When the exact factorization meets conical intersections...

Abstract

Capturing nuclear dynamics through conical intersections is pivotal to understand the fate of photoexcited molecules. The concept of a conical intersection, however, belongs to a specific definition of the electronic states, within a Born-Huang representation of the molecular wavefunction. How would these ultrafast funneling processes be translated if an exact factorization of the molecular wavefunction were to be used? In this article, we build upon our recent analysis [B.F.E. Curchod, F. Agostini, J. Phys. Chem. Lett. 8, 831 (2017)] and address this question in a broader perspective by studying the dynamics of a nuclear wavepacket through two types of conical intersections, differing by the strength of their underlying diabatic coupling. Our results generalize our previous findings by (i) showing that the time-dependent potential energy surface smoothly varies, both in time and in position, between the corresponding diabatic and adiabatic potentials, with sometimes more complex features if interferences are observed, (ii) highlighting the non-trivial behavior of the time-dependent vector potential and the fact that it cannot be gauged away in general, and (iii) justifying some approximations employed in the derivation of a mixed quantum/classical scheme based on the exact factorization.

Different flavors of nonadiabatic molecular dynamics

“…Conceptual and/or numerical issues related to the definition of the electronic basis set chosen for the expansion are naturally circumvented. In particular, this feature allows one to rethink molecular dynamics at conical intersections and phenomena related to geometric phases, which can be grounded in the Born‐Huang representation and sometimes (mis‐)interpreted as observable effects. Despite this intriguing possibility, practical numerical applications of the Exact Factorization (see Section 5.1.2 and References ) still rely on a Born‐Huang‐like expansion of the electronic wavefunction, in order to employ standard quantum‐chemistry approaches to compute electronic properties along the nuclear dynamics.…”

On the numerical solution of the exact factorization equations

“…Now, we take the inner product with φ R (r, t)| to obtain the analog of Eq. (13). Then for partial norm conservation one only has to show that Im( GD ) = 0, with the GD defined in Eq.…”

“…, shedding light on the nature of interactions between dynamical quantum subsystems as well as on interactions between quantum and classical subsystems beyond adiabatic treatments. From a practical viewpoint, the EF equations provide a rigorous starting point for methods for non-adiabatic dynamics and already we have seen the development of mixed quantumclassical approaches [23][24][25][26], with successful applications in photochemical dynamics [27], as well as density functionalizations [17,18].…”

Excited-state dynamics of molecules with classically driven trajectories and Gaussians

“…As the nuclei only have to follow a single time-dependent PES, no hopping or spawning is required in stark contrast to the Born-Huang representation. These observations greatly motivated the development of approximate nonadiabatic dynamics strategies based on the Exact Factorisation [62,214,215], with methods like the coupled-trajectory mixed quantum/classical (CT-MQC) strategy having been applied to the excited-state dynamics of molecular systems [216][217][218][219][220][221]. The Exact Factorisation has also been used to shed new lights on the dynamics through conical intersections [222,223] -conical intersections being related to a Born-Huang expansion in adiabatic electronic states -as well as the geometric phase [224].…”