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The chapter brings a brief description of semiclassical methods and their application to the calculation of ground-state and state-selected tunnelling splittings, with a special emphasis on the instanton theory. The methodologies are presented following a historical timeline, and in this journey malonaldehyde is the touchstone. For years, malonaldehyde has been the toy molecule for many scientists who have developed new theoretical approaches or have improved existing ones in the field of low-temperature reaction dynamics. The chapter summarizes some of these efforts and achievements.

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