Typically molecular motions are classified into vibrational and torsional motions. Could one apply the principles of modes of vibrations of closed 3d shapes such as spheres , ellipsoids etc and of distributions on those surfaces and how they would interact ?? Since it is known that the modes of vibrations of spheres can be expressed in terms of spherical harmonics, the distributions / functions on the spheres could also possibly be expressed in terms of spherical harmonics , so could vibrations of these be thought of as in terms of composition of spherical harmonics ?? Could these be simplified as in the case of chebyshev polynomials ?
Could the above be one way of explaining rotational vibrational coupling ?? How would this relate to quantum entanglement ??
Could these be looked at as functions along the principal axes of the molecule (axes of symmetry ??) ?? How would the above relate to vibrations along the principal axes ??
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