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I think the O from Hypoxanthine can bond with one of the Hs in NH2 from Cytosine and the H that is connected to N in Hypoxanthine with the N in Cytosine but is it possible also for the H connected to C in Hypoxanthine to bond with the O in Cytosine?

enter image description here[Hypoxantine]

Cytosine[Cytosine]

I have almost the same question between Xanthine and Adenine.(please note that I'm not talking about Xanthine and Adenine inside RNA, I know they can't bind at all in RNA because of their sizes)

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I strongly believe that it won't be possible for these compounds to form three hydrogen bonds.

Revisiting the basic definition of a hydrogen bond:

A hydrogen bond is an electrostatic attraction between two polar groups that occurs when a hydrogen (H) atom covalently bound to a highly electronegative atom such as nitrogen (N), oxygen (O), or fluorine (F) experiences the electrostatic field of another highly electronegative atom nearby.

Such electronegative atoms as oxygen and nitrogen with free lone pairs are potential hydrogen bond acceptors.

Hydrogen atoms attached to very electronegative atoms like O and N have strong partial positive charge and these are potential hydrogen bond donors

These two crucial requirements for hydrogen bond formation, have thus been summarised:

In order for a hydrogen bond to occur there must be both a hydrogen donor and an acceptor present. The donor in a hydrogen bond is the atom to which the hydrogen atom participating in the hydrogen bond is covalently bonded, and is usually a strongly electronegative atom such as N,O, or F. The hydrogen acceptor is the neighboring electronegative ion or molecule, and must posses a lone electron pair in order to form a hydrogen bond

Here is an impression of how these two would bond:

enter image description here

Note the "X" illustrating the missing requirement(s) to form a 3rd H-bond

  • missing potential donor group (electronegative atom) just C present.

Acknowledgements

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There is evidence for C-H...O and C-H...N hydrogen bonds, see e.g. the book by Desiraju and Steiner 1. These bonds are much weaker than conventional hydrogen bonds. Also, in general, hydrogen bond strength depends on the distance and the angle of donors and acceptors. In the given case, the hydrogen and oxygen atoms you are asking about are to far apart, and the atoms Y-H X (with Y the electronegative bonding partner of the hydrogen, H the bound hydrogen and X in acceptor) are not arranged in a line, which would be optimal.

So there are two strikes against a strong hydrogen bond here: A weak hydrogen bond donor in C-H, and suboptimal geometry.

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