A systematic treatment of three-dimensional quantum mechanical reaction coordinates

Summary The rigorous, collinear, canonical point transformation method with hyper-hyperbolic coordinates is extended to the infinite central mass problem in three dimensions. The initial transformation performed is (x_A, y_A, z_A, x_C, y_C, z_C) (, , , r, R, ), where (, , ) are the Euler angles; r and R are the AB and BC interatomic distances, respectively, and is the angle between r and R. A second transformation is then performed to (, , , , , ), where is the reaction coordinate mimicking the reaction path, and is the vibrational coordinate of the diatom. The transformed spaces are all one-to-one mappings from the original spaces, and thus do not have any three-to-one regions. The transformed momenta and Hamiltonians are derived, and are Hermitian in their respective transformed spaces.