Molecules, aperiodic motion

Aperiodic motions, whether intramolecular or consisting of an orientation of the molecule as a whole, are characterized by their... 

The complex, random, and seemingly aperiodic internal motions of a vibrating molecule are the result of the superposition of a number of relatively simple vibratory motions known as the normal vibrations or normal modes of vibration of the molecule. Each of these has its own fixed frequency. Naturally, then, when many of them are superposed, the resulting motion must also be periodic, but it may have a period so long as to be difficult to discern. 

The basic idea of this dynamic theory is to use the site-site intermolecular energies and forces from the static theory presented earlier in this paper to calculate friction coefficients, etc., for analytic Brownian motion calculations for the molecules. From References 32-33, the aperiodic case of Brownian motion of a harmonically-bound particle is given by... 

Vibrational Motion in Polyatomic Molecules. Normal-mode analysis of vibrational motion in polyatomic molecules is the method of choice when there are several vibrational degrees of freedom. The actual vibrations of a polyatomic molecule are completely disordered, or aperiodic. However, these complicated vibrations can be simplified by expressing them as linear combinations of a set of vibrations (i.e., normal modes) in which all atoms move periodically in straight lines and in phase. In other words, all atoms pass through their equilibrium positions at the same time. Each normal mode can be modeled as a harmonic oscillator. The following rules are useful to determine the number of normal modes of vibration that a molecule possesses ... 

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