Quantum flux densities for electronic-nuclear motion: exact versus Born-Oppenheimer dynamics

We study the coupled electronic-nuclear dynamics in a model system to compare numerically exact calculations of electronic and nuclear flux densities with those obtained from the Born-Oppenheimer (BO) approximation. Within the adiabatic expansion of the total wave function, we identify the terms which contribute to the flux densities. It is found that only off-diagonal elements that involve the interaction between different electronic states contribute to the electronic flux whereas in the nuclear case the major contribution belongs to the BO electronic state. New flux densities are introduced where in both, the electronic and the nuclear case, the main contribution is contained in the component corresponding to the BO state. As a consequence, they can be determined within the BO approximation, and an excellent agreement with the exact results is found. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Lazy electrons in graphene

Within a tight-binding approximation, we numerically determine the time evolution of graphene electronic states in the presence of classically vibrating nuclei. There is no reliance on the Born-Oppenheimer approximation within the p-orbital tight-binding basis, although our approximation is "atomically adiabatic": the basis p-orbitals are taken to follow nuclear positions. Our calculations show that the strict adiabatic Born-Oppenheimer approximation fails badly. We find that a diabatic (lazy electrons responding weakly to nuclear distortions) Born-Oppenheimer model provides a much more accurate picture and suggests a generalized many-body Bloch orbital-nuclear basis set for describing electron-phonon interactions in graphene.

Non-Born-Oppenheimer effects in molecular photochemistry: an experimental perspective

Non-adiabatic couplings between Born-Oppenheimer (BO)-derived potential energy surfaces are now recognized as pivotal in describing the non-radiative decay of electronically excited molecules following photon absorption. This opinion piece illustrates how non-BO effects provide photostability to many biomolecules when exposed to ultraviolet radiation, yet in many other cases are key to facilitating 'reactive' outcomes like isomerization and bond fission. The examples are presented in order of decreasing molecular complexity, spanning studies of organic sunscreen molecules in solution, through two families of heteroatom containing aromatic molecules and culminating with studies of isolated gas phase H₂O molecules that afford some of the most detailed insights yet available into the cascade of non-adiabatic couplings that enable the evolution from photoexcited molecule to eventual products. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.