A nonadiabatic generalized-dividing-surface instanton rate theory

The accurate prediction of quantum rates and rate mechanisms is fundamental to our understanding of chemical reactions in a variety of contexts, ranging from astrophysics to biochemistry.

Exact calculations are rarely computationally feasible. To make them tractable many chemical processes are described within the Born-Oppenheimer (BO) approximation, which assumes strong coupling between the diabatic states, and BO instanton theory is known to capture nuclear quantum effects for these systems well [1]. Alternatively, some systems are better captured by Fermi’s golden rule (GR), which is appropriate in the opposite, weak-coupling limit where Wolynes theory and GR instanton theory are well-established rate theories [2, 3].

Nevertheless, many chemical reactions are in neither of these two limits, and so a universal rate theory which generalizes the path-integral framework used in Wolynes and instanton theories is desirable.

Much work has already been done in this direction, however previous attempts often lacked in rigor resulting in theories that can experience an uncontrolled break-down. We introduce a new instanton approach rigorously derived from the generalized flux-flux correlation formulation of rate theory [4]. Our new nonadiabatic generalized-dividing-surface (NGD) instanton rate theory correctly recovers the weak- and strong-coupling limits and it also goes beyond existing, ad hoc attempts to describe general, nonadiabatic rate processes [5].

Instanton rate theories have already resolved many longstanding discrepancies between experiment and theory [6, 7] and this new rate theory will be key to address processes beyond their scope such as proton-coupled electron transfer reactions.

[1] Richardson, J. O., Int. Rev. Phys. Chem., 2018, 37:2, 171-216.

[2] Richardson, J. O., Bauer, R., Thoss, M., J. Chem. Phys., 2015, 143, 134115.

[3] Wolynes, P. G., J. Chem. Phys., 1987, 87, 6559.

[4] Lawrence, J. E., Manolopoulos D. E., J. Chem. Phys., 2020, 152, 204117.

[5] Zarotiadis, R. A., Lawrence, J. E., Richardson, J. O., Manuscript in preparation.

[6] Heller, E. R., Richardson. J. O., J. Am. Chem. Soc., 2021, 143, 20952.

[7] Zarotiadis, R. A., Fang, W., Richardson, J. O., Phys. Chem. Chem. Phys., 2020, 22, 10687.