Gaussian approximations for the exchange-energy functional of current-carrying states: Applications to two-dimensional systems

Abstract

Electronic structure calculations are routinely carried out within the framework of density-functional theory, often with great success. For electrons in reduced dimensions, however, there is still a need for better approximations to the exchange-correlation energy functional. Furthermore, the need for properly describing current-carrying states represents an additional challenge for the development of approximate functionals. In order to make progress along these directions, we show that simple and efficient expressions for the exchange energy can be obtained by considering the short-range behavior of the one-body spin-density matrix. Applications to several two-dimensional systems confirm the excellent performance of the derived approximations, and verify the gauge-invariance requirement to be of great importance for dealing with current-carrying states.

References in corpus (15)

• Correlation energy and spin polarization in the 2D electron gas
• Two-dimensional limit of exchange-correlation energy functional approximations in density functional theory
• Electronic structure of rectangular quantum dots
• Testing of two-dimensional local approximations in the current-spin and spin-density-functional theories
• Collapse of the Electron Gas to Two Dimensions in Density Functional Theory
• Exchange-energy functionals for finite two-dimensional systems
• Dimensional crossover of the exchange-correlation energy at the semilocal level
• Comparison of exact-exchange calculations for solids in current-spin-density- and spin-density-functional theory
• Rectangular quantum dots in high magnetic fields
• Density gradients for the exchange energy of electrons in two dimensions
• Optimized Effective Potential Method in Current-Spin Density Functional Theory
• Correlation energy of two-dimensional systems: Toward non-empirical and universal modeling
• 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
• Energy lowering of current-carrying single-particle states in open-shell atoms due to an exchange-correlation vector potential

Cited by in corpus (17)

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• Becke-Johnson-type exchange potential for two-dimensional systems
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• 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
• First-principles quantum corrections for carrier correlations in double-layer two-dimensional heterostructures
• Exchange torque in noncollinear spin density functional theory with a semilocal exchange functional
• 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
• Exchange-correlation potentials for inhomogeneous electron systems in two dimensions from exact diagonalization: comparison with the local-spin-density approximation
• Large two-dimensional electronic systems: Self-consistent energies and densities at low cost
• Current density functional framework for spin-orbit coupling: Extension to periodic systems
• 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