# Why isn't the side chain of arginine totally protonated at low pH?

I was wondering why arginine cannot be protonated at $\mathrm{pH\ 0}$ on all the $\ce{N}$ atoms in the side chain, as they all have a free electron pair. As this image shows, it can only be protonated once.

Why don't the other two nitrogen atoms in the side chain get protonated? Does it have something to do with resonance with the $\ce{C=N}$ double bond?

It may be hard to see from a 2D-drawing, but there are simply no more available lone pairs on arginine than the ones protonated in form $\ce{A}$.

The guanidine group ($\ce{H2N-C(=NH)-NHR}$) is isolobal to a urea group, and indeed guanidine behaves much like urea except for the common differences between $\ce{C=O}$ and $\ce{C=NH}$. The lone pairs of $\ce{-NH2}$ and of $\ce{-NHR}$ are actively taking part in resonance with the $\ce{=NH}$ group’s double bond much like an amide structure. One can equivalently say that those lone pairs are delocalised into the $\ce{C=N}$ $\pi^*$ MO. Hence, only the $\mathrm{sp^2}$ hybridised lone pair on the $\ce{=NH}$ nitrogen is basic in any way and can be protonated.

Of course, you can further protonate arginine theoretically. However, it would take superacidic media.

• Technically, it's not a $\pi$ system because this isn't a 2 atom MO. The HOMO and LUMO should both have $E$ symmetric from the $C_{3}$ point group. – Zhe Oct 4 '16 at 1:36
• @Zhe What?$%comments~$ – Jan Oct 4 '16 at 1:37
• Sorry, I think I got too technical. The $pi$ designation doesn't apply here unless you ignore the two nitrogen atoms that with the lone pairs. A $pi$ system is for two atoms. But that's clearly part of the conjugated system. For accuracy, you'd need to look at the frontier molecular orbitals. And for 3 nitrogen atoms around a central carbon, the p orbitals would form a point group that doesn't have anything with $pi$ symmetry. The group is actually $D_{3}$ (I was wrong before because we're looking at p orbitals). Please ping if I need to clarify. – Zhe Oct 5 '16 at 14:02
• @Zhe Oh, that’s what you mean; I understand. But note that at least in organic chemistry, pi system is used to denote a series of atoms with collinear p-orbitals that form an MO antisymmetric with respect to the $\sigma_\mathrm{h}$ plane (that traverses the set of atoms). – Jan Oct 5 '16 at 14:11
• Yeah, we even call it an extended $\pi$ system, but there's no way that thing has $\pi$ symmetry in aggregated... :/ – Zhe Oct 5 '16 at 14:53

The amino group of arginine at the terminal of side chain are more expose than the embeded amino group so the chance for that terminal amino group is more to be protonated and second is the charge of these terminal amino group is than stabilized by resonance which make it more stabilized when it get protonation