On the multidimensional surface intersection problem and classical trajectory ’’surface hopping’’

Stine, J. R.; Muckerman, James T.

doi:10.1063/1.432892

Cited by 146 publications

(45 citation statements)

References 23 publications

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“…The nonadiabatic dynamics is described by a swarm of classical trajectories with each trajectory evolving independently on a single electronic potential energy surface (PES) and the possibility of sudden instantaneous hops to different surfaces. However, there is not a generally accepted definition of how these transitions should be incorporated in the TSH method and the use of different hopping algorithms [1,3,[5][6][7][10][11][12] leads to slightly different TSH methods.…”

Section: Introductionmentioning

confidence: 97%

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Approximate switching algorithms for trajectory surface hopping

2008

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a b s t r a c tThree approximate switching algorithms for trajectory surface hopping calculations are presented using simple models to describe the dependence of the hopping probability on the nonadiabatic coupling strength. The switching algorithms are applied to the calculation of the electronic deexcitation in ethylene, methaniminium ion and trans-azobenzene. Compared with the results from the standard fewest switching algorithm (FSA), the simplest approximation based on a local diabatic representation shows some qualitative failures and overestimates the decay times severely. The other two approximate switching algorithms incorporate stochastic features and reproduce the FSA results well, with a deviation of typically 20-30% in the computed decay times. They offer a simple and efficient description of the nonadiabatic dynamics of the investigated systems.

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Section: Introductionmentioning

confidence: 97%

“…Trajectory surface hopping (TSH) [1][2][3][4][5][6][7][8][9][10][11][12] is a general approach to study the dynamics of non-Born-Oppenheimer processes occurring in molecular systems. In this method the system is divided into a quantum and a classical part.…”

Section: Introductionmentioning

confidence: 99%

Approximate switching algorithms for trajectory surface hopping

2008

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“…Most of the theoretical studies of the collision between H + 2 and H 2 are made using quasiclassical trajectories (QCT) on a surface hopping PES. [10][11][12][13] Baer and Ng 14 provided quantum mechanical calculations of reactive and charge transfer cross sections using a reduced 2 × 2 DIM matrix. The work devoted to the vibrational/rotational distribution of H + 3 15 uses the DIM potential which cannot provide a good description of the H + 3 .…”

Section: Introductionmentioning

confidence: 99%

Full dimensional potential energy surface for the ground state of $\mathbf {H_4^+}$H4+ system based on triatomic-in-molecules formalism

Sanz-Sanz¹,

Roncero²,

Paniagua³

et al. 2013

The Journal of Chemical Physics

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In this work, we present a global potential energy surface for the ground electronic state of the H + 4 based on ab initio calculations. The final fit is based on triatomics-in-molecules (TRIM) approximation and it includes extra four-body terms for the better description of some discrepancies found on the TRIM model. The TRIM method itself allows a very accurate description of the asymptotic regions. The global fit uses more than 19 000 multireference configuration interaction ab initio points. The global potential energy surface has an overall root mean square error of 0.013 eV for energies up to 2 eV above the global minimum. This work presents an analysis of the stationary points, reactant and product channels, and crossing between the two lowest TRIM adiabatic states. It is as well included a brief description of the two first excited states of the TRIM matrix, concluding that TRIM method is a very good approximation not only for the ground state but also for at least two of the excited states of H + 4 system.

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“…Specifically, we choose m y such that the resulting KC-RPMD TST exactly recovers the multi-dimensional Landau-Zener TST rate expression for non-adiabatic transitions in the weak-coupling regime. 73 The resulting expression, which is derived in Appendix C, is…”

Section: The Mass Of the Auxiliary Variablementioning

confidence: 99%

Kinetically constrained ring-polymer molecular dynamics for non-adiabatic chemical reactions

Menzeleev

Bell

Miller

2014

The Journal of Chemical Physics

104

139

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Communication: Full dimensional quantum rate coefficients and kinetic isotope effects from ring polymer molecular dynamics for a seven-atom reaction OH + CH4 CH3 + H2O J. Chem. Phys. 138, 221103 (2013) We extend ring-polymer molecular dynamics (RPMD) to allow for the direct simulation of general, electronically non-adiabatic chemical processes. The kinetically constrained (KC) RPMD method uses the imaginary-time path-integral representation in the set of nuclear coordinates and electronic states to provide continuous equations of motion that describe the quantized, electronically nonadiabatic dynamics of the system. KC-RPMD preserves the favorable properties of the usual RPMD formulation in the position representation, including rigorous detailed balance, time-reversal symmetry, and invariance of reaction rate calculations to the choice of dividing surface. However, the new method overcomes significant shortcomings of position-representation RPMD by enabling the description of non-adiabatic transitions between states associated with general, many-electron wavefunctions and by accurately describing deep-tunneling processes across asymmetric barriers. We demonstrate that KC-RPMD yields excellent numerical results for a range of model systems, including a simple avoided-crossing reaction and condensed-phase electron-transfer reactions across multiple regimes for the electronic coupling and thermodynamic driving force. © 2014 AIP Publishing LLC. [http://dx

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On the multidimensional surface intersection problem and classical trajectory ’’surface hopping’’

Cited by 146 publications

References 23 publications

Approximate switching algorithms for trajectory surface hopping

Approximate switching algorithms for trajectory surface hopping

Full dimensional potential energy surface for the ground state of $\mathbf {H_4^+}$H4+ system based on triatomic-in-molecules formalism

Kinetically constrained ring-polymer molecular dynamics for non-adiabatic chemical reactions

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