Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence

Subotnik, Joseph E.; Ouyang, Wenjun; Landry, Brian R.

doi:10.1063/1.4829856

Cited by 179 publications

(249 citation statements)

References 70 publications

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“…Although TSH shares the feature that wave packets evolving in different spatial regions on different surfaces experience different forces, it does not capture the electronic decoherence that should come hand-in-hand. There has been extensive and on-going developments to build decoherence into TSH 34,35,51,52,64,68,69 but it remains a challenging problem today. We now ask what we can learn about decoherence from the exact TDPES in relation to TSH.…”

Section: Further Relation With Trajectory Surface Hoppingmentioning

confidence: 99%

“…We find several aspects that are somewhat qualitatively in common: after passing through an avoided crossing region, the exact TDPES tracks one BOPES or the other piecewise in space; moreover, it displays an energy adjustment between the surfaces, which can be (gauge-)transformed to a kinetic energy contribution, reminiscent of the velocity-adjustment in TSH. We show that the exact TDPES sheds light on the notorious problem of overcoherence in TSH 34,35,51,52,[63][64][65][66][67][68][69] by comparing the electronic density-matrix associated to trajectories in each case. The force resulting from the step features in the TDPES appear to be intimately related to creating decoherence, lacking in TSH.…”

Section: Introductionmentioning

confidence: 99%

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The exact forces on classical nuclei in non-adiabatic charge transfer

Agostini

Abedi

Suzuki

et al. 2015

The Journal of Chemical Physics

110

195

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Non-adiabatic processes in the charge transfer reaction of O2 molecules with potassium surfaces without dissociation J. Chem. Phys. 141, 074711 (2014) The exact forces on classical nuclei in non-adiabatic charge transfer The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect. C 2015 AIP Publishing LLC.[http://dx

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Section: Further Relation With Trajectory Surface Hoppingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The exact forces on classical nuclei in non-adiabatic charge transfer

Agostini

Abedi

Suzuki

et al. 2015

The Journal of Chemical Physics

110

195

View full text Add to dashboard Cite

show abstract

“…The latter effect can be partially mitigated using socalled decoherence corrections; the interested reader is referred to the according literature. [132,[136][137][138][139][140][141][142][143][144][145][146][147][148][149][150][151][152][153] Tunneling effects can also not be described with surface hopping although there exist several approaches to alleviate this deficiency, see, for example, Refs. [154][155][156][157][158].…”

Section: Dynamics Simulations Of Intersystem Crossingmentioning

confidence: 99%

A general method to describe intersystem crossing dynamics in trajectory surface hopping

Mai

Marquetand

González

2015

Int J of Quantum Chemistry

266

406

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Intersystem crossing is a radiationless process that can take place in a molecule irradiated by UV‐Vis light, thereby playing an important role in many environmental, biological and technological processes. This paper reviews different methods to describe intersystem crossing dynamics, paying attention to semiclassical trajectory theories, which are especially interesting because they can be applied to large systems with many degrees of freedom. In particular, a general trajectory surface hopping methodology recently developed by the authors, which is able to include nonadiabatic and spin‐orbit couplings in excited‐state dynamics simulations, is explained in detail. This method, termed SHARC, can in principle include any arbitrary coupling, what makes it generally applicable to photophysical and photochemical problems, also those including explicit laser fields. A step‐by‐step derivation of the main equations of motion employed in surface hopping based on the fewest‐switches method of Tully, adapted for the inclusion of spin‐orbit interactions, is provided. Special emphasis is put on describing the different possible choices of the electronic bases in which spin‐orbit can be included in surface hopping, highlighting the advantages and inconsistencies of the different approaches. © 2015 Wiley Periodicals, Inc.

