Frequency-frequency correlation functions and apodization in two-dimensional infrared vibrational echo spectroscopy: A new approach

Abstract

Ultrafast two-dimensional infrared (2D-IR) vibrational echo spectroscopy can probe structural dynamics under thermal equilibrium conditions on time scales ranging from femtoseconds to approximately 100 ps and longer. One of the important uses of 2D-IR spectroscopy is to monitor the dynamical evolution of a molecular system by reporting the time dependent frequency fluctuations of an ensemble of vibrational probes. The vibrational frequency-frequency correlation function (FFCF) is the connection between the experimental observables and the microscopic molecular dynamics and is thus the central object of interest in studying dynamics with 2D-IR vibrational echo spectroscopy. A new observable is presented that greatly simplifies the extraction of the FFCF from experimental data. The observable is the inverse of the center line slope (CLS) of the 2D spectrum. The CLS is the inverse of the slope of the line that connects the maxima of the peaks of a series of cuts through the 2D spectrum that are parallel to the frequency axis associated with the first electric field-matter interaction. The CLS varies from a maximum of 1 to 0 as spectral diffusion proceeds. It is shown analytically to second order in time that the CLS is the T(w) (time between pulses 2 and 3) dependent part of the FFCF. The procedure to extract the FFCF from the CLS is described, and it is shown that the T(w) independent homogeneous contribution to the FFCF can also be recovered to yield the full FFCF. The method is demonstrated by extracting FFCFs from families of calculated 2D-IR spectra and the linear absorption spectra produced from known FFCFs. Sources and magnitudes of errors in the procedure are quantified, and it is shown that in most circumstances, they are negligible. It is also demonstrated that the CLS is essentially unaffected by Fourier filtering methods (apodization), which can significantly increase the efficiency of data acquisition and spectral resolution, when the apodization is applied along the axis used for obtaining the CLS and is symmetrical about tau=0. The CLS is also unchanged by finite pulse durations that broaden 2D spectra.

Hydrogen bond dynamics in aqueous NaBr solutions

“…Furthermore, the CLS provides a more useful quantity to plot for visualizing differences in the dynamics as a function of the NaBr concentration than a series of full 2D IR spectra (23,35). In the CLS method, frequency slices through the 2D IR spectrum parallel to the axis at various m values are projected onto the axis (35). These projections are a set of spectra with peak positions, max , on the axis.…”

“…The CLS method is a new approach for extracting the FFCF from the T w dependence of the 2D IR spectra that is accurate and much simpler to implement numerically than iterative fitting methods with calculations of all response functions based on time-dependent diagrammatic perturbation theory. Furthermore, the CLS provides a more useful quantity to plot for visualizing differences in the dynamics as a function of the NaBr concentration than a series of full 2D IR spectra (23,35). In the CLS method, frequency slices through the 2D IR spectrum parallel to the axis at various m values are projected onto the axis (35).…”

“…Here, we used the center line slope (CLS) method (23,35). The CLS method is a new approach for extracting the FFCF from the T w dependence of the 2D IR spectra that is accurate and much simpler to implement numerically than iterative fitting methods with calculations of all response functions based on time-dependent diagrammatic perturbation theory.…”

Femtosecond Hydrogen Bond Dynamics of Bulk‐like and Bound Water at Positively and Negatively Charged Lipid Interfaces Revealed by 2D HD‐VSFG Spectroscopy

“…As each OH vibration “forgets” the ω pump at which it has been photoexcited (that is, spectral diffusion), the diagonal elongation gradually vanishes with time. The degree of the diagonal elongation can be evaluated from the slope of the black straight line drawn in the 2D HD‐VSFG spectrum 11. The black line in Figure 2 is a fit for black solid markers that indicate the peak ω 2 wavenumbers of horizontal cuts at each ω pump wavenumber.…”

Transient 2D-IR spectroscopy of inorganic excited states

“…Quantification of this lineshape evolution as a function of waiting time then gives rise to an exponential-type decay with the timescales reporting the dynamics of the FFCF, which in turn report on solvent motion near the vibrational mode in question. Various methods have been developed to achieve this quantification, 25, 50-52 of which perhaps the simplest to visualise extracts the gradient of the nodal plane between the v=0-1 and v=1-2 parts of the 2D-IR diagonal feature (the Nodal Line Slope method 51 ) or the gradient of a line through the highest points of the v=0-1 peak at each pump frequency (the Central Line Slope method 50 ). All methods have been shown to be largely equivalent in terms of extraction of dynamic timescales from 2D-IR data.…”