  Ab initio simulations that account for nuclear quantum effects have been used
to examine the order-disorder transition in squaric acid, a prototypical
H-bonded antiferroelectric crystal. Our simulations reproduce the >100 K
difference in transition temperature observed upon deuteration as well as the
strong geometrical isotope effect observed on intermolecular separations within
the crystal. We find that collective transfer of protons along the H-bonding
chains - facilitated by quantum mechanical tunneling - is critical to the
order-disorder transition and the geometrical isotope effect. This sheds light
on the origin of isotope effects and the importance of tunneling in squaric
acid which likely extends to other H-bonded ferroelectrics.
