Quantum Tunneling: History and Mystery of Large Amplitude Motions over a Century.

Large amplitude motions (LAMs), most notably represented by proton tunneling, mark a significant departure from small amplitude vibrations where protons merely oscillate around their equilibrium positions. These substantial displacements require tunneling through potential energy barriers, leading to splittings in, e.g., rotational spectra. Since Hund's pioneering work in 1927, proton tunneling has offered a unique glimpse into the internal dynamics of gas-phase molecules, with microwave spectroscopy being the key technique for such investigations. The ubiquous LAM type is methyl internal rotation, characterized by 3-fold potentials arising from the interaction between methyl rotors and their molecular frame, with the barrier hindering methyl torsion and the orientation of the torsional axis being defining features. Investigating methyl internal rotations plays a key role in fields ranging from molecular physics, where the methyl rotor serves as a sensitive probe for molecular structures, to atmospheric chemistry and astrophysics, where methyl-containing species have been detected in the Earth's atmosphere and interstellar environments and even discussed as potential probes for effects beyond the standard model of physics. Despite nearly a century of study, modeling methyl internal rotations with appropriate model Hamiltonians and fully understanding the origins of these motions, particularly the factors that influence torsional barriers, remain partially unresolved, reflecting the enduring mystery of quantum tunneling. This Perspective reviews the history of LAMs, highlights advances in decoding their complex spectra, and explores future research directions aimed at uncovering the remaining mysteries of these fascinating motions.