Why does the gauche conformation of ethane-1,2-diol show hydrogen bonding?

Why does the gauche conformation of **ethane-1,2-diol** show hydrogen bonding even though there is no 6-membered ring system? If we don't consider one of the $\ce{H}$ (which is what is usually done), then there is only a 5-membered ring formed. How then does hydrogen bonding take place?


![conformation](https://i.stack.imgur.com/t2zTN.gif)


(Also, I feel that there must be some reason apart from 6-member ring for hydrogen bonding which I'm not aware of)




Cyclopentane has a relatively low strain energy, something on the order of 6.5 kcal/mol more than cyclohexane ([reference](http://ursula.chem.yale.edu/%7Echem220/chem220js/STUDYAIDS/thermo/cycloalkanes/cycloalkanes.html)). In the case of ethane-1,2-diol, the strain energy in the 5-membered ring formed by hydrogen bonding will be even less because some of the $\ce{H-C-C-H}$ and $\ce{C-C-C-C}$ interactions that produce the strain in cyclopentane are no longer present; the oxygens don't have the hydrogens attached like a methylene group does and the hydrogen used in the hydrogen bond is also much smaller than a methylene group.


A typical $\ce{O-H..H}$ hydrogen bond can stabilize a system by ~7 kcal/mol ([reference](http://en.wikipedia.org/wiki/Hydrogen_bond)). So to form a 5-membered ring in ethane-1,2-diol and create a hydrogen bond it will cost something less than 6.5 kcal/mol to overcome the strain energy in the ring, but we get 7 kcal/mol back due to hydrogen bond formation - **a net stabilization**.


$%edit$


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