Internal Molecular Motions of Large Amplitude Illustrated by the Symmetrical Vibration of Ammonia

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Abstract
A general method is developed for separating slow internal motions of molecules from their rapid vibrations, with the rotational motion. The zero approximation for the slow motion can be obtained by Schrödinger's rule from the classical motion in which the rapid vibrations are replaced by constraints. The theory is applied to the symmetrical double‐minimum vibration of ammonia, the combined vibration‐rotation energy levels being evaluated as characteristic numbers of a Sturm‐Liouville equation in one variable. The microwave absorption frequencies of N14H3 and N15H3 are computed, also the pure rotation frequencies in the far infra‐red.