Space Group from Absences
The determination as it is actually done: you have a data set, some classes of reflection are systematically missing, and the question is which of the 230 space groups you are allowed to be in. Answer the classes you have determined and the page names every group that fits — and the measurement that would shorten the list.
- You supply
- What you observe, class by class. Each menu offers only conditions some space group actually produces, so an answer can always be satisfied by something. Anything you have not determined is left alone and constrains nothing.
- Reading it
- A class left at not determined constrains nothing; answering it no condition asserts you looked and found nothing missing, which is what actually narrows the list. The strong answer is the one that can be wrong — and a wrong one removes the right group without saying so.
Worked examples: P21/c – the commonest determination there is · P21/c – the same data, empty classes too · Pbca – one pattern, two systems · P4cc – four groups, one reflection apart · Fd3m – diamond
Input
Answer only the classes you have actually determined. A class left at not determined constrains nothing, and that is the honest state for a zone you have not measured out far enough to be sure about — every answer you can give narrows the list, and a wrong one removes the right group without saying so.
What is missing?
Set the classes you have determined and this names every space group consistent with them. There are 230 groups and the eleven classes above separate them into 77 distinct answers, so the usual result is a short list rather than one group.
One missing reflection is not a condition. A structure factor can fall to nothing because of where the atoms happen to sit, with no symmetry involved — which is why a condition is read off a whole class going quiet, and why this form asks for classes rather than for a list of reflections you could not find.