Jones brought up the subject of quantum delocalization. What usually comes
to mind is the delocalization of electrons since they have a relatively
much longer quantum wavelength compared to protons. However delocalization
can in principle happen to protons as well (and maybe larger nuclei ?)This
paper describes a biological system where delocalization of protons results
in 10 000 fold increase in acidity compared to when the particles are
treated classically !

Abstract
<<Because of the low mass of the proton, nuclear quantum effects can
dramatically alter the properties of hydrogen-bond networks, especially
when short and strong hydrogen bonds occur. Here, we combine experiments
and state-of-the-art simulations that include the quantum nature of both
the electrons and nuclei to show that the enzyme ketosteroid isomerase
contains a hydrogen-bond network in its active site that facilitates
extensive quantum proton delocalization. This leads to a 10,000-fold
increase in the acidity of an active-site residue compared with the limit
where the nuclei are classical particles. This work opens up new avenues
for understanding the interplay between quantum effects and hydrogen
bonding in biological systems containing strong hydrogen bonds.>>
https://www.pnas.org/content/111/52/18454

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