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A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy
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Image of FIG. 1.

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FIG. 1.

Procedure for calculating spectra. We identify the stochastic variable best suited for the problem, propose a random distribution for the variable and convolve it with a correlation function to arrive at the instantaneous correlated trajectory of the stochastic variable. We then generate a mapping between the variable and spectroscopic quantities like transition dipole and frequency. This mapping gives rise to a correlated frequency and transition dipole trajectory, which we use to calculate response functions and spectra. In this illustration, the stochastic variable q corresponds to the collective electric field of solvating D2O molecules projected onto the O-H bond of an HOD molecule.

Image of FIG. 2.

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FIG. 2.

Comparison of the normalized three-pulse echo peak shift calculated from our model, which includes the non-Condon effect, with the normalized experimental peak shift measurement (top left) of HOD/D2O (Ref. 40). The correlation functions that went into the peak shift calculations, which gave us the best fit with experimental results for both the Condon and non-Condon response function calculations (top right). The corresponding 2D IR spectra of HOD/D2O with (bottom right) and without (bottom left) including the non-Condon effect.

Image of FIG. 3.

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FIG. 3.

Mapping of the v = 0–1 and v = 1–2 OH stretch frequencies (ω10, ω21) to δ (top) and the mapping of the corresponding transition dipoles (μ10, μ21) to δ (bottom) for HOD in NaOD/D2O. The insets in the μ vs. δ graph illustrate the potential energy curve and the position of the proton for two extreme values of δ. Equations (11) and (12) in the text show the mapping for ω10 and μ10. Mapping parameters for the other transition frequencies and dipoles are provided in the supplementary material (Ref. 56). The ω21 and μ21 variables were mapped using the following expressions: and, . Here the ω are in units of cm−1 and the μ in units of D.

Image of FIG. 4.

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FIG. 4.

(Top) Linear IR spectrum of aqueous hydroxide for different values of 〈δ〉 (in Å), with constant distribution width of σ = 0.3 Å. Below, 2D IR spectra of hydroxide for two 〈δ〉 values of 0.7 Å (middle) and 1.0 Å (bottom).

Image of FIG. 5.

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FIG. 5.

The imaginary part of the correlation function for the under-damped and over-damped cases for the coupling between the OH stretch vibration and the bath (top), and the corresponding 2D IR spectra (middle and bottom), respectively. The 2D IR spectrum for the under-damped case has been truncated to show the lower 75% of the contours to emphasize the low-intensity peaks.

Image of FIG. 6.

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FIG. 6.

Potential of mean force used for the Langevin dynamics calculation of a chemical exchange process (top). The parameters used for the potential of mean force are as follows: ωf,0 = 2729 cm‑1, σω,f = 22.4 cm−1, ωb,0 = 2683 cm−1, σω,b = 28.3 cm−1; ξf,0 = 0.465, σξ,f = 0.0316, ξb,0 = 0.378, σξ,b = 0.0387; Af = 0.88, Ab = 1.08. An example of a correlated frequency trajectory showing the exchange between the free and the bound state (bottom).

Image of FIG. 7.

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FIG. 7.

Waiting time series of 2D IR spectra calculated from Langevin simulations show the evolution of the diagonal peaks from being inhomogeneously broadened to being symmetric, along with the growth of the cross peaks signifying chemical exchange. The parameters used in solving the Langevin equations are as follows: cω = 2 cm−1s−1, cξ = 10−6 s−1, Tω = 0.030, Tξ = 0.000025, and 1/〈λ2〉 = 3×10−15 (units of cm−2 in the ω-equation and unit-less in the ξ-equation).

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/content/aip/journal/jcp/136/13/10.1063/1.3700718
2012-04-05
2014-04-24

Abstract

We present an approach for calculating nonlinear spectroscopic observables, which overcomes the approximations inherent to current phenomenological models without requiring the computational cost of performing molecular dynamics simulations. The trajectory mapping method uses the semi-classical approximation to linear and nonlinear response functions, and calculates spectra from trajectories of the system's transition frequencies and transition dipole moments. It rests on identifying dynamical variables important to the problem, treating the dynamics of these variables stochastically, and then generating correlated trajectories of spectroscopic quantities by mapping from the dynamical variables. This approach allows one to describe non-Gaussian dynamics, correlated dynamics between variables of the system, and nonlinear relationships between spectroscopic variables of the system and the bath such as non-Condon effects. We illustrate the approach by applying it to three examples that are often not adequately treated by existing analytical models – the non-Condon effect in the nonlinear infrared spectra of water, non-Gaussian dynamics inherent to strongly hydrogen bonded systems, and chemical exchange processes in barrier crossing reactions. The methods described are generally applicable to nonlinear spectroscopy throughout the optical, infrared and terahertz regions.

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Scitation: A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/13/10.1063/1.3700718
10.1063/1.3700718
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