Umbrella inversion of ammonia redux

Area of Science:

• Quantum Chemistry
• Molecular Spectroscopy
• Physical Chemistry

Background:

• Ammonia's umbrella inversion is a classic example of large-amplitude vibrational motion.
• The simplified model depicts nitrogen atom oscillation between pyramidal structures via tunneling.
• This model neglects nuclear permutations and their quantum mechanical implications.

Purpose of the Study:

• To re-examine the dynamics of ammonia's umbrella inversion by incorporating nuclear permutations.
• To demonstrate the implications of the quantum symmetrization postulate on inversion motion.
• To clarify the spatial distribution of the inversion density in ammonia wavepackets.

Main Methods:

• Evaluation of expectation values for inversion coordinate and projection operators.
• Analysis of zeroth-order eigenstates incorporating inversion, rotation, and nuclear spin.
• Inclusion of nuclear indistinguishability and the symmetrization postulate.

Main Results:

• The inversion density is always symmetrically distributed between the two potential wells for any ammonia wavepacket.
• Dynamical spatial localization of inversion density can occur for specific inversion-rotation levels.
• Localization of ammonia in a single potential well is fundamentally impossible.

Conclusions:

• The textbook picture of ammonia inversion is an oversimplification.
• Quantum effects, particularly nuclear indistinguishability, dictate a symmetric distribution of inversion density.
• While transient localization may appear, ammonia never resides in a single potential well.