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Instanton theory is a rigorous semiclassical theory to calculate tunnelling rate constants and tunnelling splittings of vibrational levels, taking movements of all atoms of a molecular system into account. Rate constants are obtained from the imaginary part of the free energy of a metastable quantum state. The free energy, in turn, is derived from partition functions calculated via Feynman's path integral formulation of quantum mechanics. Its usage has tremendously increased over the last decade in chemistry and surface science. This chapter discusses its basic foundations, its derivation, advantages and limits in applications.

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