tte power of the 2D correlation approach results primarily in an increase of the spectral resolution by dispersal of the peaks along a second dimension that also reveals the time course of the events induced by the perturbation. Correlations between bands are found through the so-called synchronous (&) and asynchronous (i9 spectra that correspond to the real and imaginary parts of the cross-correlation of spectral intensity at two wavenumbers, i.e. that two vibrations of the protein characterized by two different wavenumbers (vj and V2) are affected at the same time (synchronous) or that the vibrations of the functional groups corresponding to the different wavenumbers each change at a different time (asynchronous). In a synchronous 2D map, the peaks located in the diagonal (autopeaks) correspond to

changes in intensity induced by the perturbation, and are always positive, ^e cross-correlation peaks indicate an in-phase relationship between two bands involved. Asynchronous maps show not-in-phase cross-correlation between the bands and this gives an idea of the time course of the events produced by the perturbation.

To obtain 2D-IR correlation spectra the formalism proposed by Noda is usually followed. From the response of the system to the perturbation, a dynamic spectrum is obtained, ^e type of physical information contained in a dynamic spectrum is determined by the perturbation method. Once the dynamic spectrum has been obtained as a matrix formed by the spectra ordered according to the change produced by the perturbation, the Fourier transform gives two components, the real one corresponding to the synchronous spectrum and the imaginary one corresponding to the asynchronous one (Fig. 4.1). In terms of calculation, instead of using a Fourier transform that would require large computation times, an adequate numerical evaluation of 2D correlation intensity is used, ^us, the synchronous 2D correlation intensity expressed as

yj (vj) is the dynamic spectra calculated from the spectral intensities as a deviation from a reference spectrum at a point of physical variable tj.

^e computation of asynchronous 2D correlation intensity is somewhat more complicated. Two approaches can be used, (1) using the Hilbert transform and (2)

a direct procedure, giving similar results (for a detailed discussion on the asynchronous calculation, see Noda and Ozaki 2004).

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