Kinematic rotations for four-centre reactions: Mapping tetra-atomic potential energy surfaces on the kinetic sphere

Kinematic rotations for four body processes can be conveniently represented as arcs connecting the different reactive rearrangements, (T + UVW, TU + VW, TUV + W and all permutations). The arcs can be considered as forming great circles on a sphere, which is therefore a convenient manifold for setting up symmetric coordinates in asymptotic rearrangement channels: in the particular cases where the reactions are collinearly dominated, the sphere provides the full chart for the (fixed moment of inertia or hyperradial) mapping of the potential energy surface. Also, the representations can be extended to include connections to a formulation where two particles are symmetrically treated with respect to a third one-as introduced in the Journal of Chemical Physics (1986, 85, 1355)-and to encompass the asymptotic situation of the four body system decomposing into three fragments (T + U + VW, T + UV + W, etc...). Comments are made on other cases pertaining to the symmetric parametrizations of four centre processes.