State-to-state three-atom time-dependent reactive scattering in hyperspherical coordinates

We present a time-dependent, hyperspherical wave packet method for calculating three-atom state-to-state S-matrix elements. The wave packet is propagated in time using adiabatically adjusting, principal axes hyperspherical coordinates that treat all arrangement channels equivalently, allowing the simultaneous analysis of the products in all three arrangement channels. We take advantage of the symmetry of the potential energy surface and decompose the initial wave packet into its component irreducible representations, propagating each component separately. Each irreducible representation component of the wave packet is analyzed by projecting it onto the hyperspherical basis at a fixed, asymptotic hyperradius, and irreducible representation dependent S-matrix elements are obtained by matching the hyperspherical projections to symmetry-adapted Jacobi coordinate boundary conditions. We obtain arrangement channel-dependent S-matrix elements as linear combinations of the irreducible representation dependent elements. State-to-state H + H(2) and F + H(2) results for zero total angular momentum are presented.