A unified framework for quantum chemistry beyond the Born-Oppenheimer approximation

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In quantum chemistry the approximate formulations of quantum mechanics are applied to the behaviour of atoms, molecules, surfaces and reactions.The field is dominated by a small number of key approximations. The Born-Oppenheimer approximation, in which a separation is made between the motion of electrons and nuclei, has particular importance because it provides not only a powerful framework for modelling and simulation tools, but also the central theoretical foundation on which our understanding of molecular structure is based. However,the Born-Oppenheimer approximation breaks down in several important chemically, physically and technologically relevant contexts: key examples include practically all photo-activated processes, electrochemical reactions, transport of charge and energy, and chemical reactions where hydrogen atoms migrate. For this reason there is a huge research activity in nonadiabatic dynamics, aimed at moving beyond the Born-Oppenheimer approximation. Much of this work addresses the complexities arising from the introduction of the potential energy surface, whose introduction changes the problem from one where the Hamiltonian is a sum of one- and two-particle terms, to a Hamiltonian in which all nuclear degrees of freedom are coupled together. Here we propose to move beyond the Born-Oppenheimer approximation without introducing potential energy surfaces. The central idea of this proposal is to develop the quantum chemistry of coupled electronic-vibrational degrees of freedom, culminating in the development of time-dependent and linear-response coupled-cluster theories that capture the key effects in nonadiabatic processes. Representing the nonadiabatic dynamics whilst simultaneously describing the electronic structure at a coupled-cluster level of theory would herald a new era in the modelling of such processes, and we will perform challenging preliminary applications in photochemistry and prediction of vibronic spectra to illustrate the potential of the method.