How to calculate a centroid-centroid separation?

[oleg]

ESD on most of the structure parameters can be calculated in Olex2 once a refinement is done with shelxl with MORE command having a negative value, like MORE -3. This command informs shelxl to provide the full variance-covariance matrix. If you then define two planes, using the mpln command and select them, executing the 'esd' command will print plane to plane angle as well as the inter-centroid distance with the esd. However beware that if the atomic positions are not refined, for instance because of using AFIX 66, the calculated esd does not have much meaning. Other parameters, like plane to atom and plane centroid to atom distances, plane to a vector (defined either by a bond or two atoms) angles etc can also be calculated by providing the correct selection to the esd command.

[Rudi]

mpln? I know only MPLA in SHELXL..

[rjgildea]

mpln? I know only MPLA in SHELXL..

Hi Rudi,

mpln is an OLEX2 command, not a SHELXL command.

Just to clarify what Oleg said:

1) Refine with SHELXL with the MORE command having a negative value (such as MORE -3). In OLEX2 you can add such a command by typing

Code: Select all

addins more -3

in the command line. The negative value of a MORE command tells SHELXL to provide the full variance-covariance matrix in a file named "filename.mat", which is needed by OLEX2 to calculate esd's for derived parameters.

2) Define a plane in OLEX2 by selecting the atoms you want to be in the plane and typing

Code: Select all

mpln sel

in the command line. Do this for both planes in your case.

3) Select both planes in OLEX2 (they should turn green to indicate they are selected) and type

Code: Select all

esd

in the command line. This will then output the angle and centroid-centroid distances with their associated esd's.

If you don't currently have OLEX2 installed, you can obtain it from http://www.olex2.org

Hope that helps,

Richard

[Rudi]

If you don't currently have OLEX2 installed,

Yes, you're right, to be honest I have never used OLEX2.

I will take a look on it. Thank you!

[ALThompson]

Can you clarify exactly what this is measuring please? i.e Is this considering the centroid of the ring to be the average position of all the atoms in the ring? I ask because this would then be more precisely located than any of the individual atoms. As with all errors you should consider whether the numbers being produced are valid for the case in question. In this case, I wonder whether the centroids really are more accurate than the individual atoms, because this would make the esd on the distance between the centroids significantly smaller that the esd associated with the distance between any two pairs of atoms in the rings.

A.

[oleg]

Yes sure, it is better to use this kind of calculation with planes, as in this case the VcV elements of all contributing atoms are used. If the centroids are defined first, then (at least in Olex2) the covariance elements will be lost. Also the centroids will not be defined better (more accurate) than any atom contributing into the plane.

[ALThompson]

Yes sure, it is better to use this kind of calculation with planes, as in this case the VcV elements of all contributing atoms are used. If the centroids are defined first, then (at least in Olex2) the covariance elements will be lost. Also the centroids will not be defined better (more accurate) than any atom contributing into the plane.

Are you saying that you are actually giving the distance between two planes then? If so, what happens when the planes are not perfectly parallel?

A.

[oleg]

what I mean is that to calculate esd on the distance, you need 2x2 VcV matrix, each element of which is the 3x3 matrix of correlations between x,y and z. If you calculate a centroid (using

Code: Select all

cent sel

) in Olex2 we then have only esd of x,y and z, but not the full VcV matrix I mentioned above, therefore the calculation of esd on the distance between the centroids will not be as accurate as the calculation which is done on full atom list where that 2x2 matrix "resides"

If however you have defined two planes in Olex2 using the

Code: Select all

mpln sel

command as described above, for N atoms of plane A and M atoms of plane B, we create a VcV matrix of (N+M)x(N+M) dimension (Olex2 also takes the symmetry operations, if used for any of the plane atoms into account). Then we define a function to calculate the distance between the centroids as normally:

double calc_dist(A, B) {
vec3d c1, c2;
for i in [0..N]
c1 += A[i]
for i in [0..M]
c2 += B[i]
c1 /= N;
c2 /= M;
return c1.DistanceTo(c2);
}

using this function we calculate partial derivatives on all parameters and then sum the elements of the VcV matrix multiplied by the derivatives (as from the definition)...

[spea]

All PLATON calculations have to depend on the information in the CIF:

1 - The coordinates in the CIF are rounded and thus different from the values available
internally in SHELXL used for geometry calculations.

2 - Only variances are available

For that reason, distances, angles and torsions may have values that can deviate
slightly from those given by SHELXL (but within the reported s.u.)

Nearly all s.u.'s in derived quantities are calculated numerically (as opposed to the
use of analytical expressions) with the propagation of error formula
(but excluding the co-variances).

Ton

[oleg]

I have actually compared analytical vs numerical differentiation approaches to calculate esd's on what I could evaluate the analytical derivatives for, namely on distance, angle, torsion angle, plane centroid to an atom distance) and found no [significant] difference in the results.