Electron transfer rates between weakly coupled states are predominantly calculated using Marcus theory. Due to its inherent classical character, however, the Marcus theory result can deviate from the experimental reaction rates by several orders of magnitude by virtue of quantum tunnelling and zero-point energy. These effects prove to be of particular importance in the so called “inverted” regime, where they substantially speed up the reaction while the classical rate falls off quickly with increasing thermodynamic driving force. In principle the correct quantum mechanical rate can be obtained by applying Fermi’s golden rule. This, in turn, requires knowledge of the nuclear wavefunctions of the two reactive wells, which are not accessible for all but very small systems. Conversely, semiclassical instanton theory does not even require solution of the Schrödinger equation for the unperturbed Hamiltonian and is thus able to capture nuclear quantum effects in a numerically efficient way allowing application to complex, anharmonic systems. Recently this method has been extended to also describe the inverted regime. Thereby a well-known and longstanding obstacle in reaction-rate theory could be overcome by introducing the concept of negative temperatures or alternatively negative imaginary time leading to a formulation equivalent to that of particle-antiparticle annihilation.<br/><br/>The generality of the theory, arising from the fact that it is derived as a semiclassical approximation to Fermi's golden rule, enables to capture nuclear tunnelling effects not only in electron-transfer reactions but also in light-matter interactions, electrochemistry and many other fields, where the golden rule is applied.

Quantum tunnelling in electron-transfer reactions

ACS Spring Meeting 2021

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