Electronic transitions with quantum trajectories

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Nonadiabatic quantum interferences emerge whenever nuclear wavefunctions in different electronic states meet and interact in a nonadiabatic region.In this work, we analyze how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction. In particular, we focus our attention on the shape of the time-dependent potential energy surface-the exact surface on which the nuclear dynamics takes place. We use a one-dimensional exactly solvable model to reproduce different conditions for quantum interferences, whose characteristic features already appear in one-dimension. The time-dependent potential energy surface develops complex features when strong interferences are present, in clear contrast to the observed behavior in simple nonadiabatic crossing cases. Nevertheless, independent classical trajectories propagated on the exact time-dependent potential energy surface reasonably conserve a distribution in configuration space that mimics one of the exact nuclear probability densities. Published by AIP Publishing.[http://dx

Section: Fig 8 Contributions To the Full Tdpess Represented Inmentioning

confidence: 99%

An exact factorization perspective on quantum interferences in nonadiabatic dynamics

Curchod

Agostini

Gross

2016

“…We devote this appendix to a brief overview of the Bohmian approach 27,28 to quantum dynamics. Even though this procedure might seem somehow connected to the work presented in the paper, as it is based on the propagation of trajectories on a time-dependent potential, it will become clear here that this is not the case.…”

Section: Appendix A: Connection To Bohmian Trajectoriesmentioning

confidence: 99%

The exact forces on classical nuclei in non-adiabatic charge transfer

Agostini

Abedi

Suzuki

et al. 2015

111

195

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

“…Therefore, for an auto-correlation function we cannot use a single window function; we perform a local expansion around each trajectory as outlined in Sec. II D. The width matrix of the window function is a diagonal matrix with the elements ͕16a 11 ,16a 22 ͖. The two correlation functions are shown on Fig.…”

Section: ͑34͒mentioning

confidence: 99%

“…In the last few years several practical ways of using quantum trajectories have been suggested, such as local least-square fit, adaptive and moving grids; 16 -19 a methodology of using quantum trajectories within the Wigner representation and in dissipative and nonadiabatic dynamics have been also developed. [20][21][22] Application to multidimensional model problems performed with a small number of trajectories is encouraging. 23 However, for general problems accurate implementation of the hydrodynamic Schrödinger equation, which is a nonlinear equation resulting in a complicated and rapidly varying quantum potential, is challenging.…”

Section: Introductionmentioning

confidence: 99%

Energy conserving approximations to the quantum potential: Dynamics with linearized quantum force

Garashchuk

Rassolov

2004

Solution of the Schrödinger equation within the de Broglie-Bohm formulation is based on propagation of trajectories in the presence of a nonlocal quantum potential. We present a new strategy for defining approximate quantum potentials within a restricted trial function by performing the optimal fit to the log-derivatives of the wave function density. This procedure results in the energy-conserving dynamics for a closed system. For one particular form of the trial function leading to the linear quantum force, the optimization problem is solved analytically in terms of the first and second moments of the weighted trajectory distribution. This approach gives exact time-evolution of a correlated Gaussian wave function in a locally quadratic potential. The method is computationally cheap in many dimensions, conserves total energy and satisfies the criterion on the average quantum force. Expectation values are readily found by summing over trajectory weights. Efficient extraction of the phase-dependent quantities is discussed. We illustrate the efficiency and accuracy of the linear quantum force approximation by examining a one-dimensional scattering problem and by computing the wavepacket reaction probability for the hydrogen exchange reaction and the photodissociation spectrum of ICN in two dimensions.