 The vibrational energy of the molecule can be written in terms of coordinates with respect to the Eckart frame as
Because the Eckart frame is non-inertial, the total kinetic energy comprises also centrifugal and Coriolis energies.These stay out of the present discussion.The vibrational energy is written in terms of the displacement coordinates, which are linearly dependent because they are contaminated by the 6 external modes, which are zero, i.e., the d"A"'s satisfy 6 linear relations.