We have recently introduced an efficient semi-empirical non-adiabatic molecular dynamics method for the simulation of charge transfer/transport in molecules and molecular materials, denoted fragment orbital-based surface hopping (FOB-SH) [J. Spencer et al., J. Chem. Phys. 145, 064102 (2016)]. In this method, the charge carrier wavefunction is expanded in a set of charge localized, diabatic electronic states and propagated in the time-dependent potential due to classical nuclear motion. Here we derive and implement an exact expression for the non-adiabatic coupling vectors between the adiabatic electronic states in terms of nuclear gradients of the diabatic electronic states. With the non-adiabatic coupling vectors (NACVs) available, we investigate how different flavours of fewest switches surface hopping affect detailed balance, internal consistency, and total energy conservation for electron hole transfer in a molecular dimer with two electronic states. We find that FOB-SH satisfies detailed balance across a wide range of diabatic electronic coupling strengths provided that the velocities are adjusted along the direction of the NACV to satisfy total energy conservation upon a surface hop. This criterion produces the right fraction of energy-forbidden (frustrated) hops, which is essential for correct population of excited states, especially when diabatic couplings are on the order of the thermal energy or larger, as in organic semiconductors and DNA. Furthermore, we find that FOB-SH is internally consistent, that is, the electronic surface population matches the average quantum amplitudes, but only in the limit of small diabatic couplings. For large diabatic couplings, inconsistencies are observed as the decrease in excited state population due to frustrated hops is not matched by a corresponding decrease in quantum amplitudes. The derivation provided here for the NACV should be generally applicable to any electronic structure approach where the electronic Hamiltonian is constructed in a diabatic electronic state basis.
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7 December 2017
Research Article|
December 07 2017
Detailed balance, internal consistency, and energy conservation in fragment orbital-based surface hopping
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JCP Editors' Choice 2017
Antoine Carof
;
Antoine Carof
1
Department of Physics and Astronomy, University College London
, Gower Street, London WC1E 6BT, United Kingdom
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Samuele Giannini;
Samuele Giannini
1
Department of Physics and Astronomy, University College London
, Gower Street, London WC1E 6BT, United Kingdom
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Jochen Blumberger
Jochen Blumberger
a)
1
Department of Physics and Astronomy, University College London
, Gower Street, London WC1E 6BT, United Kingdom
2
Institute for Advanced Study, Technische Universität München
, Lichtenbergstrasse 2a, D-85748 Garching, Germany
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a)
Electronic mail: [email protected]
J. Chem. Phys. 147, 214113 (2017)
Article history
Received:
September 07 2017
Accepted:
November 03 2017
Citation
Antoine Carof, Samuele Giannini, Jochen Blumberger; Detailed balance, internal consistency, and energy conservation in fragment orbital-based surface hopping. J. Chem. Phys. 7 December 2017; 147 (21): 214113. https://doi.org/10.1063/1.5003820
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