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

Abstract

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

Molecular geometric phase from the exact electron-nuclear factorization

“…excitations to degenerate excited states with significant nuclear currents. Methods to exploit the exact factorization in coupled electron-nuclear dynamics are under active development, 75 but so far have only been applied to onedimensional systems, where A µ is trivial. The physical role of the induced vector potential is to provide a contribution A µ |χ| 2 to the nuclear current which the gradient term Imχ * ∇ µ χ is not able to provide.…”

An exact factorization perspective on quantum interferences in nonadiabatic dynamics

“…One of the questions addressed in this work is as follows: Can such recombination patterns, i.e., nonadiabatic quantum interferences, be identified in the TDPES? The importance of capturing the recombination process imposes that the analysis shall focus on the nonadiabatic region, by contrast to previous analysis 39,41 that has instead mainly placed the attention on the TDPES far from an avoided crossing. Furthermore, as interferences are fundamentally quantum-mechanical effects, the natural question arises as follows: Can classical trajectories, also in this case, correctly reproduce nuclear dynamics if the exact TDPES is known?…”

“…(5) is indeed unique up to a gauge transformation. 41 Henceforth, the time-dependent vector potential A ν (R,t) will be set to zero, fixing the gauge freedom and transferring all the electronic backreaction to the TDPES. 41 The nuclear wavefunction can be expressed in a polar form χ(R,t) = | χ(R,t)|e i S(R, t)/ and, for 1D problem, imposing to the phase S(R,t) the condition…”

“…In particular, the steps of the TDPES have been related to the spatial splitting of the (exact) nuclear wavefunction, which reproduces the dynamics of BO wavefunctions branching in different adiabatic states. Furthermore, we have employed these observations to investigate the suitability of the (quasi)classical treatment 40,41 of nuclear dynamics in situations where the electronic effect can be taken into account exactly, with the aim of proposing trajectory-based approximation schemes [65][66][67][68] to the quantum-mechanical problem.…”

“…The molecular wavefunction can, for example, be represented exactly by a simple factorization 37,38 in terms of a time-dependent nuclear wavefunction and a time-dependent electronic wavefunction, parametrically dependent on the nuclear positions. When inserted into the molecular time-dependent Schrödinger equation, the Exact Factorization (EF) leads to coupled equations driving the dynamics of the two components of the wavefunction: a timedependent Schrödinger equation [39][40][41][42] describes the evolution a) Electronic address: agostini@mpi-halle.mpg.de of the nuclear wavefunction, where the effect of the electrons is fully accounted for by a time-dependent vector potential and a time-dependent scalar potential (or time-dependent potential energy surface, TDPES); electronic dynamics is generated by an evolution equation where the coupling to the nuclei is expressed by the so-called electron-nuclear coupling operator. [43][44][45][46][47] The EF has been developed both in the time-independent [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64] and in the time-dependent [37][38][39][40][41][42][43][65][66][67][68] versions and analyzed under different perspectives.…”