Rotational Spectroscopy of Linear Polyatomic Molecules

The rotation of a linear polyatomic molecule can be viewed as an infinitesimally thin rod rotating about its one axis of rotation. This is mechanically equivalent to the rotation of a diatomic molecule. The only 

The term ry refers to the distance between the i andj atoms, in the polyatomic molecule. The summation in the numerator is between each pair of atoms in the molecule. The summation in the denominator is the sum over all of the 

Problem Calculate the moment of inertia for given that the 

Since the atoms arc viewed as point masses with the mass concentrated in the nuclei, the distance is equal to the sum of the H-C and CasN normal bond lengths, r , = r c + ra,. 

Due to the mechanical equivalence, the Schroedinger equation and the resulting rotational energy eigenvalues is the same for linear polyatomic molecules as for diatomic molecules. 

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The rotation of a rigid, linear triatomic or polyatomic molecule is mechanically equivalent to the rotation of a rigid diatomic molecule. All are the rotations of an "infinitesimally thin rod" with two or more point masses attached. The basic analysis for the rotational spectroscopy of linear polyatomic molecules follows that of diatomic molecules however, it requires a generalization of the moment of inertia to more than two atoms. For a linear arrangement of point masses, the moment of inertia, I, about the center of mass is... 

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