Potential energy surfaces molecular internal space

In the laboratory frame the motion of the three particles depends on nine variables, three of which define the position of the center-of-mass. Other three coordinates are needed to describe the rotation of the system in the space and therefore the internal motion is described by the three remaining coordinates. For example, in molecular dynamics the potential energy surface in general is calculated and presented using geometrical coordinates, such the interparticle distances, or two bond distances and an angle. But it is convenient and necessary to use different coordinate systems to describe and understand the dynamics of the particles, because of the rotational terms which appear in the full Hamiltonian. In this context, we will present the transformation equations from the interparticle distances to coordinate sets of the hyperspherical and related types, successful in the treatment of the dynamics. 

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