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Structure factors obtained from diffraction experiments are one of the mostimportant quantities for characterizing the electronic and structuralproperties of materials. Methods for calculating this quantity from plane-wavedensity functional theory (DFT) codes are typically prohibitively expensive toperform, requiring the electron density to be constructed and evaluated ondense real-space grids. Making use of the projector functions found in both theVanderbilt ultrasoft pseudopotential and projector augmented wave methods, weimplement an approach to calculate structure factors which avoids the use of adense grid by separating the rapidly changing contributions to the electrondensity and treating them on logarithmic radial grids. This approach issuccessfully validated against structure factors obtained from all-electron DFTand experiments for three prototype systems, allowing structure factors to beobtained at all-electron accuracy at a fraction of the cost of previousapproaches for plane-wave DFT.

Accurate and efficient structure factors in ultrasoft pseudopotential and projector augmented wave DFT