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We model the exchange-correlation (XC) energy density of the Si crystal andatom as calculated by variational Monte Carlo (VMC) methods with a gradientanalysis beyond the local density approximation (LDA). We find the Laplacian ofthe density to be an excellent predictor of the discrepancy between VMC and LDAenergy densities in each system. A simple Laplacian-based correction to the LDAenergy density is developed by means of a least square fit to the VMC XC energydensity for the crystal, which fits the homogeneous electron gas and Si atomwithout further effort.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

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