Local correlation functional for electrons in two dimensions

Abstract

We derive a local approximation for the correlation energy in two-dimensional electronic systems. In the derivation we follow the scheme originally developed by Colle and Salvetti for three dimensions, and consider a Gaussian approximation for the pair density. Then, we introduce an ad-hoc modification which better accounts for both the long-range correlation, and the kinetic-energy contribution to the correlation energy. The resulting functional is local, and depends parametrically on the number of electrons in the system. We apply this functional to the homogeneous electron gas and to a set of two-dimensional quantum dots covering a wide range of electron densities and thus various amounts of correlation. In all test cases we find an excellent agreement between our results and the exact correlation energies. Our correlation functional has a form that is simple and straightforward to implement, but broadly outperforms the commonly used 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
• Density functional theory using an optimized exchange-correlation potential
• Two-dimensional limit of exchange-correlation energy functional approximations in density functional theory
• Diffusion Monte Carlo study of circular quantum dots
• Electronic structure of rectangular quantum dots
• Testing of two-dimensional local approximations in the current-spin and spin-density-functional theories
• Exchange-energy functionals for finite two-dimensional systems
• Correlation kinetic energy of many-electron systems: a modified Colle-Salvetti approach
• Spin projected unrestricted Hartree-Fock ground states for harmonic quantum dots
• Spin and Conductance-Peak-Spacing Distributions in Large Quantum Dots: A Density Functional Theory Study
• Erratum: Diffusion Monte Carlo study of circular quantum dots
• Spin-droplets in confined quantum Hall systems
• Variational Monte Carlo for Interacting Electrons in Quantum Dots

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• Inhomogeneity Induced and Appropriately Parameterized Semilocal Exchange and Correlation Energy Functionals in Two-Dimensions
• Engineered spin phase diagram of two interacting electrons in semiconductor nanowire quantum dots
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