Quantum indistinguishability in chemical reactions

Three representations of a rotating diatomic molecule composed of identical nuclei. (A) An explicit physical representation. (B) An effective model for the dynamics of the angular coordinate, φ=2ϕ∈[0,2π), for a molecule with C2 symmetry, represented as a quantum bead on a ring with Berry flux, Φ0 determined by the nuclear spin wavefunction. The bead wavefunction, ψa(φ), is discontinuous across an nth root branch cut (red squiggly line), ψ+=eiΦ0ψ−. (C) Placing the bead on an n-fold cover of the ring with φ∈[0,2πn)—a Mobius strip for the n=2 double cover—resolves any ambiguity in the placement of the branch cut.

Two representations of a nonrotating diatomic molecule composed of identical nuclei. (A) An explicit physical representation with impenetrable potential wedges inserted around ϕ=0 and π that restrict the molecular rotation angle and constrain one nucleus to the upper half-plane and the other to the lower half-plane. These wedges strictly forbid all rotational motions that dynamically exchange the two nuclei. The identical nuclei thus become effectively distinguishable. (B) An effective quantum bead model, where the ring, now restricted to the angular range, φ∈[δ,2π−δ), has been cut open—and the bead is constrained to move on a line segment.

Two representations of a bond-broken diatomic molecule composed of identical but distinguishable nuclei. (A) An explicit physical representation with impenetrable potential wedges inserted at ϕ=0 and π, allowing for a bond-breaking process to the distinguishable-nuclei state. (B) An effective quantum bead on a ring model, restricted to the angular coordinate range φ∈[δ,2π−δ), with bond breaking modeled by tunneling the bead off the ring.