Beyond the local approximation to exchange and correlation: the role of the Laplacian of the density in the energy density of Si

Abstract

We model the exchange-correlation (XC) energy density of the Si crystal and atom as calculated by variational Monte Carlo (VMC) methods with a gradient analysis beyond the local density approximation (LDA). We find the Laplacian of the density to be an excellent predictor of the discrepancy between VMC and LDA energy densities in each system. A simple Laplacian-based correction to the LDA energy density is developed by means of a least square fit to the VMC XC energy density for the crystal, which fits the homogeneous electron gas and Si atom without further effort.

arXiv comment4 pages, 3 figures, submitted to Phys. Rev. Lett

References in corpus (3)

• Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids
• Quantum Monte Carlo Analysis of Exchange and Correlation in the Strongly Inhomogeneous Electron Gas
• Comparative study of density functional theories of the exchange-correlation hole and energy in silicon

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• Reproducibility of density functional approximations: how new functionals should be reported
• The scaling properties of exchange and correlation holes of the valence shell of second row atoms