A three-fold twin in B2₁

1/7: Introduction

Sometimes it makes good sense to use an unconventional space group setting. Probably the most common examples are P2₁/n and I2/a (instead of P2₁/c and C2/c). Such settings are preferred if they give a monoclinic β angle that is closer to 90° than the standard setting. Other common reasons for alternative settings stem from the inherent advantage of using the same (or similar) crystal axes for isotypic structures, or for those related by phase transition(s).

This tutorial describes a situation in which an unconventional setting, B2₁, is preferred using SHELXL because it facilitates efficient refinement of a pseudo-hexagonal three-fold twin. Given the complexity of the problem, this tutorial goes into some detail, not all of which will be relevant (or perhaps comprehensible) to all readers. The crystals in question are of 1-{(R)-1-[(3-oxo-2-isoindolinoyl)methyl]-2-propenyl}-5-methyl-2,3-indolinedione, (C₂₁H₁₆N₂O₄), a chiral compound from the laboratory of Prof. Barry Trost at Stanford University. The molecular structure looks like this:

In the paper describing the chemistry [Trost et al., Org. Lett. (2020), 22:7, 2584-2589.], the compound is designated '9mj', a moniker that we'll use throughout this tutorial. While writing this tutorial, it became clear that a rigorous description of the twinning required a rather more in depth analysis than could be covered (in section 6) in this tutorial. That has now been addressed in a second paper, written with Prof. Massimo Nespolo, who developed the specific nomenclature used to describe such systems. If you are interested, it might prove worthwhile to read Nespolo, Smaha, & Parkin (2020). Acta Cryst. B76, 643-649. Diffraction data were collected using CuKα X-rays by Rebecca Smaha at Stanford. To follow along you will need the diffraction data, available here:

9mj.hkl

... and the cell dimensions:

a = 15.5993(8) Å
b = 49.062(2) Å
c = 15.6099(8) Å
β = 119.896(2)°

The first thing to notice is that a ≈ c and β ≈ 120°, so it is tempting to transform this cell to a hexagonal setting. Indeed, the data collection software tried to push for a hexagonal cell. Hexagonal (or trigonal) symmetry, however, is not especially common for molecular compounds that don't themselves have 6-fold (or 3-fold) point symmetry. Three-fold twinning in monoclinic crystals with a ≈ c and β ≈ 120° is also not common in molecular crystals, but the phenomenon is well known; it even gets specific mention in the SHELXL manual. The crystal structure of 9mj delivers an additional twist, as we shall see.

This tutorial uses (and assumes familiarity with) the following programs:

XPREP for analysis and file setup
SHELXD for structure solution
SHELXL for structure refinement
ShelXle for model building
Mercury for visualization

To proceed, click on the 'Set up instructions using XPREP ' link below.