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Nonadiabatic excited-state molecular dynamics: Treatment of electronic decoherence
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10.1063/1.4809568
/content/aip/journal/jcp/138/22/10.1063/1.4809568
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/22/10.1063/1.4809568

Figures

Image of FIG. 1.
FIG. 1.

Cartoon depicting the evolution of the quantum amplitudes c during nonradiative relaxation. The wavefunction is initialized as a pure state. The red state symbolizes the “current state.” (a) During the standard Tully procedure, the wavepacket continues to broaden but remains at relatively high energy even as the system transitions to lower energy states. (b) Following instantaneous decoherence the wavepacket is allowed to broaden, but the coefficients are reinitialized after each hop so that the new current state has a probability of unity. In this way, the wavepacket center follows the relaxation to lower energy. (c) In energy-based decoherence, the wavepacket broadens slightly after each timestep and the coefficients are rescaled to narrow the wavepacket before the next timestep. The damping factor is related to the energy separation from the current state. Population removed from other states is deposited into the current state so that the center of the wavepacket follows the relaxation to lower energy.

Image of FIG. 2.
FIG. 2.

The model molecular systems studied with the NA-ESMD approach: A 3-ring oligomer of PPV (PPV3), and a system composed of meta-substituted linear PPE segments of 2-, 3-, and 4-rings (2-3-4 PPE).

Image of FIG. 3.
FIG. 3.

(Top) Equilibrium absorption spectrum for PPV3 showing absorbance from the ground state (S → S), the lowest excited state (S → S) and equilibrium density of states. (Bottom) Density of excited states for the lowest 15 excited states at T = 300 K computed using all initial ground state configurations. S is the state with the largest oscillator strength from S, and the excitation is performed using a simulated laser pulse centered at λ = 245 nm with FWHM = 100 fs.

Image of FIG. 4.
FIG. 4.

(Top) Equilibrium absorption spectrum for 2-3-4 PPE showing absorbance from the ground state (S → S) and equilibrium density of states. (Bottom) Density of excited states for the lowest 6 excited states at T = 300 K computed using all initial ground state configurations. The excitation is performed using a simulated laser pulse centered at λ = 346 nm with FWHM = 100 fs.

Image of FIG. 5.
FIG. 5.

Histograms of the energy gap between S and S are shown for PPV3 (top) and 2-3-4 PPE (bottom), while the system is evolving on S ( ) and S ( ) as well as the energy gap for the final effective hop to S ( ) during Standard Tully dynamics and for G-EDC. Energy gaps are smaller in 2-3-4 PPE and the final effective hop corresponds to the most probably energy gap for S. In PPV3, energy gaps are large, and the final effective hop can only be made from lower energies, which are infrequent in the S spectrum.

Image of FIG. 6.
FIG. 6.

(Top) Combined population rise of the two lowest energy states (S + S) and (bottom) population rise of the lowest energy S state. Results are shown for ID-S, ID-A, and G-EDC using the recommended parameters (C = 1; E = 0.1 hartree) compared to the Standard Tully algorithm. Populations for the classical system are depicted as solid lines while the corresponding dashed lines represent the average quantum probabilities.

Image of FIG. 7.
FIG. 7.

Comparison of (top) G-EDC and (bottom) T-EDC populations using the recommended parameters (C = 1; E = 0.1 hartree). For PPV3, the populations are shown for S, S, and the initial S state. Populations for S, S, and S are shown for 2-3-4 PPE. Classical populations and average quantum probabilities are depicted as solid and dashed lines, respectively.

Image of FIG. 8.
FIG. 8.

Combined population rise for the lowest two excited states (S + S) using G-EDC algorithm with varying parameters (C, E) for (top) PPV3 and (bottom) 2-3-4 PPE. Classical populations are shown as solid lines and the corresponding dashed lines represent the average quantum probabilities.

Image of FIG. 9.
FIG. 9.

Quantum wavepacket evolution for relaxation in PPV3 following excitation to S compared for the different decoherence methods. The height of each point corresponds to the population of the state with a given energy, where the energy is plotted as the energy difference with respect to the current running state, α. Wavepackets are plotted at 2 fs intervals for the first 100 fs of the dynamics.

Image of FIG. 10.
FIG. 10.

Quantum wavepacket evolution for relaxation in 2-3-4 PPE following excitation to S compared for the different decoherence methods. The height of each point corresponds to the population of the state with a given energy, where the energy is plotted as the energy difference with respect to the current running state, α. Wavepackets are plotted at 1 fs intervals for the first 50 fs of the dynamics.

Image of FIG. 11.
FIG. 11.

Time evolution of the ensemble averaged ratio of coefficients for the current state, α, and the state directly below in energy, α − 1, is compared for the different decoherence methods in (top) PPV3 and (bottom) 2-3-4 PPE.

Tables

Generic image for table
Table I.

Energy gaps between states S and S for the AM1 optimized structures and averaged during dynamics while running on S, S, and the final effective hop to S.

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/content/aip/journal/jcp/138/22/10.1063/1.4809568
2013-06-14
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nonadiabatic excited-state molecular dynamics: Treatment of electronic decoherence
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/22/10.1063/1.4809568
10.1063/1.4809568
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