The magnitude of the errors in the LDA energy densities has recently been
estimated by computing the energy density of bulk silicon with variational quantum
Monte Carlo (V-QMC) calculations. In Figure 3the difference between LDA
densities and the, V-QMC result is plotted. There are very significant errors in the
exchange and correlation energies but, as the exchange energy is generally
underestimated and the correlation energy overestimated, these errors tend to cancel.
The success of the LDA appears to be in part due to this cancellation of errors.
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