How to calculate a centroid-centroid separation?

[Rudi]

Sometimes I read in the literature that centroid-centroid separations of benzene rings are given, when pi-pi interactions are discussed. But how can I calculate them (with s.u.)? Is it possible with SHELXL to write them in the *.lst or *.cif file?

PS: These centroids can be easily calculated with Mercury and one can measure the distance via mouse click, but it is given without s.u.?

[pmueller]

This is possible but not trivial. There is no function in SHELXL, but you can work around the limitation.

Assume you have two phenyl rings, C(11) to C(16) and C(21) to C(26) and you want the distance between the centroids (with s.u. of course). First find the centroids with a program like XP and introduce dummy atoms at these coordinates. In XP you could use CENT /X c11 c12 c13 c14 c15 c16 and CENT /X c21 c22 c23 c24 c25 c26. This gives you X1A and X1B which you can write into a new .ins file using the FILE command.

Once you have the dummy atoms in your .ins file, reduce their occupancies to zero, fix the value of the Ueq and fix the coordinates by adding 10 to their value. Then introduce free commands to keep the two dummy atoms from binding to any real atoms. In the example here you'd probably need
FREE C11 X1A
FREE C12 X1A
FREE C13 X1A
FREE C14 X1A
FREE C15 X1A
FREE C16 X1A
FREE C21 X1B
FREE C22 X1B
FREE C23 X1B
FREE C24 X1B
FREE C25 X1B
FREE C26 X1B

Now, in order to calculate the distance between the two dummy atoms you include an RTAB command:
RTAB X1X2 X1A X1B

Don't calculate too many cycles in SHELXL to keep the other atoms from moving away from your dummy atoms. 1 Cycle is safe, but I have found that even 10 or more usually don't do much. You can check in XP whether the dummy atoms are still in the center of the rings after your refinement.

All this is to be done at the end of the refinement when the model does not change any more. For publication you probably should to remove all this dummy stuff from the .ins file. This is, as I said above, not exactly straightforward or obvious, but it gets the job done.

Cheers,

Peter

[Rudi]

Hi Peter, thank you for your answer. I supposed there is an elegant way similar to the MPLA instruction, which I didn't know. But this is obviously not the case.

btw: Is it possible to get distances in Mercury with s.u.?

[pmueller]

Is it possible to get distances in Mercury with s.u.?

I don't think so. But, of course, you can calculate the s.u.s yourself by hand. It is not magic but (relatively) simple math. Then again, the dummy atom method is not really complicated either...

[ALThompson]

Hi Peter, thank you for your answer. I supposed there is an elegant way similar to the MPLA instruction, which I didn't know. But this is obviously not the case.

btw: Is it possible to get distances in Mercury with s.u.?

In order to calculate any derived parameters (distances, angles etc.) you need the variance-covariance matrix. This is because the variance-covariance matrix includes details of the correlations between refined parameters as well as the errors on the parameters themselves. Thus, as far as I know, the only way to get accurate esds is from a full-matrix least-squares refinement as the variance-covariance matrix is generally not stored and transfered (e.g. in a CIF). A number of programs (e.g. PLATON and CrystalMaker?) will have a go at estimating esds on derived parameters from the errors on the refined parameters, but these are inherently incorrect.

More importantly, in your case, I think you need to consider what exactly you are trying to measure and propagate the errors accordingly. In order to do this, you may consider that the centroid of a ring is the average position of all the atoms in the ring and will thus be more precisely located than any of the individual atoms.



i.e. the esd of the centroid is given by:



However, is the centroid actually more accurate than the individual atoms? Had there been a real atom at the centroid of the ring, it would have an esd very similar to that of the surrounding atoms... Either way, the esd for the distance between two such points can then be calculated.

What SHELX actually does using Peter's method is unknown without intimate knowledge of the software. However, since the positional parameters are fixed, it seems that the errors associated with the atoms in the two rings and the correlations between them are being ignored.

A (with a lot of help from her learned friends).

[guber]

You can create centroids very easily in X-seed but I'm not certain about calculating the standard uncertainties on distances between them.

[johnewarren]

I've seen an interesting bug report on the Olex2 pages

ESDs with Geometric Measuerements
Currently, this is only possible if the structure has been refined with ShelXL and if the "MORE -3" command was present in the ShelX instructions (type 'editins' to add the MORE -3 instruction to the file, or use 'addins MORE -3' from the command line, which will do the same thing.

