Extracting 2D IR frequency-frequency correlation functions from two component systems

Abstract

The center line slope (CLS) method is often used to extract the frequency-frequency correlation function (FFCF) from 2D IR spectra to delineate dynamics and to identify homogeneous and inhomogeneous contributions to the absorption line shape of a system. While the CLS method is extremely efficient, quite accurate, and immune to many experimental artifacts, it has only been developed and properly applied to systems that have a single vibrational band, or to systems of two species that have spectrally resolved absorption bands. In many cases, the constituent spectra of multiple component systems overlap and cannot be distinguished from each other. This situation creates ambiguity when analyzing 2D IR spectra because dynamics for different species cannot be separated. Here a mathematical formulation is presented that extends the CLS method for a system consisting of two components (chemically distinct uncoupled oscillators). In a single component system, the CLS corresponds to the time-dependent portion of the normalized FFCF. This is not the case for a two component system, as a much more complicated expression arises. The CLS method yields a series of peak locations originating from slices taken through the 2D spectra. The slope through these peak locations yields the CLS value for the 2D spectra at a given T(w). We derive analytically that for two component systems, the peak location of the system can be decomposed into a weighted combination of the peak locations of the constituent spectra. The weighting depends upon the fractional contribution of each species at each wavelength and also on the vibrational lifetimes of both components. It is found that an unknown FFCF for one species can be determined as long as the peak locations (referred to as center line data) of one of the components are known, as well as the vibrational lifetimes, absorption spectra, and other spectral information for both components. This situation can arise when a second species is introduced into a well characterized single species system. An example is a system in which water exists in bulk form and also as water interacting with an interface. An algorithm is presented for back-calculating the unknown FFCF of the second component. The accuracy of the algorithm is tested with a variety of model cases in which all components are initially known. The algorithm successfully reproduces the FFCF for the second component within a reasonable degree of error.

Solvent-Independent Anharmonicity for Carbonyl Oscillators

“…36–38 The CLS increases in a solvent-dependent manner from hexanes to D 2 O (Figure 3A,B, red lines), suggesting increasing inhomogeneous broadening contributions to the line shapes. 36–39 Analysis and comparison to the simulated 2D spectra are presented below.…”

2D IR spectroscopy reveals the role of water in the binding of channel-blocking drugs to the influenza M2 channel

“…The doublets observed for Gly34 and Ala30 at pH 5, however, make an accurate assessment of their spectral diffusion dynamics difficult, as it has been shown that for overlapping bands, the commonly used metrics, such as the center line slope, do not yield relaxation functions that represent the decay of the underlying frequency-frequency correlation function. 58 Fortunately, as shown in Sec. III D, the correlation dynamics can be evaluated by analyzing the cross-peak dynamics.…”

Intrinsic Structural Heterogeneity and Long-Term Maturation of Amyloid β Peptide Fibrils

“…To characterize the rate of spectral diffusion, values for the inverse slope (IS) were calculated as a function of waiting time T for various transitions in each sample (Table 1, Figure 3h, and Supporting Information Figure S2). 30,31 Earlier studies have suggested that spectral diffusion on a picosecond time scale is due to mobile water molecules in the immediate environment of the isotope label. 28,32,33 Spectral diffusion due to side chain conformational changes or backbone motions is markedly slower.…”