Extraction of directional electron-density features from diffraction data using spherical-harmonic decomposition

Authors

Panjikar, S., Weiss, M., Jayatilaka, D.

Abstract

Directional anisotropy in electron density provides key information about chemical bonding that is not readily accessible from conventional electron density maps. Here, a model-independent framework is presented for decomposing experimental structure factors into angular components using spherical harmonics. Reciprocal-space projection onto spherical harmonics followed by standard Fourier synthesis yields angularly filtered density maps. The {ell} = 0 component captures the isotropic part of the density,22 while the {ell} = 1 components resemble px, py and pz-like dipolar functions that highlight 23 directional electronic structure. Applications to high-resolution datasets, including urea, the Gly-Ala dipeptide and a 25 0.97 [A]{beta}lactamase structure, reveal chemically interpretable dipolar features associated 26 with carbonyl and amide bonds, N-H interactions and aromatic {pi} systems. Quantita27 tive analysis using bond centred sampling demonstrates stable dipolar signatures that 28 remain detectable under moderate resolution truncation. These results establish spherical-harmonic angular decomposition as a practical framework for extracting directional electronic information from crystallographic electron-density maps.

Preprint server: bioRxiv
The authors list and abstract were imported from bioRxiv on 10 Aug 2026.

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