional systems: Toward non-empirical and universal modeling
• Exact Coulomb cutoff technique for supercell calculations in two dimensions
• Global hybrids from the semiclassical atom theory satisfying the local density linear response
• Orbital-free energy functional for electrons in two dimensions
• Parameter-free density functional for the correlation energy in two dimensions
• Laplacian-level density functionals for the exchange-correlation energy of low-dimensional nanostructures
• Semi-local density functional for the exchange-correlation energy of electrons in two dimensions
• Semi-local Exchange Energy Functional For Two-Dimensional Quantum Systems: A Step Beyond Generalized Gradient Approximations
• Colle-Salvetti-type local density functional for the exchange-correlation energy in two dimensions
• Exchange and correlation energy functionals for two-dimensional open-shell systems
• Constraints of reduced density-matrix functional theory for the two-dimensional homogeneous electron gas
• Exchange-correlation potentials for inhomogeneous electron systems in two dimensions from exact diagonalization: comparison with the local-spin-density approximation
• Inhomogeneity Induced and Appropriately Parameterized Semilocal Exchange and Correlation Energy Functionals in Two-Dimensions
• Density-functional approach to the band gaps of finite and periodic two-dimensional systems
• Stability of spin droplets in realistic quantum Hall devices