Valence-electron distribution inMgB2by accurate diffraction measurements and first-principles calculations

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We use synchrotron x-ray and precision electron-diffraction techniques to determine accurately the structure factors of reflections that are sensitive to the valence-electron distribution in the superconductor ${\mathrm{MgB}}_{2}.$ These values deviate significantly from those calculated using the scattering factors of free (or neutral) atoms, but agree well with our calculated structure factors based on density-functional theory. Having experimentally established the reliability of our first-principles-based structure factors, we present electron-density maps of the redistribution of the valence electrons that takes place when hypothetical free atoms of Mg and B in ${\mathrm{MgB}}_{2}$ interact to form the real crystal.