# How to interpret this formula about hydrogen bond energy

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).

• 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 Feb 9 at 20:16
• Thank you, it worked! (the numbers are powers) Feb 9 at 20:37

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.