Once you have refined with the MORE -3 instuction, you can select the objects you wish to measure and type 'esd' - the output of the measurement will appear on the screen.

You can measure distances (two atoms selected), angles (three atoms selected), atom-plane distances (after you have defined a plane!) etc.

Could this be of help in the centroid, centroid puzzle? Only if we can add centroids I guess?

[ALThompson]

I've seen an interesting bug report on the Olex2 pages

ESDs with Geometric Measuerements
Currently, this is only possible if the structure has been refined with ShelXL and if the "MORE -3" command was present in the ShelX instructions (type 'editins' to add the MORE -3 instruction to the file, or use 'addins MORE -3' from the command line, which will do the same thing.

Once you have refined with the MORE -3 instuction, you can select the objects you wish to measure and type 'esd' - the output of the measurement will appear on the screen.

You can measure distances (two atoms selected), angles (three atoms selected), atom-plane distances (after you have defined a plane!) etc.

Could this be of help in the centroid, centroid puzzle? Only if we can add centroids I guess?

I haven't checked, but I believe this is because MORE -3 includes some secret knowledge in the the list file, including the variance-covariance matrix. Once you have that, many things become possible, but you still need to decide whether you are trying to calculate the esd on the difference between the average of the two sets of atomic positions, or the esd of an atom at the centre of the ring...

A.

[Rudi]

Only if we can add centroids I guess?

I would agree..

Recently a reviewer pleased me to mention a centroid-centroid separation in the text and he wrote me also a value (with s.u.). In view of the fact that only the final cif-file was available for the reviewer, I guess there exists however a possibility to calculate it, may be in Platon?

[ALThompson]

Only if we can add centroids I guess?

I would agree..

Recently a reviewer pleased me to mention a centroid-centroid separation in the text and he wrote me also a value (with s.u.). In view of the fact that only the final cif-file was available for the reviewer, I guess there exists however a possibility to calculate it, may be in Platon?

You can only calculate esds "correctly" if you have the variance-covariance matrix, which is not currently stored in a CIF. Thus, esds will have been generated as follows:

1) As a function of the refinement using the full variance-covariance matrix (see the discussion above), but you said he only had the CIF.

2) Using only the errors from the atoms and the cell, neglecting the off-diagonal terms of the variance-covariance matrix (which gives a result that can be wrong by 30+%, depending on the correlation between paramteters).

3) Estimated using some other mechanism (e.g. Carpenters rules; comparison with other distances in the structures; or some other guestimate like the average of the esds associated with the C-C distances for the ring, or even (2) with some arbitrary multiplier).

If it was done with software, a citation should be given, or if it is not a standard calculation listed in the cited software documentation, details should be given as appropriate.

A.

[Rudi]

Well, anyway in this context something in Platon is conspicuous: I read in a cif-file and used Publish -> Tables from the Platon task bar but the s.u.'s in the output where not identical to those in the cif-file. Thus Platon does apparently its own geometrical calculations.

[ALThompson]

Well, anyway in this context something in Platon is conspicuous: I read in a cif-file and used Publish -> Tables from the Platon task bar but the s.u.'s in the output where not identical to those in the cif-file. Thus Platon does apparently its own geometrical calculations.

My understanding is that it does just that as a validation mechanism, so that it can check that esds are "reasonable" as part of checkCIF...

A.

[Rudi]

Yes, but I didn't talk about checkCIF. I mean this possibility in Platon to generate tables with molecular geometry parameters (like ciftab).

[ALThompson]

Yes, but I didn't talk about checkCIF. I mean this possibility in Platon to generate tables with molecular geometry parameters (like ciftab).

I know, but as far as I know, all the checkCIF checks are part of PLATON, so all I was saying is that PLATON clearly *can* do these calculations, and presumably, that's what it is tabulating. I'm sure Ton has an explanation as to why it does this though, when the values obtained from the refinement are also available from the CIF. Initially I thought "PLATON should tabulate the values if they are there and make the best guess if they aren't," but that could lead to confusion. So, maybe it just always calculates them for itself. I'm sure Ton will explain though...

A.

[Rudi]

Here is not very much to read about this Platon feature:

http://www.cryst.chem.uu.nl/platon/pl000604.html