Abstract
The Born–Oppenheimer picture has forged our representation and interpretation of photochemical processes, from photoexcitation down to the passage through a conical intersection, a funnel connecting different electronic states. In this work, we analyze a full in silico photochemical experiment, from the explicit electronic excitation by a laser pulse to the formation of photoproducts following a nonradiative decay through a conical intersection, by contrasting the picture offered by Born–Oppenheimer and that proposed by the exact factorization. The exact factorization offers an alternative understanding of photochemistry that does not rely on concepts such as electronic states, nonadiabatic couplings, and conical intersections. On the basis of nonadiabatic quantum dynamics performed for a two-state 2D model system, this work allows us to compare Born–Oppenheimer and exact factorization for (i) an explicit photoexcitation with and without the Condon approximation, (ii) the passage of a nuclear wavepacket through a conical intersection, (iii) the formation of excited stationary states in the Franck–Condon region, and (iv) the use of classical and quantum trajectories in the exact factorization picture to capture nonadiabatic processes triggered by a laser pulse.
Highlights
Our way of picturing molecules and chemical processes has been greatly shaped by the Born−Oppenheimer approximation, the assumption that the motion of electrons and nuclei can be treated separately in a molecule.[1,2] The discussion of chemical structures, properties, and reactivity usually intrinsically assumes that the molecule remains in a given electronic eigenstate or, in other words, that electrons can adapt instantaneously to any nuclear motion, which is a direct consequence of the Born−Oppenheimer approximation
This post-Born−Oppenheimer picture is at the heart of our way to regard photochemical processes, and the vocabulary used for such processes is intrinsically shaped by Born−Oppenheimer concepts: potential energy surfaces,[4] conical intersections,[13,14] the Berry phase,[15,16] and the transition dipole moment
We introduced in this work a comparison between the Born− Oppenheimer and exact-factorization picture of an in silico photochemical experiment, from the initial photoexcitation with an ultrashort laser pulse to the formation of photoproducts
Summary
Our way of picturing molecules and chemical processes has been greatly shaped by the Born−Oppenheimer approximation, the assumption that the motion of electrons and nuclei can be treated separately in a molecule.[1,2] The discussion of chemical structures, properties, and reactivity usually intrinsically assumes that the molecule remains in a given electronic eigenstate or, in other words, that electrons can adapt instantaneously to any nuclear motion, which is a direct consequence of the Born−Oppenheimer approximation. There is a real curiosity in unraveling how the exact factorization would describe a full photochemical experiment for a 2D two-state molecular model, from photoexcitation with a laser pulse to the formation of photoproducts, and in comparing this picture to the more conventional Born− Oppenheimer representation These simulations will allow us to shed light on other interesting aspects of an in silico photochemical experiment, such as (i) the effect of the Condon approximation, (ii) the analysis of the dynamics using representation-free quantities, and (iii) the use of classical and quantum trajectories to depict the entire nuclear dynamics during a photochemical process.
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