Two-Dimensional Parameterized Model for H2 Rotation

M can be considered to be a fixed reference frame wherein the H2 is described by the usual spherical coordinates , , and . The complete description of the exchange process involves the four dynamical coordinates , , , and z, which can be simplified because presumably the H2 remains perpendicular to the z axis during the rotation and is not displaced appreciably relative to M along . In contrast to r and , the two coordinates z and do not play an important role in the dynamics 

For three other systems studied, the 2D model also gives excellent results that compare well with experiment, e.g., dm in [FeH(H2)(dppe)2]+ is 0.82 A by neutron diffraction and is 0.822 A with the 2D model. However, it is only useful if a sufficient number of INS transitions are observed. While instrumental limitations confine the observation of the tunneling transition to H2 complexes with a rotational barrier of less than 3 kcal/mol, transitions to the torsional states can in principle be observed for any such compound. The 2D methodology could then be applied to any experiment in which the dynamic process involves permutation of two identical particles, e.g., the quantum exchange coupling phenomenon (see Section 6.3.4). 

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