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Surface hopping modeling of two-dimensional spectra
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Figures

Image of FIG. 1.

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FIG. 1.

Schematic illustration of the model used for mixed quantum-classical dynamics. Each site n comprises a quantum two-state unit with transition energy ω n . Such unit couples to a classical oscillator x n , which in turn interacts with a stochastic environment corresponding to a temperature T. Arrows indicate couplings, purely quantum mechanical (J n, m ), quantum-classical (λ n ), and classical-stochastic (γ).

Image of FIG. 2.

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FIG. 2.

Double sided Feynman diagrams illustrating the six Liouville pathways that contribute to the 2D optical signal. Shown are the diagrams for ground state bleach (GB), stimulated emission (SE), and excited state absorption (EA), where |g⟩, |e⟩, and |f⟩ denote the quantum ground state and excitations in the singly and doubly excited manifold, respectively. Dashed lines represent interactions with a light pulse. The arrows on the left-side indicate the time-direction, and serve to specify the interaction times τ1, τ2, τ3, and τ4, as well as the intervals t 1, t 2, and t 3. The upper row shows the rephasing diagrams, whereas the nonrephasing variants are demonstrated in the bottom row.

Image of FIG. 3.

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FIG. 3.

Decomposition of the NR-SE diagram into contributions from populations |ϕ k ⟩⟨ϕ k | and interstate coherences |ϕ k ⟩⟨ϕ l | (kl).

Image of FIG. 4.

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FIG. 4.

Real part of the calculated 2D spectra for a dimer system at waiting times t 2 = 0 ps (top row), 1.5 ps (middle row), and 15 ps (bottom row). Left column displays results obtained using the conventional NISE method, neglecting quantum feedback. Results for the surface hopping approaches are shown in the second and third columns, where the response is obtained through the primary and auxiliary wavefunctions, respectively. The outcome of HEOM is demonstrated in the right column. Contours indicate levels for every 10% of the maximum absolute value. This value is used to normalize each spectrum. The labels I and II in the top-left plot indicate the two cross-peaks (see text).

Image of FIG. 5.

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FIG. 5.

(a) Calculated transfer of population from the higher to the lower-energy adiabatic state (curves), as a function of waiting time t 2. Also shown is the intensity of cross-peak I (circles), taken from simulated 2D spectra. Results are demonstrated for the conventional NISE method (green) and for surface hopping using the primary (blue) and auxiliary (red) wavefunction. The black curve indicates the Boltzmann factor, as derived from the instantaneous adiabatic energies in the course of the surface hopping calculations. Note that the peak intensities are rescaled so as to overlap the curves at t 2 = 1 ps and 15 ps. The corresponding scaling factors are reported in Table I . (b) Results for cross-peak II and population transfer from the lower to the higher-energy adiabat.

Tables

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Table I.

Time scales, obtained by fitting the data from Fig. 5(a) to the exponential C 1 + C 2 exp (−t 2/t c ). Also tabulated are factors used to rescale the cross-peak intensities in this figure.

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/content/aip/journal/jcp/138/16/10.1063/1.4801519
2013-04-23
2014-04-21

Abstract

Recently, two-dimensional (2D) electronic spectroscopy has become an important tool to unravel the excited state properties of complex molecular assemblies, such as biological light harvesting systems. In this work, we propose a method for simulating 2D electronic spectra based on a surface hopping approach. This approach self-consistently describes the interaction between photoactive chromophores and the environment, which allows us to reproduce a spectrally observable dynamic Stokes shift. Through an application to a dimer, the method is shown to also account for correct thermal equilibration of quantum populations, something that is of great importance for processes in the electronic domain. The resulting 2D spectra are found to nicely agree with hierarchy of equations of motion calculations. Contrary to the latter, our method is unrestricted in describing the interaction between the chromophores and the environment, and we expect it to be applicable to a wide variety of molecular systems.

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Scitation: Surface hopping modeling of two-dimensional spectra
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/16/10.1063/1.4801519
10.1063/1.4801519
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