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

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.

The key potential beneficiaries of this research include (i) academics working in quantum chemistry, electronic structure theory and nonadiabatic dynamics; (ii) academics working on challenges where nonadiabatic dynamics plays a role; (iii) industries using or devising processes or materials where nonadiabatic dynamics plays a role. Impact will first be felt in (i), with benefits (ii) and (iii) accruing over a longer time period.

The detailed benefits to each group include the following.

(i) Academics working in quantum chemistry and electronic structure theory will gain a valuable new perspective on the challenges of modelling molecular matter, bypassing the almost ubiquitous conceptual device of the potential energy surface. Academics working on nonadiabatic dynamics will benefit from (1) benchmark results against which to validate other approximate schemes; (2) access to a new class of theoretical tools for modelling nonadiabatic processes; (3) access to new ideas that could influence developments in other sub-fields.

(ii) Academics investigating the conduction of energy and charge through complex systems will benefit from the theoretical insights and benchmark computed data arising from model Hamiltonians that capture the basic phenomenology. Spectroscopists will have access to new tools for predicting, interpreting and assigning vibronic spectra. Researchers in a wide range of disciplines will benefit from new insights made in our groups and by the beneficiaries identified in (i), as well as from collaboration with theoreticians on complex problems that involve nonadiabatic dynamics.

(iii) Ultimately we aim for lasting impact through uptake by industrial end-users. This is a long-term goal that is unlikely to materialise in the time-frame of the proposed research. Nevertheless, there are grounds for optimism that this can be done because (a) research from both our groups is already used widely in industry through the Molpro software package; and (b) there are many industrial contexts where access to readily usable modelling techniques of the kind we are proposing could offer significant advantage.

We have set out clear plans to deliver impact through these three key beneficiary groups in our Pathways to Impact document.