Internal motion of a non-rigid molecule and its relation to the reaction path

The Eckart-Sayvetz and Hofacker-Marcus conditions for separation of large- and small-amplitude motions are discussed. Some advantages of rectilinear vibrational coordinates are outlined and a local equivalence between them and geodesic coordinates is proved. It is shown that the extremum condition for the adiabatic potential and the local Hofacker-Marcus conditions determine a unique geometrical structure of any one-parameter semirigid bound-state model and a unique reaction path in the space of internal variables. These conditions lead to the so-called intrinsic path. Some properties of this path as a particular case of steepest descent (ascent) paths in a Riemann space are analysed. The accurate hamiltonian based on a linear semirigid model and the global Eckart-Sayvetz conditions is projected into the subspace of internal variables describing linear configurations and the resulting extra potential term is discussed.