Fourier-synthesis approach for static charge-density reconstruction from theoretical structure factors of CaB₆

In a pilot study, electron-density (ED) and ED Laplacian distributions were reconstructed for the challenging case of CaB₆ (Pearson symbol cP7) with conceptually fractional B-B bonds from quantum-chemically calculated structure-factor sets with resolutions 0.5 Å^-1 ≤ [sin(θ)/λ]_max ≤ 5.0 Å^-1 by means of Fourier-synthesis techniques. Convergence of norm deviations of the distributions obtained with respect to the reference ones was obtained in the valence region of the unit cell. The QTAIM (quantum theory of atoms in molecules) atomic charges, and the ED and ED Laplacian values at the characteristic critical points of the Fourier-synthesized distributions have been analysed for each resolution and found to display a convergent behaviour with increasing resolution. The presented method(exponent) (ME) type of Fourier-synthesis approach can qualitatively reconstruct all characteristic chemical bonding features of the ED from valence-electron structure-factor sets with resolutions of about 1.2 Å^-1 and beyond, and from all-electron structure-factor sets with resolutions of about 2.0 Å^-1 and beyond. Application of the ME type of Fourier-synthesis approach for reconstruction of ED and ED Laplacian distributions at experimental resolution is proposed to complement the usual extrapolation to infinite resolution in Hansen-Coppens multipole model derived static ED distributions.