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Two-Dimensional Vibrational Spectroscopy of a Dissipative System with the Optimized Mean-Trajectory Approximation.

Alemi M, Loring RF - J Phys Chem B (2014)

Bottom Line: Here we apply this method to an anharmonic chromophore coupled to a harmonic bath.The OMT is shown to well reproduce line shapes and waiting time dynamics in the pure dephasing limit of weak coupling to an off-resonant bath.The OMT is also shown to describe a case where energy transfer is the predominant source of line broadening.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, United States.

ABSTRACT
The optimized mean-trajectory (OMT) approximation is a semiclassical method for computing vibrational response functions from action-quantized classical trajectories connected by discrete transitions representing radiation-matter interactions. Here we apply this method to an anharmonic chromophore coupled to a harmonic bath. A forward-backward trajectory implementation of the OMT method is described that addresses the numerical challenges of applying the OMT to large systems with disparate frequency scales. The OMT is shown to well reproduce line shapes and waiting time dynamics in the pure dephasing limit of weak coupling to an off-resonant bath. The OMT is also shown to describe a case where energy transfer is the predominant source of line broadening.

No MeSH data available.


Rabs(ω3,ω1;t2) for a thermal ensemble ofMorse oscillators with bilinear coupling to a harmonic bath is shownas a function of ωat2. Fluctuating frequency approximation results are shownin panel (a), and OMT results are shown in panel (b). Spectra at ωat2 = 0 are shownin row (i), at ωat2 = 150 in row (ii), and at ωat2 = 1200 in row (iii). All spectraare normalized to the maximum absolute value at t2 = 0. Six contours equally spaced between −1 and0 and between 0 and +1 are shown, with negative contours in blue andpositive in red.
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fig6: Rabs(ω3,ω1;t2) for a thermal ensemble ofMorse oscillators with bilinear coupling to a harmonic bath is shownas a function of ωat2. Fluctuating frequency approximation results are shownin panel (a), and OMT results are shown in panel (b). Spectra at ωat2 = 0 are shownin row (i), at ωat2 = 150 in row (ii), and at ωat2 = 1200 in row (iii). All spectraare normalized to the maximum absolute value at t2 = 0. Six contours equally spaced between −1 and0 and between 0 and +1 are shown, with negative contours in blue andpositive in red.

Mentions: Figures 3–5 show results inthe pure dephasing regime where the fluctuatingfrequency approximation is expected to accurately reproduce the responsefunction.69 This approximation will notdescribe a case in which energy transfer between the system and bathis significant. Figure 6 shows 2DIR spectrafor such a model, where the width of the bath spectral density hasbeen increased relative to that of Figures 3–5 and the chromophore–bathcoupling is bilinear, facilitating single quantum excitation transferbetween the chromophore and bath. The bath parameters are γ= 9.90 × 10–2ωa, Nb = 125, and Ω = 1.4654ωa , with the maximum bath frequency chosen to avoid resonanceswith the chromophore mode. The coupling parameters are νLL = 0.222 and νSL = 0. These are the samecoupling strengths used in row (i) of Figure 3 in ref (69) but here the width ofthe spectral distribution is a factor of 5 smaller to reduce the numberof oscillators in the finite bath. Fluctuating frequency results areshown in column (a) of Figure 6, and OMT resultscomputed from 5000 initial conditions are shown in column (b). Rowsshow results for the same waiting times as in the corresponding rowsof Figures 3 and 4.Time-domain results were not fully decayed so, to reduce artifacts12 caused by taking the discrete Fourier transformof aperiodic data, the response functions used to compute Figure 6 were multiplied by the product of one-sided cosine-squaredwindow functions for the t1 and t3 time variables. Applying this window functionto the time-domain results used to compute Figures 3 and 4 did not result in significantadditional broadening.


Two-Dimensional Vibrational Spectroscopy of a Dissipative System with the Optimized Mean-Trajectory Approximation.

Alemi M, Loring RF - J Phys Chem B (2014)

Rabs(ω3,ω1;t2) for a thermal ensemble ofMorse oscillators with bilinear coupling to a harmonic bath is shownas a function of ωat2. Fluctuating frequency approximation results are shownin panel (a), and OMT results are shown in panel (b). Spectra at ωat2 = 0 are shownin row (i), at ωat2 = 150 in row (ii), and at ωat2 = 1200 in row (iii). All spectraare normalized to the maximum absolute value at t2 = 0. Six contours equally spaced between −1 and0 and between 0 and +1 are shown, with negative contours in blue andpositive in red.
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fig6: Rabs(ω3,ω1;t2) for a thermal ensemble ofMorse oscillators with bilinear coupling to a harmonic bath is shownas a function of ωat2. Fluctuating frequency approximation results are shownin panel (a), and OMT results are shown in panel (b). Spectra at ωat2 = 0 are shownin row (i), at ωat2 = 150 in row (ii), and at ωat2 = 1200 in row (iii). All spectraare normalized to the maximum absolute value at t2 = 0. Six contours equally spaced between −1 and0 and between 0 and +1 are shown, with negative contours in blue andpositive in red.
Mentions: Figures 3–5 show results inthe pure dephasing regime where the fluctuatingfrequency approximation is expected to accurately reproduce the responsefunction.69 This approximation will notdescribe a case in which energy transfer between the system and bathis significant. Figure 6 shows 2DIR spectrafor such a model, where the width of the bath spectral density hasbeen increased relative to that of Figures 3–5 and the chromophore–bathcoupling is bilinear, facilitating single quantum excitation transferbetween the chromophore and bath. The bath parameters are γ= 9.90 × 10–2ωa, Nb = 125, and Ω = 1.4654ωa , with the maximum bath frequency chosen to avoid resonanceswith the chromophore mode. The coupling parameters are νLL = 0.222 and νSL = 0. These are the samecoupling strengths used in row (i) of Figure 3 in ref (69) but here the width ofthe spectral distribution is a factor of 5 smaller to reduce the numberof oscillators in the finite bath. Fluctuating frequency results areshown in column (a) of Figure 6, and OMT resultscomputed from 5000 initial conditions are shown in column (b). Rowsshow results for the same waiting times as in the corresponding rowsof Figures 3 and 4.Time-domain results were not fully decayed so, to reduce artifacts12 caused by taking the discrete Fourier transformof aperiodic data, the response functions used to compute Figure 6 were multiplied by the product of one-sided cosine-squaredwindow functions for the t1 and t3 time variables. Applying this window functionto the time-domain results used to compute Figures 3 and 4 did not result in significantadditional broadening.

Bottom Line: Here we apply this method to an anharmonic chromophore coupled to a harmonic bath.The OMT is shown to well reproduce line shapes and waiting time dynamics in the pure dephasing limit of weak coupling to an off-resonant bath.The OMT is also shown to describe a case where energy transfer is the predominant source of line broadening.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, United States.

ABSTRACT
The optimized mean-trajectory (OMT) approximation is a semiclassical method for computing vibrational response functions from action-quantized classical trajectories connected by discrete transitions representing radiation-matter interactions. Here we apply this method to an anharmonic chromophore coupled to a harmonic bath. A forward-backward trajectory implementation of the OMT method is described that addresses the numerical challenges of applying the OMT to large systems with disparate frequency scales. The OMT is shown to well reproduce line shapes and waiting time dynamics in the pure dephasing limit of weak coupling to an off-resonant bath. The OMT is also shown to describe a case where energy transfer is the predominant source of line broadening.

No MeSH data available.