Automated Space Group Determination for Periodic Volumetric Data

Theoretical simulation methods such as self-consistent field theory (SCFT) have enabled the discovery of numerous novel ordered structures, making space-group identification an important and challenging problem. Existing methods for space-group determination are primarily designed for discrete atomic coordinates or diffraction data. However, many structures obtained from theoretical calculations are represented as periodic scalar fields sampled on regular grids within a unit cell, i.e., volumetric data. Moreover, the origin of such data is generally unknown and may not coincide with the standard origin of a candidate space group. Consequently, existing methods cannot be straightforwardly applied to these data. To address this issue, we propose an automated space-group determination method that combines reciprocal-space analysis with real-space verification. Candidate space groups are initially prescreened using systematic absence rules. For each prescreened space group, the origin of the scalar field is recovered using Fourier components whose phase angles are constrained by symmetry. This recovery is achieved by minimizing the deviations of these phase angles from their symmetry-allowed values. All symmetry operations of each candidate space group are subsequently applied to the registered scalar field. The space group is then assigned by quantifying the agreement between the original and symmetry-transformed volumetric data. The method is validated on several representative structures, yielding the correct space groups. Without requiring atomic-coordinate models, the proposed method provides a general framework for determining space groups from periodic volumetric data. It enables subsequent structural classification, analysis of formation mechanisms, and property calculations using standardized primitive cells.