Synchronous spectrum

The synchronous spectrum (Fig. 3-31 A) is symmetric with respect to the diagonal line corresponding to coordinates vi = V2. Several peaks (A, B, C and D) on this line are called autopeaks which are always positive. The stronger the peak, the larger the variation of its band intensity due to external... 

Some luminescence instruments allow simultane-ously scanning both the excitation and the emission wavelengths with a sntall w avelength difference between them. The spectrum that results is known as a synchronous spectrum. A luminescence signal Is ob-... 

FIGURE 15-7 Synchronous fluorescence spectra, in (a), the excitation and emission spectra of telracene are shown, in (b), the synchronous spectrum is shown for a fixed-waveiength difference of 3 nm, (From T. Vo-Dinh, Anal. Cherrh. 1978, 50, 396. Figure i, p. 397. Copyright 1978 American Chemical Society.)... 

Figure 10.1 General scheme for obtaining 2D-IR spectra. From the response of the system to perturbation, a dynamic spectrum is obtained. The Fourier transform gives two components, the real one corresponding to the synchronous spectrum and the imaginary one corresponding to the...

To increase interpretability, the dynamic IR spectra are snbjected to mathematical cross-correlation to prodnce two different types of 2D1R correlation spectra, or two-dimensional correlation maps. These maps, in which the. r- and y- axes are independent wavenumber axes (vi, V2), show the relative proportions of in-phase (synchronous) and ont-of-phase (asynchronons) response (Figs. 3.51 and 3.52). Initially, the mathematical formalism was based on the complex Fourier transformation of dynamic spectra [277]. To simplify the computational difficulties, the Hilbert pansform approach was developed [280], which produces two-dimensional correlation maps from a set of dynamic spectra as follows. First, the average spectrum y(v) is subtracted from each spectrum in the set, y(v, Pj) = y v, Pj) — y(v), where Pj is the dynamic parameter. Then, the synchronous spectrum, 5 (vi,V2), and the asynchronous spectrum, A(vi,V2), are calculated as... 

A synchronous spectrum, with a constant energy difference (Av), is performed by scanning the emission monochromator at a slightly faster rate than the excitation monochromator Al = —1,. ). Syn-... 

Figure 5.4 2D IR correlation spectra based on the spectral changes induced by the static compression of linear low-density polyethylene (LLDPE) at 608 °C. Synchronous spectrum (left) Negative intensity peaks indicating anti-correlation are shaded. Asynchronous spectrum (right) Shaded peaks indicate that intensity changes at i/, occur at higher pressure than changes at i 2- Reprinted from Noda et al. [49], Copyright 1999, with permission from Elsevier.

There is a strong correlation in the synchronous spectrum and no appreciable asynchronicity in the asynchronous spectrum between the mesogen band (2230 cm" ) and the (CH ) bands (2926 and 2863 cm" ). The main part of the intensity changes in the region of 2850-2950 cm" is due to the spacer thus, on the basis of the 2D results we may draw the conclusion that the spacer and the mesogen reorient simultaneously. 

The real and imaginary components of the complex 2D correlation intensities, 0(vi, V2) and (vi, V2), are referred to, respectively, as the generalized synchronous and asynchronous correlation spectra of the dynamic spectral intensity variations. The synchronous spectrum represents the simultaneous or coincidental changes spectral intensities at vi and V2, whereas the asynchronous spectrum represents sequential or unsychronized variations. 

Figure 3.12A and B, depicts schematic contour maps of synchronous and asynchronous 2D correlation spectra, respectively (the terms synchronous and asynchronous are always used even when the spectral variation is measured as a function of not time but another physical variable) (13). A one-dimensional refernce spectrum is provided at the top and left side of the contour map to show the basic feature of spectra of the system during experiment. A synchronous spectrum is symmetric with respect to a diagonal line corresponding to spectral coordinates = V2. Peaks... 

They are respectively referred to as the synchronous and asynchronous 2D infrared spectra. The synchronous spectrum characterizes the degree of coherence between the dynamic fluctuations of signals measured at two wavenumbers, and the correlation intensity becomes significant only if the reorientation rates of dipole transition moments are similar to each other. The asynchronous spectrum, however, characterizes the independent, uncoordinated out-of-phase fluctuations of the signals. Hence the asynchronous correlation intensity becomes non-vanishing only if the signals vary at difierent rates. 

The synchronous spectrum 0(vi, V2) represents the pattern similarity or in-phase nature of spectral intensity changes observed at vj and V2 along the perturbation variable t. On the other hand, the asynchronous spectrum V2) represents the dissimilarity or out-phase nature of intensity variation patterns. Although the procedure described is a highly simplified one, it should be applicable to many practical cases of spectral analysis. More general treatment of 2D correlation analysis, including the case for unevenly sampled spectral data, is discussed in Appendix F. 

Figure 21.8 shows the 2D IR correlation spectra of the N-isomeric form of HSA in a buffer solution, derived from the pH-dependent (pH 5.0,4.8,4.6, and 4.4) spectral variations. The synchronous spectrum shows a major autopeak around 1654 cm assigned to the a-helix. The analysis of several peaks in the asynchronous spectrum allows one to identify several bands at 1715, 1667, 1654, and 1641 cm The band at 1715 cm is assignable to a C=0 stretching mode of the hydrogen-bonded COOH groups of Glu and Asp residuals of HSA. On the other hand, the bands at 1667 and 1641 cm i are assigned to the -turn and -strand of HSA, respectively. 

The real part (vj, V2) of the complex cross correlation function is referred to as the synchronous spectrum, while the imaginary part 9 (vi, V2) is called the asynchronous spectrum. The practical significance of the correlation spectra related to applications in physical science and the step-by-step derivation of the above equation central to the two-dimensional correlation analysis are provided in this appendix. 

The formal definition of synchronous spectrum and asynchronous correlation spectrum given in Equation (F3) is mathematically concise and rigorous. However, the requirement for obtaining the Fourier transforms of signals with respect to the variable t at every point of wavenumber v for a given dynamic spectrum makes the computation of correlation spectra rather cumbersome, even with the aid of the fast Fourier transform (FFT) algorithm. Fortunately, there is a simple way to circumvent the use of the Fourier transforms to efficiently compute the desired correlation spectra [2]. 

It is straightforward to obtain the expression for the synchronous spectrum without the need for the Fourier transform directly from the cross correlation function given in Equation (F6). By setting the correlation time as t = 0, we have... 

The synchronous and asynchronous spectrum, especially those expressed in terms of the amplitudes of cosine and sine function, clearly reveal the close resemblance of the functional forms to the ones given for the cospectrum and quad-spectrum in Equations (FIO) and (Fll). The amplitudes of cosine and sine component, respectively, of the dynamic spectrum with a single frequency 5 reflect the real and imaginary parts of the Fourier transform of the dynamic spectrum at the Fourier frequency of s = 5. Alternatively, the more general synchronous spectrum and asynchronous spectrum in Equation (F15) derived for the dynamic spectrum with arbitrary waveforms may be viewed as the collective sum totals of individual correlation spectra obtained for the corresponding Fourier components. 

The collective summation by integration of all cospectra for the entire positive range of i yields the synchronous spectrum in Equation (FI3), and the same for quad-spectra to obtain the asynchronous spectrum in Equation (F14). 

The synchronous spectrum and asynchronous correlation spectrum are now obtained as nxn correlation matrices, 0 and F. Their matrix elements correspond, respectively, to the value of correlation spectra 0 = (Vp, Vq) and = P(Vp, Vq). Equations (F30) and (F31) are now presented concisely by the matrix notation as... 

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