A self-consistent eikonal treatment of electronic transitions in molecular collisions

Micha, David A.

doi:10.1063/1.444753

Cited by 232 publications

(156 citation statements)

References 22 publications

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“…nuclei evolve on top of a single effective potential energy surface defined as a weighted average of the involved adiabatic BOPEs. Entanglement is hardly described by these (Ehrenfest-like) approaches because the back-reaction between classical and quantum subsystems is described under mean-field assumptions [41][42][43][44]. Multiconfiguration schemes, such as Tully's surface hopping, are in general required to account for bifurcation paths with entaglement [45,46].…”

Section: Nonadiabatic Molecular Dynamicsmentioning

confidence: 99%

“…a solution to the trajectory branching problem by creating a new type of quantum back-reaction on the classical subsystem. In the quantum-classical Ehrenfest approximation, which is the most common approach, a single average classical trajectory is generated [41][42][43][44]. In contrast, in [60] an ensemble of quantum-classical Bohmian trajectories is created for a single initial quantum-mechanical wave function.…”

Section: Nonadiabatic Molecular Dynamicsmentioning

confidence: 99%

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Applied Bohmian mechanics

et al. 2014

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Abstract. Bohmian mechanics provides an explanation of quantum phenomena in terms of point-like particles guided by wave functions. This review focuses on the use of nonrelativistic Bohmian mechanics to address practical problems, rather than on its interpretation. Although the Bohmian and standard quantum theories have different formalisms, both give exactly the same predictions for all phenomena. Fifteen years ago, the quantum chemistry community began to study the practical usefulness of Bohmian mechanics. Since then, the scientific community has mainly applied it to study the (unitary) evolution of single-particle wave functions, either by developing efficient quantum trajectory algorithms or by providing a trajectorybased explanation of complicated quantum phenomena. Here we present a large list of examples showing how the Bohmian formalism provides a useful solution in different forefront research fields for this kind of problems (where the Bohmian and the quantum hydrodynamic formalisms coincide). In addition, this work also emphasizes that the Bohmian formalism can be a useful tool in other types of (nonunitary and nonlinear) quantum problems where the influence of the environment or the nonsimulated degrees of freedom are relevant. This review contains also examples on the use of the Bohmian formalism for the many-body problem, decoherence and measurement processes. The ability of the Bohmian formalism to analyze this last type of problems for (open) quantum systems remains mainly unexplored by the scientific community. The authors of this review are convinced that the final status of the Bohmian theory among the scientific community will be greatly influenced by its potential success in those types of problems that present nonunitary and/or nonlinear quantum evolutions. A brief introduction of the Bohmian formalism and some of its extensions are presented in the last part of this review.

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Section: Nonadiabatic Molecular Dynamicsmentioning

confidence: 99%

Section: Nonadiabatic Molecular Dynamicsmentioning

confidence: 99%

Applied Bohmian mechanics

et al. 2014

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“…The most widely used approaches to account for the nonadiabatic effects are surface hopping, 23 mean-field 28,29 and the method combining them. 30 In this package, the nonadiabatic effects were taken into account by means of the Zhu-Nakamura theory 31,32 and the relevant electronic structure calculations were performed by an external chemical program which is linked to this package.…”

Section: B Nonadiabatic Ab Initio Dynamicsmentioning

confidence: 99%

Nonadiabatic ab initio molecular dynamics of photoisomerization in bridged azobenzene

Gao

Zhang

et al. 2012

The Journal of Chemical Physics

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The photoisomerization mechanisms of bridged azobenzene are investigated by means of surface hopping dynamics simulations based on the Zhu-Nakamura theory. In the geometry optimizations and potential energy surface calculations, four minimum-energy conical intersections between the ground state and the lowest excited state are found to play important roles in the trans-cis and cis-trans isomerization processes. The trans-cis photoisomerization proceeds through two minimum-energy conical intersections. Ultrafast pedal motion of the N atoms and twisting of phenyl rings around their N-C bonds allows the molecule to move to a minimum-energy conical intersection, after which surface hopping from S 1 to S 0 occurs. In the S 0 state, further rotation occurs around the N=N bond and two N-C bonds until the azo moiety and phenyl rings complete their isomerization. Finally, the cis form is achieved by subsequent adjustment of the ethylene bridge. In the cis-trans photodynamics, there is one rotational pathway, in the middle of which two CIs are responsible for the surface hopping to the S 0 state. After the nonadiabatic transition, the molecule reaches the trans form through a barrierless pathway and the two phenyl rings and the additional bridge complete their reorientation almost at the same time.

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“…38 Recently, other methods based on the mapping approach have appeared for treating thermal initial states, 39 using a ring-polymer molecular dynamics (RPMD) Hamiltonian, 40,41 or in combination with partially linearized real-time path integrals. 42 Other dynamical approaches employ mean-field approximations, 43 multiple spawning, 44 the quantumclassical Liouville equation 45 or an exact factorization of the complete molecular Hamiltonian. 46 Approximate methods for the estimation of the rate of nonadiabatic processes include those which treat the transferred electron explicitly with RPMD, 47,48 employ semiclassical instanton theory, 49 or use a modified RPMD Hamiltonian to enforce the correct 2 dependence in the golden-rule limit.…”

Section: Introductionmentioning

confidence: 99%

Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory

Richardson

Thoss

2014

The Journal of Chemical Physics

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Quantum mechanical canonical rate theory: A new approach based on the reactive flux and numerical analytic continuation methods J. Chem. Phys. 112, 2605 (2000); 10.1063/1.480834Erratum: "A unified framework for quantum activated rate processes. II. The nonadiabatic limit" [J. Chem. Phys. 106, 1769 There is currently much interest in the development of improved trajectory-based methods for the simulation of nonadiabatic processes in complex systems. An important goal for such methods is the accurate calculation of the rate constant over a wide range of electronic coupling strengths and it is often the nonadiabatic, weak-coupling limit, which being far from the Born-Oppenheimer regime, provides the greatest challenge to current methods. We show that in this limit there is an inherent sign problem impeding further development which originates from the use of the usual quantum flux correlation functions, which can be very oscillatory at short times. From linear response theory, we derive a modified flux correlation function for the calculation of nonadiabatic reaction rates, which still rigorously gives the correct result in the long-time limit regardless of electronic coupling strength, but unlike the usual formalism is not oscillatory in the weak-coupling regime. In particular, a trajectory simulation of the modified correlation function is naturally initialized in a region localized about the crossing of the potential energy surfaces. In the weak-coupling limit, a simple link can be found between the dynamics initialized from this transition-state region and an generalized quantum goldenrule transition-state theory, which is equivalent to Marcus theory in the classical harmonic limit. This new correlation function formalism thus provides a platform on which a wide variety of dynamical simulation methods can be built aiding the development of accurate nonadiabatic rate theories applicable to complex systems. © 2014 AIP Publishing LLC. [http://dx

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A self-consistent eikonal treatment of electronic transitions in molecular collisions

Cited by 232 publications

References 22 publications

Applied Bohmian mechanics

Applied Bohmian mechanics

Nonadiabatic ab initio molecular dynamics of photoisomerization in bridged azobenzene

Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory

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