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We develop a first-principles scheme based on the continued fraction approachan d ultrasoft pseudopotentials to calculate K-edge X-ray absorption spectra insolids. The method allows for calculations of K-edge X-ray absorption spectrain transition metal and rare-earths compounds with substantially reducedcutoffs respect to the norm-conserving case. We validate the method bycalculating Si and O K-edges in $\alpha$ quartz, Cu K-edge in Copper and inLa$_2$CuO$_4$. For the case of Si and O edges in $\alpha$ quartz and in Copperwe obtain a good agreement with experimental data. In the Cu K-edge spectra ofLa$_2$CuO$_4$, a material considered a real challeng e for density functionaltheory we attribute all the near-edge and far-edge peaks to single particleexcitations.

First principles calculations of X-ray absorption in an ultrasoft pseudopotentials scheme: from $\alpha$-quartz to high-T$_c$ compounds