Nuclear spin relaxation times are calculated for quadrupolar nuclei situated at the center of octahedral and tetrahedral molecules. Vibrational distortion of such a molecule generates an electric field gradient at the center, which does not average to zero when the molecule is in an excited state of a degenerate vibration. The electric field gradient causes quadrupolar relaxation because of randomness in the vibrational state of the molecule. The theory relates the nuclear spin relaxation time to constants derived from the high resolution infrared spectrum of the molecule in the gas phase.
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