How to recover Marcus theory with fewest switches surface hopping: Add just a touch of decoherence

In a recent paper, we presented a road map for how Tully's fewest switches surface hopping (FSSH) algorithm can be derived, under certain circumstances, from the mixed quantum-classical Liouville equation. In this communication, we now demonstrate how this new interpretation of surface hopping can yield significantly enhanced results for electronic properties in nonadiabatic calculations. Specifically, we calculate diabatic populations for the spin-boson problem using FSSH trajectories. We show that, for some Hamiltonians, without changing the FSSH algorithm at all but rather simply reinterpreting the ensemble of surface hopping trajectories, we recover excellent results and remove any and all ambiguity about the initial condition problem.

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“…13,14,18 One method uses exclusively the electronic wavefunction of each trajectory. The other uses only the active surface of each trajectory.…”

Section: Theory: Basis Set Conversionmentioning

confidence: 99%

Communication: The correct interpretation of surface hopping trajectories: How to calculate electronic properties

Landry¹,

Falk²,

Subotnik³

2013

The Journal of Chemical Physics

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140

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“…Subotnik and Shenvi 21 proposed a prescription for decoherence correction to FSSH dynamics. Landry et al 22 showed that implementing a decoherence correction in the FSSH algorithm leads to the recovery of Marcus theory in the calculation of transition rates between adiabatic electronic states within the spin-boson model. As will be discussed later, in the present work trajectories quickly leave the interaction region and almost never return to it.…”

Section: Introductionmentioning

confidence: 99%

Ultrafast hydrogen migration in acetylene cation driven by non-adiabatic effects

Madjet

Zheng

Vendrell

2013

The Journal of Chemical Physics

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One-photon mass-analyzed threshold ionization (MATI) spectroscopy of pyridine: Determination of accurate ionization energy and cationic structure J. Chem. Phys. 141, 174303 (2014) Non-adiabatic dynamics of the acetylene cation is investigated using mixed quantum-classical dynamics based on trajectory surface hopping. To describe the non-adiabatic effects, two surface hopping methods are used, namely, Tully's fewest switches and Landau-Zener surface hopping. Similarities and differences between the results based on those two methods are discussed. We find that the photoionization of acetylene into the first excited state A 2 + g drives the molecule from the linear structure to a trans-bent structure. Through a conical intersection the acetylene cation can relax back to either the ground state of acetylene or vinylidene. We conclude that hydrogen migration always takes place after non-radiative electronic relaxation to the ground state of the monocation. Based on the analysis of correlation functions we identify coherent oscillations between acetylene and vinylidene with a period of about 70 fs after the electronic relaxation.

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“…(6) corresponds to electronic dephasing is also the main reason for why predictions based on methods like fewest-switches surfacehopping, [20][21][22]59,60 Ehrenfest dynamics, 20 and ring-polymer molecular dynamics 19 …”

Section: Preliminary Considerationsmentioning

confidence: 99%

“…(A. 22). To this end, we start out by noting that the Jacobian of changing integration variables from y 1 , .…”

Section: Appendix B Proof Of Identity Equation A22mentioning

confidence: 99%

Equilibrium Fermi’s Golden Rule Charge Transfer Rate Constants in the Condensed Phase: The Linearized Semiclassical Method vs Classical Marcus Theory

Sun

Geva

2015

J. Phys. Chem. A

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In this article, we present a comprehensive comparison between the linearized semiclassical expression for the equilibrium Fermi's golden rule rate constant and the progression of more approximate expressions that lead to the classical Marcus expression. We do so within the context of the canonical Marcus model, where the donor and acceptor potential energy surface are parabolic and identical except for a shift in both the free energies and equilibrium geometries, and within the Condon region. The comparison is performed for two different spectral densities and over a wide range of frictions and temperatures, thereby providing a clear test for the validity, or lack thereof, of the more approximate expressions. We also comment on the computational cost and scaling associated with numerically calculating the linearized semiclassical expression for the rate constant and its dependence on the spectral density, temperature, and friction.

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How to recover Marcus theory with fewest switches surface hopping: Add just a touch of decoherence

Cited by 135 publications

References 50 publications

Communication: The correct interpretation of surface hopping trajectories: How to calculate electronic properties

Communication: The correct interpretation of surface hopping trajectories: How to calculate electronic properties

Ultrafast hydrogen migration in acetylene cation driven by non-adiabatic effects

Equilibrium Fermi’s Golden Rule Charge Transfer Rate Constants in the Condensed Phase: The Linearized Semiclassical Method vs Classical Marcus Theory

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