Trajectory Surface Hopping in the Time-Dependent Kohn-Sham Approach for Electron-Nuclear Dynamics

Craig, Colleen F.; Duncan, Walter R.; Prezhdo, Oleg V.

doi:10.1103/physrevlett.95.163001

Cited by 670 publications

(838 citation statements)

References 51 publications

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“…(11)). 12,20 In time-dependent Kohn-Sham theory, 29 the time evolution of the single-particle KS orbitals is obtained from the time-dependent Schrödinger-like equation:…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…3, 5, and 30-32) and surface hopping methods. 19,20,25,26,[33][34][35] In the Ehrenfest approach, the nuclei move classically on a single effective PES obtained by averaging over all the adiabatic states involved, whereas in surface hopping methods, the classical degrees of freedom (nuclei coordinates) evolve on single adiabatic surfaces (PES), and make probabilistic hops from one PES to another; when a transition takes place, energy conservation is imposed re-scaling velocities along the direction of the nonadiabatic coupling vectors 8,25,27 (if the NACVs are not available, as is usually the case, energy conservation is achieved re-scaling all velocities). Surface hopping methods present well-known advantages over Ehrenfest methods (e.g., see Ref.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…(5)) since they are easily obtained as a numerical finite difference formula. 19,20 However, it is both interesting and useful to explicitly calculate the NACVs for instance, in order to search for conical intersections or avoided crossing regions, [21][22][23][24] or for the rescaling of the atomic velocities when an electronic transition takes place along the non-adiabatic molecular dynamics (MD) simulation. 8,[25][26][27] In Sec.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Calculation of non-adiabatic coupling vectors in a local-orbital basis set

Abad

Lewis

Zobač

et al. 2013

The Journal of Chemical Physics

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Most of today's molecular-dynamics simulations of materials are based on the Born-Oppenheimer approximation. There are many cases, however, in which the coupling of the electrons and nuclei is important and it is necessary to go beyond the Born-Oppenheimer approximation. In these methods, the non-adiabatic coupling vectors are fundamental since they represent the link between the classical atomic motion of the nuclei and the time evolution of the quantum electronic state. In this paper we analyze the calculation of non-adiabatic coupling vectors in a basis set of local orbitals and derive an expression to calculate them in a practical and computationally efficient way. Some examples of the application of this expression using a local-orbital density functional theory approach are presented for a few simple molecules: H 3 , formaldimine, and azobenzene. These results show that the approach presented here, using the Slater transition-state density, is a very promising way for the practical calculation of non-adiabatic coupling vectors for large systems. © 2013 AIP Publishing LLC. [http://dx

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“…(11)). 12,20 In time-dependent Kohn-Sham theory, 29 the time evolution of the single-particle KS orbitals is obtained from the time-dependent Schrödinger-like equation:…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Calculation of non-adiabatic coupling vectors in a local-orbital basis set

Abad

Lewis

Zobač

et al. 2013

The Journal of Chemical Physics

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“…24 and applied to carbon solids and nanostructures. 12,23,[25][26][27] The problem of nonadiabatic molecular dynamics has also been treated with methods of surface hopping [28][29][30] and the quantum-classical mean field ͑Ehrenfest͒ method. [31][32][33] In the following we summarize the main points of our approach.…”

Section: Theorymentioning

confidence: 99%

Microscopic investigation of laser-induced structural changes in single-wall carbon nanotubes

et al. 2007

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Extensive excited-state molecular dynamics simulations of femtosecond laser-induced structural transformation in single-walled carbon nanotubes ͑SWNTs͒ are presented. We considered in the simulation two limiting cases; one where only a short portion of the tube is irradiated and the other where the whole tube is affected by the laser pulse. We have analyzed the role of chirality ͑zigzag versus armchair and some chiral tube cases͒ in the damage threshold as a function of tube diameter. Nontrivial dependence of the damage threshold as a function of diameter has been found. We find that for equal laser parameters, zigzag SWNTs are on average equally stable with respect to laser excitation as armchair SWNTs, but their stabilities show different dependencies on diameter. Due to the higher stiffness of the ͑n , n͒ tubes in the direction perpendicular to its axis as compared to the ͑n ,0͒ tubes, we find the formation of standing waves in the nanotube wall for zigzag and not for armchair tubes. We also studied the role of the laser pulse duration and show that in general longer laser pulses increase the damage threshold. This result is rationalized in terms of electron-ion relaxation times. Implications of laser-induced structural transformations are analyzed.

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“…[33][34][35][36][37][38] Furthermore, there has been considerable interest in the extension of TDDFT to study situations where there is an interplay between electronic and nuclear degrees of freedom and both are explicitly included in the simulation. [39][40][41][42][43][44][45] An alternative approach to this problem relies on Open Quantum Systems (OQS) theory, where the electronic degrees of freedom are evolved as a quantum master equation (ME), with the bath of phonons affecting the electrons via fluctuations and dissipation. [46][47][48][49][50][51][52][53][54][55] We hereby restrict the definition of OQS to the domain of systems that exchange energy-but not particles, with an environment.…”

mentioning

confidence: 99%

Remarks on time-dependent [current]-density functional theory for open quantum systems

Yuen-Zhou

Aspuru‐Guzik

2013

Phys. Chem. Chem. Phys.

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Time-dependent [current]-density functional theory for open quantum systems (OQS) has emerged as a formalism that can incorporate dissipative effects in the dynamics of many-body quantum systems.Here, we review and clarify some formal aspects of these theories that have been recently questioned in the literature. In particular, we provide theoretical support for the following conclusions: (1) contrary to what we and others had stated before, within the master equation framework, there is in fact a one-to-one mapping between vector potentials and current densities for fixed initial state, particleparticle interaction, and memory kernel; (2) regardless of the first conclusion, all of our recently suggested Kohn-Sham (KS) schemes to reproduce the current and particle densities of the original OQS, and in particular, the use of a KS closed driven system, remains formally valid; (3) the Lindblad master equation maintains the positivity of the density matrix regardless of the time-dependence of the Hamiltonian or the dissipation operators; (4) within the stochastic Schrödinger equation picture, a one-to-one mapping from stochastic vector potential to stochastic current density for individual trajectories has not been proven so far, except in the case where the vector potential is the same for every member of the ensemble, in which case, it reduces to the Lindblad master equation picture; (5) master equations may violate certain desired properties of the density matrix, such as positivity, but they remain as one of the most useful constructs to study OQS when the environment is not easily incorporated explicitly in the calculation. The conclusions support our previous work as formally rigorous, offer new insights into it, and provide a common ground to discuss related theories.

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Trajectory Surface Hopping in the Time-Dependent Kohn-Sham Approach for Electron-Nuclear Dynamics

Cited by 670 publications

References 51 publications

Calculation of non-adiabatic coupling vectors in a local-orbital basis set

Calculation of non-adiabatic coupling vectors in a local-orbital basis set

Microscopic investigation of laser-induced structural changes in single-wall carbon nanotubes

Remarks on time-dependent [current]-density functional theory for open quantum systems

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