  Quantum indistinguishability plays a crucial role in many low-energy physical
phenomena, from quantum fluids to molecular spectroscopy. It is, however,
typically ignored in most high temperature processes, particularly for ionic
coordinates, implicitly assumed to be distinguishable, incoherent and thus
well-approximated classically. We explore chemical reactions involving small
symmetric molecules, and argue that in many situations a full quantum treatment
of collective nuclear degrees of freedom is essential. Supported by several
physical arguments, we conjecture a "Quantum Dynamical Selection" (QDS) rule
for small symmetric molecules that precludes chemical processes that involve
direct transitions from orbitally non-symmetric molecular states. As we propose
and discuss, the implications of the Quantum Dynamical Selection rule include:
(i) a differential chemical reactivity of para- and ortho-hydrogen, (ii) a
mechanism for inducing inter-molecular quantum entanglement of nuclear spins,
(iii) a new isotope fractionation mechanism, (iv) a novel explanation of the
enhanced chemical activity of "Reactive Oxygen Species", (v) illuminating the
importance of ortho-water molecules in modulating the quantum dynamics of
liquid water, (vi) providing the critical quantum-to-biochemical linkage in the
nuclear spin model of the (putative) quantum brain, among others.
