Exact Factorization of the Electron–Nuclear Wave Function: Theory and Applications

Nonadiabatic Dynamics with Coupled Trajectories

“…In this context, the present paper proposes new advances focusing on coupled-trajectory methods for excited-state dynamics. The working framework is provided by the exact factorization of the time-dependent electron–nuclear wave function. − The exact-factorization Ansatz allows one to factor the molecular wave function as the product of a nuclear wave function and a conditional electronic factor, and it is then proven to be an exact rewriting of the molecular time-dependent wave function. Evolution equations for the two terms of the factored wave function can be derived from the time-dependent Schrödinger equation, and have led, in previous work by Gross and collaborators, − to derive a coupled-trajectory mixed quantum-classical (CT-MQC) scheme for excited-state nonadiabatic dynamics.…”

Electronic Structure and Excited States of the Collision Reaction O(3P) + C2H4: A Multiconfigurational Perspective

“…Nonetheless, effects due to excited states have usually been neglected, , which allowed, together with the use of fitted PESs, us to propagate a large number of trajectories and to achieve, consequently, good statistics for the prediction of cross sections and branching ratios. Significant contributions to the characterization of the electronic structure of this system have been made based on density functional theory (DFT) methods. ,,− However, DFT is unable to describe systems that show a significant multiconfigurational character, especially when the system undergoes bond breaking or bond formation, which is exactly the situation studied here. DFT simply has problems in handling fragmentation which, instead, multiconfigurational methods can properly account for.…”

Quantum-classical nonadiabatic dynamics of Floquet driven systems

“…The solution of the time-dependent Schr ödinger equation (tdSE), Ψ(r, R, t), with Hamiltonian (1) can be factored as the product of a nuclear wavefunction, χ(R, t), and an electronic conditional factor, Φ(r, t; R), that parametrically depends on R, namely 44,45 Ψ(r, R, t) = χ(R, t)Φ(r, t; R)…”

“…In this paper, we focus on the combination of the exact factorization of the electronic-nuclear wavefunction 29,[44][45][46] with the Floquet formalism 38,47 , devoting particular attention to the coupledtrajectory mixed quantum-classical (CT-MQC) algorithm [48][49][50][51][52][53] . CT-MQC is the numerical scheme allowing to solve the exact-factorization equations based on the quantum-classical approximation [54][55][56][57] of the nonadiabatic electron-nuclear problem, by introducing a trajectory-based solution of nuclear dynamics as formulated within the exact factorization.…”