A natural decay of mixing algorithm for non-Born–Oppenheimer trajectories

Hack, Michael D.; Truhlar, Donald G.

doi:10.1063/1.1368388

Cited by 105 publications

(131 citation statements)

References 21 publications

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“…25,27,[32][33][34]36,[41][42][43][44]46,53 Because it has been impractical to study dynamics for systems with very small semiclassical transition probabilities, these tests have been carried out for systems with nonadiabatic probabilities of 3ϫ10 Ϫ4 and larger. The army ants algorithm allows us to extend these tests down to much lower probabilities; for example, in the present paper we present well-converged calculations for a system with a nonadiabatic transition probability of 1ϫ10…”

Section: Introductionmentioning

confidence: 99%

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

Nangia¹,

Jasper²,

Miller³

et al. 2004

The Journal of Chemical Physics

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The most widely used algorithm for Monte Carlo sampling of electronic transitions in trajectory surface hopping ͑TSH͒ calculations is the so-called anteater algorithm, which is inefficient for sampling low-probability nonadiabatic events. We present a new sampling scheme ͑called the army ants algorithm͒ for carrying out TSH calculations that is applicable to systems with any strength of coupling. The army ants algorithm is a form of rare event sampling whose efficiency is controlled by an input parameter. By choosing a suitable value of the input parameter the army ants algorithm can be reduced to the anteater algorithm ͑which is efficient for strongly coupled cases͒, and by optimizing the parameter the army ants algorithm may be efficiently applied to systems with low-probability events. To demonstrate the efficiency of the army ants algorithm, we performed atom-diatom scattering calculations on a model system involving weakly coupled electronic states. Fully converged quantum mechanical calculations were performed, and the probabilities for nonadiabatic reaction and nonreactive deexcitation ͑quenching͒ were found to be on the order of 10Ϫ8 . For such low-probability events the anteater sampling scheme requires a large number of trajectories (ϳ10 10 ) to obtain good statistics and converged semiclassical results. In contrast by using the new army ants algorithm converged results were obtained by running 10 5 trajectories. Furthermore, the results were found to be in excellent agreement with the quantum mechanical results. Sampling errors were estimated using the bootstrap method, which is validated for use with the army ants algorithm.

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Section: Introductionmentioning

confidence: 99%

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

Nangia¹,

Jasper²,

Miller³

et al. 2004

The Journal of Chemical Physics

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“…Eqn. (15) includes the pure dephasing contribution but not the bath overlap decay contribution. In the present case the bath consists of the nuclear degrees of freedom, and the nuclear overlap decay has been emphasized by Prezhdo and Rossky, 13 who describe it as the nonradiative analog to Franck-Condon overlap factors 123 in radiative processes.…”

Section: Semiclassical Trajectory Methodsmentioning

confidence: 99%

Introductory lecture: Nonadiabatic effects in chemical dynamics

et al. 2004

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Recent progress in the theoretical treatment of electronically nonadiabatic processes is discussed. First we discuss the generalized Born-Oppenheimer approximation, which identifies a subset of strongly coupled states, and the relative advantages and disadvantages of adiabatic and diabatic representations of the coupled surfaces and their interactions are considered. Ab initio diabatic representations that do not require tracking geometric phases or calculating singular nonadiabatic nuclear momentum coupling will be presented as one promising approach for characterizing the coupled electronic states of polyatomic photochemical systems. Such representations can be accomplished by methods based on functionals of the adiabatic electronic density matrix and the identification of reference orbitals for use in an overlap criterion. Next, four approaches to calculating or modeling electronically nonadiabatic dynamics are discussed: (1) accurate quantum mechanical scattering calculations, (2) approximate wave packet methods, (3) surface hopping, and (4) self-consistent-potential semiclassical approaches. The last two of these are particularly useful for polyatomic photochemistry, and recent refinements of these approaches will be discussed. For example, considerable progress has been achieved in making the surface hopping method more applicable to the study of systems with weakly coupled electronic states. This includes introducing uncertainty principle considerations to alleviate the problem of classically forbidden surface hops and the development of an efficient sampling algorithm for low-probability events. A topic whose central importance in a number of quantum mechanical fields is becoming more widely appreciated is the introduction of decoherence into the quantal degrees of freedom to account for the effect of the classical treatment on the other degrees of freedom, and we discuss how the introduction of such decoherence into a self-consistent-potential approximation leads to a reasonably accurate but very practical trajectory method for electronically nonadiabatic processes. Finally, the performances of several dynamical methods for Landau-Zener-type and Rosen-Zener-Demkov-type reactive scattering problems are compared.

