Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions

Abstract

Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasi-one dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained, and give evidence of an interesting dimensional crossover between two and one dimensions.

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• Statistical Mechanics of the Uniform Electron Gas
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• Non-empirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound
• Challenging the Lieb-Oxford Bound in a systematic way
• Universal Functionals in Density Functional Theory
• Improved Lieb-Oxford bound on the indirect and exchange energies
• Integer Discontinuity of Density Functional Theory
• On the violation of a local form of the Lieb-Oxford bound
• Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Coulomb and Riesz potentials
• Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model
• A New Estimate on the Two-Dimensional Indirect Coulomb Energy
• Testing and Using the Lewin-Lieb Bound in Density Functional Theory
• Constraints of reduced density-matrix functional theory for the two-dimensional homogeneous electron gas
• Inhomogeneity Induced and Appropriately Parameterized Semilocal Exchange and Correlation Energy Functionals in Two-Dimensions
• Indirect Coulomb Energy for Two-Dimensional Atoms
• On the validity of power functionals for the homogeneous electron gas in reduced.density-matrix-functional theory
• Homogeneous electron gas in arbitrary dimensions
• One-Dimensional Lieb-Oxford Bounds
• On the lower bound on the exchange-correlation energy in two dimensions