Trajectory-based mixed quantum-classical approaches to coupled electron-nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability of reproducing the spatial splitting of a nuclear wave packet in Ehrenfest-like dynamics. In the context of electronic nonadiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics. In this paper, we propose a solution to these issues by approximating the coupled electronic and nuclear equations within the framework of the exact factorization of the electron-nuclear wave function. We present a simple quantum-classical scheme based on coupled classical trajectories and test it against the full quantum mechanical solution from wave packet dynamics for some model situations which represent particularly challenging problems for the above-mentioned traditional methods.

We present a novel quantum-classical approach to non-adiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electronnuclear wave function. The method is based on the quasi-classical interpretation of the nuclear wave function, whose phase is related to the classical momentum and whose density is represented in terms of classical trajectories. In this approximation, electronic decoherence is naturally induced as effect of the coupling to the nuclei and correctly reproduces the expected quantum behaviour. Moreover, the splitting of the nuclear wave packet is captured as consequence of the correct approximation of the time-dependent potential of the theory. This new approach offers a clear improvement over Ehrenfest-like dynamics. The theoretical derivation presented in the Letter is supported by numerical results that are compared to quantum mechanical calculations. 31.15.xg, 31.50.Gh, 82.20.Gk The theoretical description of phenomena such as vision [1], photo-synthesis [2], photo-voltaic processes [3], proton-transfer and hydrogen storage [4] is among the most challenging problems in Condensed Matter Physics and Theoretical Chemistry. The underlying quantum dynamics of electrons and nuclei exhibit a non-adiabatic character, meaning that it cannot be explained by employing the Born-Oppenheimer (BO) approximation. In this respect, the major challenge for theory resides in the explicit treatment of electronic excitedstate dynamics coupled to the nuclear motion. While methods that retain quantum features of the nuclear dynamics [5] are the most accurate to address this problem, they cannot be applied to systems with hundreds, or even thousands, of atoms. Therefore, a treatment of nuclear dynamics in terms of (semi)classical trajectories [5][6][7][8][9] represent the most promising and numerically feasible approach for actual calculations. Despite the great effort that has been devoted over the years to the development of such methods, actual applications are still limited [10]. Well-known issues are connected to the lack of, or incorrect account for, decoherence and to the inability of reproducing the spatial splitting of a nuclear wave packet, as in Ehrenfest-like dynamics. In the study of electronic non-adiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics.We have recently proposed a new formalism that can be employed to overcome the above issues, the so-called exact factorization of the electron-nuclear wave function [11]. In this framework, the full wave function is written as the product of a nuclear wave function and an electronic factor with a parametric dependence on the nuclear configuration. Coupled equations drive the dynamics of the two components of the wave function. In particular, a time-dependent Schrödinger equation (TDSE) describes the evolution of the nuclear wave function where the effect of the electrons, beyond BO, is accounted ...

We report the first nonadiabatic molecular dynamics study based on the exact factorization of the electron-nuclear wave function. Our approach (a coupled-trajectory mixed quantum-classical, CT-MQC, scheme) is based on the quantum-classical limit derived from systematic and controlled approximations to the full quantum-mechanical problem formulated in the exact-factorization framework. Its strength is the ability to correctly capture quantum (de)coherence effects in a trajectory-based approach to excited-state dynamics. We show this by benchmarking CT-MQC dynamics against a revised version of the popular fewest-switches surface-hopping scheme that is able to fix its well-documented overcoherence issue. The CT-MQC approach is successfully applied to investigation of the photochemistry (ring-opening) of oxirane in the gas phase, analyzing in detail the role of decoherence. This work represents a significant step forward in the establishment of the exact factorization as a powerful tool to study excited-state dynamics, not only for interpretation purposes but mainly for nonadiabatic ab initio molecular dynamics simulations.

Non-adiabatic processes in the charge transfer reaction of O2 molecules with potassium surfaces without dissociation J. Chem. Phys. 141, 074711 (2014) The exact forces on classical nuclei in non-adiabatic charge transfer The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect. C 2015 AIP Publishing LLC.[http://dx