What are the limits of size differences in a host–guest complex?

We learn in my chemistry course that there must be a snug fit for a host-guest complex to form. So, something like benzene (0.6 nm in diameter) can form a host-guest complex with a β-cyclodextrin host (0.7 nm cavity). Other than this vaguely-worded ‘snug-fit’ rule, we are not given a lot of information of what molecules would fit.

Would something like methane (0.38 nm diameter, according to Wikipedia) form a stable host–guest complex with β-cyclodextrin, or would it be too small?

I know that methyl red fits in a β-cyclodextrin cavity, but what about something slightly larger like anthracene?

These questions are a small part of something that contributes a small amount towards my overall course grade. Please, if you are able to, give me some kind of guidance so that I can work out answers on my own. I've tried to look independently online but I come up with nothing.

• Why do you think anthracene is larger then methyl red? Would orange be bigger then banana if they had same volume? Mar 27, 2021 at 15:57

The size of the cavity is one of the many factors collaborating to host-guest chemistry with cyclodextrin (CD). For example, depending on the size and the properties of the guest molecule, CD may form complexes with either the entire molecule or only a part of the molecule (The diameter and the volume of the cavity of β-CD are around $$\pu{7.8 Å}$$ ($$\pu{0.78 nm}$$) and $$\pu{262 Å^3}$$, respectively, and β-CD complexes well with aromatic rings; Ref.1). It is accepted in general (Ref.2) that the binding forces involved in complex (host-guest) formation are:

1. Van der Waals type interactions (or hydrophobic interactions) between the hydrophobic units of the guest molecules and the CD cavity.
2. Hydrogen bond between the polar functional groups of the guest molecules and the hydroxyl groups of the CD rims.
3. Release of high energy water molecules from the cavity during the complex formation process.
4. Release of strain energy into the ring structure system of the CD.

Note that the role of hydrogen bonding is not universal since stable complexes are formed with hosts and hydrophobic guests such as benzene derivatives (Ref.3), which do not form hydrogen bonds.

Also, regardless of which types of stabilizing forces are involved, the most important factors in determining the stability of the inclusion of the complexes are: (i) The geometric capability (which is the OP's concern); (ii) the polarity of the guest molecule; (iii) medium; and (iv) the temperature. The reference 2 states that:

Geometric, rather than the chemical factors, are critical in determining the type of guest molecules that can penetrate into the cavity. If the guest is too small, it passes easily through the cavity and the bond will be weak or will not occur. The formation of complexes with the molecules significantly larger than the cavity is also possible, but only some limited groups or the side chains penetrate into the cavity.

It is also important to note that cavity size of CD seems to depend on the method used by the researcher (Ref.4). For instance, Ref.2 reported that inner diameters of $$\pu{5.7 Å}$$ for $$\alpha$$-cyclodextrin, $$\pu{7.8 Å}$$ for $$\beta$$-cyclodextrin, and $$\pu{9.5 Å}$$ for $$\gamma$$-cyclodextrin, but did not verify each was the upper or the lower or middle diameter. Meantime, Ref.3 reported that top and bottom inner-diameters of $$5.3$$ and $$\pu{4.7 Å}$$ for $$\alpha$$-cyclodextrin, $$6.5$$ and $$\pu{6.0 Å}$$ for $$\beta$$-cyclodextrin, and $$8.3$$ and $$\pu{7.5 Å}$$ for $$\gamma$$-cyclodextrin. Therefore, it is hard to predict which molecule would bind to appropriate CD without knowing exact parameters of their cavity. Regardless of the reported cavity sizes, Ref.3 shows that the grafting of $$\beta$$-cyclodextrin to silica gel conveniently removed water soluble organic molecules with different sizes such as p-nitrophenol, p-nitroaniline, m-nitrophenol, p-chlorophenol, and phenol.

It is also evident that cyclodextrin-catalyzed organic synthesis can be achieved using $$\beta$$-cyclodextrin as the catalyst. In these reactions, you may find part of starting materials with different sizes making stable host-guest complexes with $$\beta$$-CD (Ref.5).

On the other hand, an identical molecule can be bound to all three CDs ($$\alpha$$-, $$\beta$$-, and $$\gamma$$-cyclodextrin) grafted to a biomolecule with different impact (Ref.5). For example, $$\mathrm{^1H \ NMR}$$ studies suggested that methyl-$$\beta$$-CD forms inclusion complexes with the lipid guest molecules such as cholesterol, linoleic acid, and $$\beta$$-sitosterol within the CD cavity regardless of their sizes (Ref.6):

Note: Although it is not relevant to the question in hand, it is worth noting that the chiral nature of the cavity in these molecules makes them useful for enantiomeric separation applications (Ref.7).

References:

1. Vijaykumar Parmar, Gayatri Patel, Nedal Y. Abu-Thabit, “Chapter 20: Responsive cyclodextrins as polymeric carriers for drug delivery applications,” In Stimuli Responsive Polymeric Nanocarriers for Drug Delivery Applications, Volume 1: Types and Triggers (Woodhead Publishing Series in Biometerials); Abdel Salam Hamdy Makhlouf, Nedal Y. Abu-Thabit, Eds.; Woodhead Publishing, an imprint of Elsevier: Duxford, United Kingdom, 2018, pp. 555-580 (ISBN: 978-0-08-101977-9).
2. Julia Martin, Enrique Jacobo Díaz-Montaña, Agustín G. Asuero, “Chapter 1: Cyclodextrins: Past and Present,” In Cyclodextrin: A Versatile Ingredient; Poonam Arora, Neelima Dhingra, Eds.; IntechOpen: London, United Kingdom, 2018, pp. 3-44 (ISBN: 978-1-78923-068-0).
3. A. Bibby, L. Mercier, "Adsorption and separation of water-soluble aromatic molecules by cyclodextrin-functionalized mesoporous silica," Green Chem. 2003, 5, 15-19 (DOI: 10.1039/B209251B).
4. Avilasha A. Sandilya, Upendra Natarajan, M. Hamsa Priya, "Molecular View into the Cyclodextrin Cavity: Structure and Hydration," ACS Omega 2020, 5(40), 25655–25667 (DOI: https://doi.org/10.1021/acsomega.0c02760).
5. Chang Cai Bai, Bing Ren Tian, Tian Zhao, Qing Huang, Zhi Zhong Wang, "Cyclodextrin-Catalyzed Organic Synthesis: Reactions, Mechanisms, and Applications," Molecules 2017, 22(9), 1475 (17 pages) (DOI: https://doi.org/10.3390/molecules22091475).
6. Lajos Szente, Ashutosh Singhal, Andras Domokos, Byeongwoon Song, "Cyclodextrins: Assessing the Impact of Cavity Size, Occupancy, and Substitutions on Cytotoxicity and Cholesterol Homeostasis," Molecules 2018, 23(5), 1228 (15 pages) (DOI: https://doi.org/10.3390/molecules23051228).
7. Mikhail V. Rekharsky, Yoshihisa Inoue, "Complexation Thermodynamics of Cyclodextrins," Chem. Rev. 1998, 98(5), 1875-1918 (DOI: https://doi.org/10.1021/cr970015o).