Separation of External Motion

Considering N particles in Cartesian space-fixed coordinates. 

Following Curtiss, we take as an instructive illustration the separation of the external translational motion for the system of two molecules, c and d, with c particles belonging to molecule c, 

With the assumption that is independent of X, (no external force on the system), the following separation of Eq. (110) may be made  

For one molecule, or considering the system as a whole without separating into molecules, Eq. (112c) is reduced to 

As the overall rotation of a system is likewise unlinked to the potential energy in free space, a separation of this motion may be accomplished. The procedure, however, is rather complicated and is usually not employed, largely because of the degeneracy in the rotational states, which causes the wave function g not to be separable directly as a product, but as a sum of products. 

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