I want to evaluate some chemistry related formulas, which I don't understand.

In proteins, hydrogen bonding often occurs between the oxo group = O oxygen of one amino acid and the α-amino group (N − H) of another amino acid. The bond energy is determined by the distance between oxygen and hydrogen and by the angle enclosed by the N-H and H-Bonds.

Let's assume the $E = (\frac{1}{d_{HO}^{10}} - \frac{1}{d_{HO}^{12}}) * cos(\alpha)$ model describes the energy of the hydrogen bond.

What is the meaning of the number 10 and 12 in the formula?

I know the angle and the distances between one O, one H and one N atom (that's all the input we got).

maybe related: https://www.sciencedirect.com/topics/biochemistry-genetics-and-molecular-biology/hydrogen-bond

  • 1
    $\begingroup$ Those are exponents. You are missing two parameters to replace the ones in the numerator, see e.g. slide 8 of this document: ncbr.muni.cz/~martinp/C3210/StructBioinf7.pdf $\endgroup$
    – Karsten
    Commented Feb 9, 2021 at 20:16
  • $\begingroup$ Thank you, it worked! (the numbers are powers) $\endgroup$ Commented Feb 9, 2021 at 20:37

1 Answer 1


These exponents $10$ and $12$ are a little bit arbitrary. They have been chosen so as to obtain an energy curve corresponding to the measured H-bond energies. Other attempts have been published, like the famous Morse curve, which is, for covalent bonds versus HO distance $d$ : $$E(d) = D[1 - e^{-k(d - d_o)}]^2$$ where $D$ is the dissociation energy of the covalent H-O bond. Apparently the curve with the two exponents $10$ and $12$ gives a better fit.


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