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

We study the exact time-dependent potential energy surface (TDPES) in the presence of strong nonadiabatic coupling between the electronic and nuclear motion. The concept of the TDPES emerges from the exact factorization of the full electron-nuclear wave function [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. Employing a one-dimensional model system, we show that the TDPES exhibits a dynamical step that bridges between piecewise adiabatic shapes. We analytically investigate the position of the steps and the nature of the switching between the adiabatic pieces of the TDPES.

The exact nuclear time-dependent potential energy surface arises from the exact decomposition of electronic and nuclear motion, recently presented in [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. Such time-dependent potential drives nuclear motion and fully accounts for the coupling to the electronic subsystem. We investigate the features of the potential in the context of electronic non-adiabatic processes and employ it to study the performance of the classical approximation on nuclear dynamics. We observe that the potential, after the nuclear wave-packet splits at an avoided crossing, develops dynamical steps connecting different regions, along the nuclear coordinate, in which it has the same slope as one or the other adiabatic surface. A detailed analysis of these steps is presented for systems with different non-adiabatic coupling strength. The exact factorization of the electron-nuclear wave-function is at the basis of the decomposition. In particular, the nuclear part is the true nuclear wave-function, solution of a time-dependent Schroedinger euqation and leading to the exact many-body density and current density.As a consequence, the Ehrenfest theorem can be extended to the nuclear subsystem and Hamiltonian, as discussed here with an analytical derivation and numerical results. equation (TDSE) is expanded in the complete system of BO electronic states, leading to a nuclear wave-packet with contributions on several BOPESs that undergo transitions in the regions of strong non-adiabatic coupling. This approach provides a formally exact description of the complete system if all the electronic states are taken into account. However, practical applications are limited to a small number of degrees of freedom. For large systems, the only feasible way of dealing with non-adiabatic processes is the introduction of classical or semi-classical approximations for the nuclear motion, coupled, non-adiabatically, to the (quantum mechanical) electrons.Although widely investigated [14][15][16][17], the nature of the force driving the classical nuclei in this mixed quantum-classical treatment has not yet been fully identified.Recently [18], this problem has been addressed from a novel perspective by referring to the exact representation of the full molecular wave-function [19,20] as a single product of a purely nuclear wave-function and an electronic factor that parametrically depends on the nuclear coordinates. In this framework, a TDSE for the nuclear wave-function is derived, where a timedependent potential energy surface (TDPES) and a time-dependent vector potential arise as exact concepts and provide the driving force for the nuclear evolution.The present paper discusses situations where the vector potential can be set to zero by an appropriate choice of gauge, thus leaving the TDPES as the only potential responsible for the nuclear dynamics. In this case, the force on the nuclei, in a classical sense, can be obtained as the gradient of the TDPES. But, is this the true classical f...

We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are completely missed by adiabatic approximations that, consequently, significantly underestimate the scattering probability. A recently proposed nonadiabatic approximation is shown to correctly capture the approach of the electron to the target when the initial Kohn-Sham state is chosen judiciously, and it is more accurate than standard adiabatic functionals but ultimately fails to accurately capture reflection. These results may explain the underestimation of scattering probabilities in some recent studies on molecules and surfaces.

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