Symmetry Analysis

The Symmetry module identifies the underlying crystallographic space group of the loaded structure. It is essential for reducing computational cost in DFT calculations and validating experimental structures.

Algorithmic Implementation

CView utilizes the Moyo library (a Rust ecosystem equivalent to Spglib) to perform symmetry determination. The analysis pipeline proceeds as follows:

1. Lattice Standardization: The internal Structure (Cartesian coordinates) is converted into a Moyo::Cell, utilizing the lattice vectors as columns of a $3\times3$ matrix.
2. Coordinate Transformation: Atomic positions are transformed from Cartesian ($r_{cart}$) to Fractional ($r_{frac}$) coordinates via the inverse lattice matrix: $$r_{frac} = M_{lattice}^{-1} \cdot r_{cart}$$
3. Symmetry Search: The algorithm searches for symmetry operations (rotations $R$ and translations $t$) that map the crystal onto itself: $$R \cdot r + t \equiv r' \pmod 1$$ where $r$ and $r'$ are atomic positions of the same species.

Tolerance (SYMPREC)

The code applies a default symmetry precision (SYMPREC) of 1e-3 Å. This tolerance accommodates minor numerical noise common in file formats like .cif or .xyz, ensuring that slightly distorted experimental structures are correctly identified.

Outputs

The module returns a SymmetryInfo struct containing:

• Space Group Number: The International Tables for Crystallography (ITA) number (1–230).
• International Symbol: The Hermann-Mauguin notation (e.g., $Pm\overline{3}m$, $Fm\overline{3}m$).
• Crystal System: The classification (Triclinic, Monoclinic, Orthorhombic, Tetragonal, Trigonal, Hexagonal, or Cubic).

Usage Reference

This analysis is performed "read-only" regarding the structure; it calculates descriptors without altering the atomic coordinates of the active tab.