# Prevalence and Significance of Approximate Symmetry in Z’ > 1 Orgainc Structures

## TL;DR

This paper explores the common occurrence of approximate symmetry in organic crystal structures with Z’ > 1, particularly in specific space groups.

## Contribution

The study identifies patterns of approximate symmetry in low-symmetry space groups and suggests possible formation mechanisms.

## Key findings

- Approximate symmetry is prevalent in organic structures with Z’ > 1 in space groups P1, C2, Pc, and Cc.
- Approximate inversion centers are common across all four space groups.
- Layer offsets of about a quarter of a layer width are typical in structures with approximate 2D symmetry.

## Abstract

Approximate symmetry that is periodic in at least one dimension has been found to be pervasive in organic structures with Z’ > 1 in space groups P1,1 C2,2 Pc,3 and now Cc, and in all space groups when Z’ > 4.4 The four space groups considered are the four most common triclinic and monoclinic groups for which the number of archived structures is less than 104. Structures in those groups were included in the surveys if R ≤ 0.050.

The approximate symmetry is usually obvious if the right view is found. It is usually easy to distinguish between excellent and too-good approximate symmetry.

Different space groups are associated with different types of approximate symmetry, but approximate inversion centers are common in all four groups.

While some of these structures were determined below a temperature-driven phase transition from a higher-symmetry phase, in most cases the required changes seem too large (e.g., more than 2° in a cell angle) for such a transition. Another possibility is nucleation in a higher-symmetry group followed by distortion during crystal growth.

In the case of approximate 2D symmetry adjacent layers are very often offset by ca. alayer/4. Illustrations show that such an offset allows the layers to fit together better than they would if the approximate symmetry were 3D.

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Source: https://tomesphere.com/paper/PMC12585518