Calculating Interplanar Angles with Associated ESD in TOPAS

TitasP

Hello,
I am Titas Pramanik, working at the University of Birmingham.
I am currently using TOPAS for Rietveld refinement of a ZIF-8 system and would like to calculate the angle (along with its estimated standard deviation, ESD) between two planes:

The plane formed by the 6-membered Zn ring (highlighted in red in the attached figure).
The plane of the 2-methylimidazolate (mlm) linker (highlighted in yellow).
To ensure planarity, I have applied the "flatten" macro to restrain the mlm ring and have also included bond distance restraints in the refinement (see attached screenshot of the .inp file for details).
While I was able to compute the interplanar angle in Mercury, it does not provide the associated ESD. Could you advise if it is possible to calculate this angle and its ESD directly in TOPAS?
Thank you in advance for your time and assistance.
Best regards,
Titas

rowlesmr

I'm guessing you could do it from first principles.

If you get three atoms' positions in cartesian coordinates from each plane, you can define two vectors in the plane, do their cross product to get the normal, and then dot product the two normals to get the angle between them.

johnsoevans

I don't know another way to Matthew's in topas if you're not working with rigid bodies.
The other thing to consider is how meaningful the esd will be. If you've applied a flatten macro then you are imposing restraints on the model (effectively by including extra observations) with no quantitative basis on how to weight them. This will influence the esds of many of the derived parameters such as the angle you're after.