We present the first wavelet-based all-electron density-functional calculations to include gradient corrections and the first in a solid. Direct comparison shows this approach to be unique in providing systematic ``transparent convergence, convergence with a priori prediction of errors, to beyond chemical (millihartree) accuracy. The method is ideal for exploration of materials under novel conditions where there is little experience with how traditional methods perform and for the development and use of chemically accurate density functionals, which demand reliable access to such precision.
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