Instanton theory of nonadiabatic tunnelling

Abstract

In addition to rearrangements of the molecular structure, chemical reactions may involve transitions between different electronic states. In these nonadiabatic reactions, which comprise electron transfers, spin crossovers and reactions featuring conical intersections, the customary Born–Oppenheimer approximation (BOA) breaks down, and many standard methods for the calculation of reaction rates like transition-state theory are no longer valid. The predominant approach for the calculation of reaction rates between two weakly coupled electronic states is Marcus theory. However, Marcus theory can deviate from experimental rates by orders of magnitude because it neglects nuclear quantum effects (NQEs) such as quantum tunnelling and zero-point energy. Conceptually, these quantum effects can be captured by Fermi's golden rule, but the required nuclear wavefunctions of the two reactive states are only accessible for very small molecules. While there exist several appropriate rate theories built on the BOA to approximately describe NQEs in complex molecular systems, the study of tunnelling in nonadiabatic reactions largely relies on ad hoc assumptions about the reaction mechanism or the shape of the underlying potential-energy surfaces (PESs). In this thesis, we develop and implement semiclassical golden-rule instanton theory (SCI), a rigorous first-principles approach to calculating nonadiabatic reaction rates. In SCI, the optimal tunnelling pathway, or instanton, is located on the full-dimensional PESs of the reactants and the products. As in the established Born–Oppenheimer instanton theory, the instanton pathway travels in imaginary time and therefore in the classically forbidden region, beneath the potential-energy barrier providing intuitive insight into the reaction mechanism. We extend SCI to describe reactions in the inverted regime, where tunnelling effects are known to be prevalent. Thereby a well-known and longstanding obstacle in reaction-rate theory is overcome by introducing the concept of negative temperature or, equivalently, negative imaginary time, giving rise to reaction mechanisms that feature molecule–antimolecule creation and annihilation. Furthermore, we describe the coupling of the reactive system to solvent baths as well as optical cavities and develop an instanton rate theory for reactions through conical intersections, which sheds light on how the geometric phase affects chemical reactions. In each case, we first benchmark SCI against quantum-mechanical results for model systems and then apply the method in conjunction with on-the-fly electronic-structure calculations to real molecular systems. For the first time, agreement between theory and experiment is achieved for the spin crossovers of two nitrenes and thiophosgene. We unveil how nonadiabatic heavy-atom tunnelling drastically changes reaction rates and mechanisms, explaining the failure of previous studies that used ad hoc approximations. Contrary to received wisdom, we predict that heavy-atom tunnelling can dominate nonadiabatic reactions even at room temperature.