Mixed quantum–classical dynamics

Tully, John C.

doi:10.1039/a801824c

Cited by 563 publications

(652 citation statements)

References 42 publications

(35 reference statements)

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“…One must therefore rely on approximate '' semiclassical '' methods where the full dynamics of the system is approximated or simplified in some way using classical ideas. 83 Although many semiclassical methods have been proposed and reviewed, 21,48,[84][85][86][87] few have been systematically tested against accurate quantum mechanical calculations for realistic, fully-dimensional chemical systems, due to the difficulty in obtaining quantum mechanical results. As discussed in Section 4, we have developed a broad test set of atom-diatom scattering calculations, and we focus our attention in this section on methods that have been validated using these test cases to determine their accuracy and applicability.…”

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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Section: Semiclassical Trajectory Methodsmentioning

confidence: 99%

Introductory lecture: Nonadiabatic effects in chemical dynamics

et al. 2004

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“…5, the difference between the final population in the two models is probably due to the difference in the model potentials and due to the well-known deficiencies of the FSSH dynamics, namely, the "overcoherence" and the in- consistency between the propagation in the adiabatic and diabatic basis. 69,93,94 Reassuringly, the effect of such differences on spectra is quite weak (see Fig. 6).…”

Section: Msdr Calculations Using a 30-dimensional Four-surface On-mentioning

confidence: 99%

Efficient on-the-fly ab initio semiclassical method for computing time-resolved nonadiabatic electronic spectra with surface hopping or Ehrenfest dynamics

Zimmermann

Vaníček

2014

The Journal of Chemical Physics

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Articles you may be interested inEvaluation of the importance of spin-orbit couplings in the nonadiabatic quantum dynamics with quantum fidelity and with its efficient "on-the-fly" ab initio semiclassical approximation J. Chem. Phys. 137, 22A516 (2012) We derive a somewhat crude, yet very efficient semiclassical approximation for computing nonadiabatic spectra. The resulting method, which is a generalization of the multiple-surface dephasing representation, includes quantum effects through interference of mixed quantum-classical trajectories and through quantum treatment of the collective electronic degree of freedom. The method requires very little computational effort beyond the fewest-switches surface hopping or Ehrenfest locally mean-field dynamics and is very easy to implement. The proposed approximation is tested by computing the absorption and time-resolved stimulated emission spectra of pyrazine using the fourdimensional three-surface model which allows for comparison with the numerically exact quantum spectra. As expected, the multiple-surface dephasing representation is not suitable for high-resolution linear spectra, yet it seems to capture all the important features of pump-probe spectra. Finally, the method is combined with on-the-fly ab initio evaluation of the electronic structure (i.e., energies, forces, electric-dipole, and nonadiabatic couplings) in order to compute fully dimensional nonadiabatic spectra of pyrazine without approximations inherent to analytical, including vibronic-coupling models. The Appendix provides derivations of perturbative expressions for linear and pump-probe spectra of arbitrary mixed states and for arbitrary laser pulse shapes. © 2014 AIP Publishing LLC.

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“…11.] We stress here that, even when a restricted number of quantized modes is included in the dynamics, we do not impose any constraint to the dynamics ofR andP (apart from the boundary conditions).…”

Section: Representation Of the Quantum Fluctuations Of The Ionsmentioning

confidence: 99%

“…Efficient surface hopping algorithms make use of adiabatic electronic states in order to minimize the number of hops attempted during the simulation. 11,12 However, working with adiabatic electronic states requires the diagonalization of the electronic Hamiltonian at each molecular dynamics time step, which is a costly numerical operation.…”

Section: Introductionmentioning

confidence: 99%

“…6 Including electronic transitions and-possibly classical-atomic motion in a consistent 7,8 and computationally effective molecular dynamics scheme has been the object of intense theoretical and computational investigations during the last decades. [9][10][11][12][13][14][15][16][17][18][19] In the surface hopping algorithm 10 -and similar approaches 12,14,18 that treat atomic evolution classicallyvertical electronic transitions are included in a stochastic way. By averaging over a large ensemble of such stochastic quantum-classical evolutions, one obtains a reliable approximation to the quantum electron-ion 20 dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Analog of Rabi oscillations in resonant electron-ion systems

Stella

Miranda

Horsfield

et al. 2011

The Journal of Chemical Physics

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Observation of longitudinal-optic-phonon-plasmon-coupled mode in n-type AlGaN alloy films Appl. Phys. Lett. 99, 251904 (2011) Band-gap-dependent emissions from conjugated polymers coupled silver nanocap array Appl. Phys. Lett. 99, 233112 (2011) Hot carriers relaxation in highly excited polar semiconductors: Hot phonons versus phonon-plasmon coupling J. Appl. Phys. 110, 113108 (2011) Strain control of orbital polarization and correlated metal-insulator transition in La2CoMnO6 from first principles Appl. Phys. Lett. 99, 202110 (2011) The role of plasmons and interband transitions in the color of AuAl2, AuIn2, and AuGa2 Appl. Phys. Lett. 99, 111908 (2011) Additional information on J. Chem. Phys. Quantum coherence between electron and ion dynamics, observed in organic semiconductors by means of ultrafast spectroscopy, is the object of recent theoretical and computational studies. To simulate this kind of quantum coherent dynamics, we have introduced in a previous article [L. Stella, M. Meister, A. J. Fisher, and A. P. Horsfield, J. Chem. Phys. 127, 214104 (2007)] an improved computational scheme based on Correlated Electron-Ion Dynamics (CEID). In this article, we provide a generalization of that scheme to model several ionic degrees of freedom and many-body electronic states. To illustrate the capability of this extended CEID, we study a model system which displays the electron-ion analog of the Rabi oscillations. Finally, we discuss convergence and scaling properties of the extended CEID along with its applicability to more realistic problems.

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Mixed quantum–classical dynamics

Cited by 563 publications

References 42 publications

Introductory lecture: Nonadiabatic effects in chemical dynamics

Introductory lecture: Nonadiabatic effects in chemical dynamics

Efficient on-the-fly ab initio semiclassical method for computing time-resolved nonadiabatic electronic spectra with surface hopping or Ehrenfest dynamics

Analog of Rabi oscillations in resonant electron-ion systems

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