Quantum wavepacket method for state-to-state reactive cross sections in hyperspherical coordinates

We present theory for calculating state-to-state differential cross sections (DCS) of triatomic reactive scattering in hyperspherical coordinates using a quantum wavepacket method. The adiabatically adjusting, principal axes hyperspherical coordinates proposed by Pack and Parker [J. Chem. Phys. 87, 3888 (1987)] are applied, which deal with all arrangement channels equivalently, allowing the analysis of the products in all three arrangement channels with one main propagation. The propagated wavepacket is analyzed by projecting it onto the product ro-vibrational states at a fixed, asymptotic radius, R, of the corresponding Jacobi coordinates; thus, the channel-specified S-matrix elements can be calculated by matching the projections with the boundary conditions in the Jacobi coordinates. For numerical demonstrations, state-to-state DCS of the H + HD ( $$ ₀ = 0, j ₀ = 0) reaction and state-to-state reaction probabilities of the O + O₂ ( $$ ₀ = 0, j ₀ = 0) reaction and the F + HCl ( $$ ₀ = 0, j ₀ = 0) → HF + Cl reaction for zero total angular momentum are presented. The second order split operator method and the Chebyshev polynomial expansion method were applied to propagate the wavefunction. The relative numerical efficiencies for calculating the state-to-state information of triatomic reactive scattering using the hyperspherical coordinate and the reactant Jacobi coordinate are discussed.