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# Molecular Rotation

### Centrifugal Distortion

In our calculations so far, we have been treating molecules as rigid rotors – assuming that they do not distort under the stress associated with rotation.

### Rotational Selection Rules

A selection rule is a statement about which transitions are allowed (and thus which lines may be observed in a spectrum). The classical idea is that for a molecule to interact with the electromagnetic field and absorb or emit a photon of frequency ν, it must possess, even if only momentarily, a dipole oscillating at that frequency.

### Rotational Raman Spectra

The gross selection rule for rotational Raman spectroscopy is that the molecule must be anisotropically polarisable, which means that the distortion induced in the electron distribution in the molecule by an electric field must be dependent upon the orientation of the molecule in the field.

### Linear and Asymmetric Rotors

Linear rotors are linear molecules, for example CO2, C2H2 (ethyne) and all diatomic molecules. The moment of inertia of a linear molecule about an axis that lies along the molecular axis is necessarily zero, as the atoms all lie on this axis and so are at zero distance from it.

### Symmetric Rotors

In a symmetric rotor, two of the moments of inertia are equal, but different from the third. Molecules belonging to this category include ammonia (NH3), benzene (C6H6), and chloromethane(CH3Cl).

### Intensities of Spectral Lines

The intensity of a spectral line at a given frequency is related to the net rate of absorption (or emission) at that frequency.

### Introduction to Rigid Rotors

In a discussion of rotational energy levels, a very important property is the moment of inertia, I, of the molecule about any particular rotational axis. The moment of inertia of a molecule is generated by taking the mass of each atom in the molecule, multiplying it by the square of its perpendicular distance from the rotational axis, and summing these values together. i.e.

### Spherical Rotors

A spherical rotor is one for which the three moments of inertia (about mutually perpendicular axes) are equal. This implies that the molecule must be highly symmetric. (In fact, molecules that are spherical rotors must belong to a cubic or icosahedral point group – see the symmetry section, here, for a further explanation.)

### An Introduction to Spectroscopy

Spectroscopy is, in general terms, the study of the interaction of electromagnetic radiation with matter.