The question is not really well formulated. Like: what is the height of Mount Everest (winter? summer? after/before a snow storm?) or what is the distance between two sides of a river at a definite point (windy? lull? or flooding/drought period?).

The cyclodextrin molecule is not a static something. Not only because the glucopyranoside rings can distort in- and outward from the "centre" of the molecules but because flexibility of the CH2OH group: their (constant) conformational change can give only an average value. The secondary OH is also not a rigid something, depending on the solvent, the hydrogen bonds can fix (or not, when they are lacking) the conformation of the sec. OHs.

Additionally, what does it mean at all the height? The distance of "theoretical" center of atoms? - I mean that creating parallel lines (with a theoretical plane) with some atoms and the distance of the lines. Or considering also the van der waals radius? Do we need to take into consideration the solvation? Please, consider that how can we determine (calculate) size of an atom. The size of the electron cloud is a statistical value.

But, anyway, do you think that does it matter if the the value is 7.8 angstrom or 7.6 or 8.2? (or larger).

A possible method is for the calculation of the height is from the xyz coordinates (eg. of the Xray structure) using a molecular drawing program - there are many free but, of course it is better to find that one which does not change the coordinates when you are rotating the molecule - e.g. by one of the following method:

1. arrange the molecule that the side is parallel with the screen; set center (0,0,0) of the hydrogen of the visually largest distance primary OH from the secondary ones. Then y coordinates of the secondary hydroxyls shows the heights of the atomic centers.

2a. You can do it for one secondary hydroxyl and do the same the for the primary ones

2b. - or you can simply subtract the appropriate coordinates from the previous sets.

Then you can calculate the average distance which is approximately the average height of the molecule, at the atom centers.

3. After it you can add the 2x of the H vdW radius and you can get a reasonable value.

See a attached figs (the green inside the cavity is the geometric center, it has importance, I used it to help in the orientation of the molecule only).

Another method might be if you are calculating the distances ("heights") on the same glucopyranoside rings and then calculates the average the largest values.

You can use, of course, the original coordinates of the OH hydrogens, too, but that requires more maths.

Please, note that the crystal geometries (coordinates) are not identical with the solution state structures.

Good luck.

http://www1.lsbu.ac.uk/water/cyclodextrin.html. It has references... but what is a 'strong' reference?

“Asking a question is the simplest way of focusing thinking…asking the right question may be the most important part of thinking.”

—Edward de Bono (1994).... Yes I probably not ask "technically right question", but this question lead to extensive knowledge and discussion present and at future also. I shall not forget to acknowledge Sir Laszlo Jicsinszk.

I mean this! Given 7.8 A( Ångström )... Kindly see the picture

• May you please see this attachment? Sir. Then you may get my point, Sir Laszlo Jicsinszky

Hi Raja,

First of all, I would like to call your attention that the attached schemes contain a small but essential bug. There is a common misbelief that the cyclodextrin cavity is hydrophobic: well no! The cavity is only less - although considerably - hydrophilic but not hydrophobic. See the pptx file for explanation. Almost all crystal structures of various cyclodextrins contain water in the cavity. If you see a really hydrophobic cyclodextrin, e.g. the peracetylated ones, the cavities contain water. Although the formation of the "inclusion" complex is explained by the replacement of the thermodynamically unstable location of water but usually water is necessary not only for the complex formation but for the dissociation, as well. In many cases the completely dried cyclodextrins are not forming complexes. Additionally, the hydrophilicity/polarity is often mixed with the "polarity". And, the cavity is not apolar, too! (see e.g.E. Juquera, Role of Hydrophobic Effect on the Noncovalent Interactions Between Salicylic Acid and a Series of b-Cyclodextrins. Journal of Colloid and Interface Science 216, 154–160, 1999)

But back to the original question:

I assume the values are from "direct" measurements and the values have been wandering from publication to publication. The direct means that many decades ago when computer modeling was only an unachievable dream chemist - usually to understand conformational and stereochemical problems - built so called calotte models.

Two popular methods were that time very common, the spacefilling model (calotte or CPK model) and the wire (really wire!) model (called Dreiding but do not mix it with the molecular mechanics Deriding forcefield!). And of course, they were very expensive because more or less but the atomic dimensions were modelized the real dimensions, at least at the level of the actual knowledge. In some old publications you can find also pictures, even about cyclodextrins (see: F. Cramer, Einschlußverbindungen. Angew. Chem. 64(16) 437-464, 1952; F. Cramer, W. Saenger, H.-Ch. Spatz, Inclusion Compounds. XIX.The Formation of Inclusion Compounds of a-Cyclodextrin in Aqueous Solutions. Thermodynamics and Kinetics. JACS 1967 14-20, 1967; p.6 M L. Bender, M. Komiyama Cyclodextrin Chemistry Springer, 1978; cover page and p23. of J. Szejtli Cyclodextrins and Their Inclusion Complexes, Akadémiai Kiadó; etc.)

After building the molecules you the dimension could be measured with a ruler. It is not precise but usually it was enough. Please, note that in the '950s years the X-ray structures of CDs were unknown.

The calculation ("measurement") of dimensions from real values not only touch some philosophical - and practical, too - questions but it is difficult - if not impossible - to find a software which can handle the situations for multicyclic compounds. I mentioned some of them in my first comment and I do not want to waste the place and your time to repeat it or adding some new aspects. I do not know a chemistry software which is able to visualize a molecule and fit a surface to the defined locations and measure the appropriate distances.

Because of an ongoing manuscript I have intended to calculate some more "precise" - means this anything - but at least more more recent data. Lack of enough time I pushed this from time to time but now I made a short calculation for you. I am attaching the structures and the calculations if you can deal more with this topic.

I used some neglects, (incorrect) approximations, and simplifications, like: - I used the crystal structures (structures without guests other than water);

- I did not calculated the distances in a trigonometrically correct way (I presumed that all atoms in the distance calculations were in plane, which is absolutely not correct);

- for the height calculation I aligned the molecules by eyes

- I used the covalent radius of the atoms which are not necessarily true (practically the same as in the CPK model);

- I used a non-crystallographic software, so the conversion of structures may give some errors in the coordinates;

- As a common weakness of the X-ray structures the - other than the e.g. the thermal uncertainties the lack of hydrogen atoms. Those are added by the software used for the conversions..

So, the obtained values are not really precise and although they are usually larger than the published values my opinion is that the differences are not really essential, at least in the real life.

If you (or other followers of this question) do not want to deal with the molecules I put here also a picture. The relevant literatures are in the spreadsheet, and I use the Biovia's Discovery Studio Visualizer (free) for the visualization and distance calculations. The relevant files are in the 7z file. I also converted the structures to PDB file, just in case, if you do not want to deal with them too much. Please, remember that PDB files contains the coordinates only for 3 decimal digits.

Good luck,

Laszlo

PS: please, forgive me the occasional errors in the spreadsheet.