Is ammonia inversion due to quantum tunnelling? In this Wikipedia article, it is said that the inversion of ammines happens due to tunnelling effects and superposition of states and gives Feynman lectures as citation. I have not done a quantum course but out of curiosity I opened the specific lecture which was linked (this) and in it he has not mentioned the word 'tunnelling' / quantum tunnelling effects.
The explanation that I got from a few of my friends is that the electron moves through the nucleus through quantum tunnelling effects and he becomes a p orbital, and I thought this was fairly reasonable explanation till I came to this discrepancy.
I'm not sure, if he did mention it and I'm not understanding or otherwise. Where exactly can I find a citation/ reference for this claim? That is if it is right at all..
 A: The energy barrier for the inversion is $24.2$ kJ/mol or about $0.25$ eV. At room temperature the thermal energy $kT$ is about $0.02$ eV or about a factor of $13$ times less than the energy required to get through the barrier. So the proportion of molecules with enough energy to go over the barrier and invert would be:
$$ P = e^{-13} \approx 2.28 \times 10^{-6} \tag{1} $$
The frequency of the vibrational mode that leads to inversion, is about $3.4 \times 10^{13}$ Hz, and multiplying this by our fraction from equation (1) gives us the expected number of nitrogen molecules inverting per second:
$$ N = 3.4 \times 10^{13} \times 2.28 \times 10^{-6} \approx 75.7 \times 10^7 ~ \textrm{s}^{-1}$$
But the observed inversion rate is about 30 billion times per second, or about 400 times faster than we would expect based on a classical analysis. This factor of 400 comes from the quantum tunnelling through the barrier. So yes, quantum tunnelling does occur and needs to be taken into account to explain the observed inversion frequency.
