The Born-Oppenheimer (BO) approximation is among the most basic approximations in the quantum theory of molecules and solids. It is based on the fact that electrons usually move much faster than the nuclei. This allows us to visualize a molecule or solid as a set of nuclei moving on a potential energy surface (PES) generated by electrons in a specific electronic state. This picture breaks down when the electronic and nuclear motions become correlated. The interplay between the nuclear and electronic dynamics beyond the BO approximation leads to many fascinating phenomena in physics, chemistry and biology. For example, in the processes such as Joule heating in atomic devices, vision, photovoltaic, proton transfer and hydrogen-storage, that are of fundamental importance in the workings of solar-cell devices, molecular electronics and energy storage, the electron-nuclear correlation is a key player. These processes include some of the most difficult phenomena to theoretically model including an accurate calculation of the time-resolved dynamics of the electrons and ions, while their correlations and quantum features of the nuclear motion are indispensable. For example, one of the future key challenges will be to learn how to produce artificial light-harvesting complexes for photovoltaic systems.
The CoEND project’s aim was to develop an efficient and accurate first-principle method to treat the correlated electron-nuclear dynamics. The project’s goal was to provide a theoretical tool to study a wide range of phenomena that lie beyond the capability of existing methods in terms of efficiency and/or accuracy. For example, in the processes such as Joule heating in atomic devices, vision, photovoltaic, proton transfer and hydrogen-storage, the electron-nuclear correlation is a key player, hence, these processes cannot be described within the standard Born-Oppenheimer approximation and existing mean-field approaches such as Ehrenfest method.