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“…The Ehrenfest method removes these difficulties, but it may produce unphysical mixed states at the outcome. The improved Ehrenfest method solves the mixed-state problem by including a decoherence effect (33). However, implementation of the method to a large system such as ours is still intractable.…”

Section: Methodsmentioning

confidence: 99%

Regulating energy transfer of excited carriers and the case for excitation-induced hydrogen dissociation on hydrogenated graphene

Bang

Meng

Sun

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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Understanding and controlling of excited carrier dynamics is of fundamental and practical importance, particularly in photochemistry and solar energy applications. However, theory of energy relaxation of excited carriers is still in its early stage. Here, using ab initio molecular dynamics (MD) coupled with time-dependent density functional theory, we show a coverage-dependent energy transfer of photoexcited carriers in hydrogenated graphene, giving rise to distinctively different ion dynamics. Graphene with sparsely populated H is difficult to dissociate due to inefficient transfer of the excitation energy into kinetic energy of the H. In contrast, H can easily desorb from fully hydrogenated graphane. The key is to bring down the H antibonding state to the conduction band minimum as the band gap increases. These results can be contrasted to those of standard ground-state MD that predict H in the sparse case should be much less stable than that in fully hydrogenated graphane. Our findings thus signify the importance of carrying out explicit electronic dynamics in excited-state simulations.photodissociation | nonadiabatic dynamics | first-principles calculation C arrier dynamics are a key to the understanding of energy transfer in molecules and solids (1). Recent advances in femtosecond and attosecond laser techniques have also led to heightened interest in excited-state dynamics (2, 3). However, the theory of nonradiative energy relaxation of excited carriers is still rather immature. One of the fundamental reasons for this immaturity is the difficulty in going beyond the Born-Oppenheimer approximation (BOA) (4). The BOA allows us to simulate ground-state dynamics and determine the structure and phonon modes (5). However, inferring the behavior of excited states from groundstate dynamics is physically unfounded (6).The physical quantity to be examined during the dynamics is the system energy, which can be divided into kinetic energy (KE) and potential energy (PE) of the ions. The latter includes electron kinetic energy and electron-electron, electron-ion, and ion-ion interactions. Therefore, electron excitation always increases the PE of the ions. Because the excited state is not in equilibrium, the excited carriers must undergo relaxation. Among several possible relaxation mechanisms, the electron-electron (e-e) and electron-phonon (e-ph) coupling are the dominant processes in the femtosecond time regime whereas the timescales for others such as radiative recombination are about three to four orders of magnitude longer (7). In the case of e-e coupling, the energy exchange takes place only within the electronic degree of freedom, and the energy of the excited carriers is dissipated to background electrons without changing the overall PE of the ions. In contrast, in the case of e-ph coupling, the excited PE is transferred to the KE of the ions, and the KE of the ions is increased. Depending on the energy transfer mechanism, excited-state dynamics can show qualitatively different behaviors and therefore the energy...

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A natural decay of mixing algorithm for non-Born–Oppenheimer trajectories

Cited by 105 publications

References 21 publications

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

Introductory lecture: Nonadiabatic effects in chemical dynamics

Regulating energy transfer of excited carriers and the case for excitation-induced hydrogen dissociation on hydrogenated graphene

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