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“…From the theoretical point of view, however, any SH scheme is inherently a phenomenological approach. The ad hoc assumption of stochastic jumps between electronic potential energy surfaces (PES) has, so far, never been rigorously deduced from the time-dependent Schrödinger equation (TDSE) for electrons and nuclei, and even the choice of the applied PES is ambiguous.Very recently, however, first attempts have been made to justify the SH methodology on Born-Oppenheimer surfaces (BOSs), solely for the laser-free non-adiabatic dynamics [6][7][8][9]. A close similarity between the exact wavepacket propagation and SH on BOSs has been found in the framework of the exact factorization of the molecular wavefunction [6].…”

mentioning

confidence: 99%

“…Very recently, however, first attempts have been made to justify the SH methodology on Born-Oppenheimer surfaces (BOSs), solely for the laser-free non-adiabatic dynamics [6][7][8][9]. A close similarity between the exact wavepacket propagation and SH on BOSs has been found in the framework of the exact factorization of the molecular wavefunction [6].…”

mentioning

confidence: 99%

Surface hopping in laser-driven molecular dynamics

et al. 2017

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A theoretical justification of the empirical surface hopping method for the laser-driven molecular dynamics is given utilizing the formalism of the exact factorization of the molecular wavefunction [Abedi et al., PRL 105, 123002 (2010)] in its quantum-classical limit. Employing an exactly solvable H + 2 -like model system, it is shown that the deterministic classical nuclear motion on a single timedependent surface in this approach describes the same physics as stochastic (hopping-induced) motion on several surfaces, provided Floquet surfaces are applied. Both quantum-classical methods do describe reasonably well the exact nuclear wavepacket dynamics for extremely different dissociation scenarios. Hopping schemes using Born-Oppenheimer surfaces or instantaneous Born-Oppenheimer surfaces fail completely. For more than two decades, surface hopping (SH) [1] has been among the most popular and successful methods to describe non-adiabatic phenomena in atomic manybody systems (for reviews see [2][3][4][5]). From the theoretical point of view, however, any SH scheme is inherently a phenomenological approach. The ad hoc assumption of stochastic jumps between electronic potential energy surfaces (PES) has, so far, never been rigorously deduced from the time-dependent Schrödinger equation (TDSE) for electrons and nuclei, and even the choice of the applied PES is ambiguous.Very recently, however, first attempts have been made to justify the SH methodology on Born-Oppenheimer surfaces (BOSs), solely for the laser-free non-adiabatic dynamics [6][7][8][9]. A close similarity between the exact wavepacket propagation and SH on BOSs has been found in the framework of the exact factorization of the molecular wavefunction [6]. In this theory, the so-called exact time-dependent potential energy surface (EPES), together with an exact time-dependent vector potential, governs the true nuclear wavepacket dynamics. The EPES can exhibit nearly discontinuous step-like features, just in the vicinity of avoided crossings between BOSs, leading simultaneously to acceleration and deceleration of certain parts of the quantum wavepacket and resulting in its splitting. In close analogy, the SH mechanism can create branches of classical trajectories at avoided crossings. The findings [6] justify, albeit qualitatively but anyhow convincingly, the SH methodology on BOSs, in the field-free case.For the laser-driven dynamics, any validation of SH is still lacking and the appropriate choice of the applicable PES is discussed controversially, at present [10][11][12]. In fact, the hitherto purely intuitively chosen PES in SH models are fundamentally different from each other, and include BOSs [10,[13][14][15][16][17], instantaneous BOSs (IBOSs) [18][19][20][21][22] as well as Floquet surfaces (FSs) [22][23][24]. From the massive differences in definition and properties of these PESs, one can hardly expect that the appendant SH schemes can describe the same physics. Obviously, the situation requires clarification and the general questions persist: Is ther...

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Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence

Cited by 179 publications

References 70 publications

The exact forces on classical nuclei in non-adiabatic charge transfer

The exact forces on classical nuclei in non-adiabatic charge transfer

A general method to describe intersystem crossing dynamics in trajectory surface hopping

Surface hopping in laser-driven molecular dynamics

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