Line shape absorption mode

It was quantitatively interpreted (Rice et al., 1977) as originating from bond alternation phase oscillations (in contrast to the bond alternation amplitude oscillations mentioned in subsection 4.8.2D). The vibrational absorption lines labeled 2 to 10 are directly related to the Ag Raman lines of TCNQ. The broad peak above 1600 cm originates from the single electron transition across the gap, and the indented line shape of mode 2 is a consequence of Fano interference between the single electron continuum and the phonon mode. The line intensities are determined by the respective electron - vibration coupling constants. 

Pump-probe absorption experiments on the femtosecond time scale generally fall into two effective types, depending on the duration and spectral width of the pump pulse. If tlie pump spectrum is significantly narrower in width than the electronic absorption line shape, transient hole-burning spectroscopy [101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112 and 113] can be perfomied. The second type of experiment, dynamic absorption spectroscopy [57, 114. 115. 116. 117. 118. 119. 120. 121 and 122], can be perfomied if the pump and probe pulses are short compared to tlie period of the vibrational modes that are coupled to the electronic transition. 

Fig. la-c. Theoretical 2H NMR line shapes for axially symmetric FGT (r = 0) in rigid solids, cf. Equ. (1). a Line shapes for the two NMR transitions b 2H spectrum (Pake diagram) in absorption mode as obtained by Fourier transform methods c 2H spectrum in derivative mode as obtained by wide line methods... 

There are generally three types of peaks pure 2D absorption peaks, pure negative 2D dispersion peaks, and phase-twisted absorption-dispersion peaks. Since the prime purpose of apodization is to enhance resolution and optimize sensitivity, it is necessary to know the peak shape on which apodization is planned. For example, absorption-mode lines, which display protruding ridges from top to bottom, can be dealt with by applying Lorentz-Gauss window functions, while phase-twisted absorption-dispersion peaks will need some special apodization operations, such as muliplication by sine-bell or phase-shifted sine-bell functions. 

Peaks in homonuclear 2D /-resolved spectra have a phase-twisted line shape with equal 2D absorptive and dispersive contributions. If a 45° projection is performed on them, the overlap of positive and negative contributions will mutually cancel and the peaks will disappear. The spectra are therefore presented in the absolute-value mode. 

Absorption-mode spectrum The spectrum in which the peaks appear with Lorentzian line shapes. NMR spectra are normally displayed in absolute-value mode. 

Dispersion mode A Lorentzian line shape that arises from a phase-sensitive detector (which is 90 out of phase with one that gives a pure-absorption-mode line). Dispersion-mode signals are dipolar in shape and produce long tails. They are not readily integrable, and we need to avoid them in a 2D spectrum. 

Lorentzian line shape The normal line shape of an NMR peak that can be displayed either in absorption or dispersion mode. 

Phase-sensitive data acquisition NMR data are acquired in this manner so that peaks are recorded with pure absorption-mode or pure dispersionmode line shapes. 

The vibrational frequency of the special pair P and the bacteriochlorophyll monomer B have also been extracted from the analysis of the Raman profiles [39,40,42,44,51]. Small s group has extensively performed hole-burning (HB) measurements on mutant and chemically altered RCs of Rb. Sphaeroides [44,45,48-50]. Their results have revealed low-frequency modes that make important contribution to optical features such as the bandwidth of absorption line-shape, as well as to the rate constant of the ET of the RCs. 

It is easiest to formulate this problem in the case of a single high-frequency vibrational mode, or chromophore, so let us consider this situation first. For the absorption line shape, which involves only the ground and excited state of the chromophore, a cmcial element is the 0 —> 1 transition frequency and its dependence on the classical bath coordinates. Second, one needs (in the case of IR spectroscopy) the projection of the transition dipole in the direction p of the electric field axis. This projection can depend on bath coordinates in two ways. 

Fig. 15. Absorption line shapes for an Alg - > Tlu transition, (a) Coupling due to the rasl vibration. (b) Coupling due to both t2g and al9 vibrational modes. These absorption profiles were calculated by Toyozawa and Inoue (123) invoking the semiclassical approximation.

To determine the excitation energy of the lowest electronic level the contributions in the absorption spectrum from transitions to different vibrational modes of the excited state have to be separated. In the deconvolution of the absorption spectra Gaussian line shapes are assumed for the transitions to the different vibrational levels. The analysis leads to the transition wavelength A00 for the excitation from the ground state to the zero vibrational level of the excited state. 

The Bloch equations can be solved analytically under the condition of slow passage, for which the time derivatives of Eq. 2.48 are assumed to be zero to create a steady state. The nuclear induction can be shown to consist of two components, absorption, which is 90° out of phase with B, and has a Lorentzian line shape, and dispersion, which is in phase with B,. The shapes of these signals are shown in Fig. 2.10. By appropriate electronic means (see Section 3.3), we can select either of these two signals, usually the absorption mode. 

Equation 10.9 represents a complicated line shape, which is a mixture of absorptive and dispersive contributions. Figure 10.11 gives an example of such a phase-twisted line shape. The broad base of the line, caused by the dispersive contribution, and the difficulty in correctly phasing such a resonance make it unattractive for practical use. The phase twist problem can be alleviated by displaying only the absolute value mode... 

Optical properties of organic conductors also reflect the appearance of the energy gap, 2A, in the electronic energy spectrum of low-dimensional solids. The approximate value for the total gap from the g-mode line shapes can be estimated by comparing the IR spectra of the organic conductor, measured for the frequencies above and below the energy gap sharp absorption bands are produced at the frequencies w < 2A, whereas for to > 2A sharp indentations occur [87,88]. 

This simple phase-incrementation idea, not particularly emphasized by the authors at the time, has more recently had a considerable impact on NMR methodology. First, it was made the basis of one of the standard methods for obtaining pure-phase two-dimensional spectra, replacing the undesirable phase-twist line shape with a pure absorption-mode signal. Secondly, it has provided a neat way to generate an extensive array of simultaneous soft radiofrequency pulses covering an... 

Figure 2-11 Comparison of shapes of absorption (solid line) and dispersion (dotted line) signals. Spectra are usually phase corrected to give pure absorption-mode peaks. The arrows indicate the full width at half maximum. (Reprinted from J. C. Hoch and A. S. Stern, NMR Data Processing, 1996 by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc.)...

Figure 6. Pulse sequences and coherence transfer pathway diagrams for (a) a 2D CRAMPS experiment incorporating a z-filter to ensure that pure absorption-mode line shapes are obtained and (b) a 2D constant-time CRAMPS experiment. The relative performance of the two experiments with respect to yielding high-resolution H NMR spectra in the indirect (F ) dimension is illustrated by Figure 5c,d and is discussed in the text. (Adapted with permission from Figure 2 of ref 78. Copyright 2001 American Chemical Society.)...

In solution-state NMR, many important experiments incorporate the creation and evolution of MQ coherence (MQC).5,6,84-86 Since MQC cannot be directly detected, experiments that follow the evolution of a MQC are inherently at least two-dimensional. This is the case with H- H DQ MAS spectroscopy. Figure 7 shows a corresponding pulse sequence and coherence transfer pathway diagram first, a DQC is excited, which subsequently evolves during an incremented time period q the DQC is then converted into observable single-quantum (SQ) coherence (SQC), which is detected in the acquisition period, q. To select the desired coherence transfer pathways, e.g., only DQC during q, a phase cycling scheme is employed.79,80 Pure absorption-mode two-dimensional line shapes are ensured by the selection of symmetric pathways such that the time-domain... 

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