Response function spectroscopy

S. Tanaka, V. Chernyak, and S. Mukamel, Time-resolved X-ray spectroscopies nonlinear response functions and Liouville space pathways. Phys. Rev. A 63(6), 063405 (2001). 

If b and g are peaked functions (such as in a spectral line), the area under their convolution product is the product of their individual areas. Thus, if b represents instrumental spreading, the area under the spectral line is preserved through the convolution operation. In spectroscopy, we know this phenomenon as the invariance of the equivalent width of a spectral line when it is subjected to instrumental distortion. This property is again referred to in Section II.F of Chapter 2 and used in our discussion of a method to determine the instrument response function (Chapter 2, Section II.G). 

We have shown that the radiant flux spectrum, as recorded by the spectrometer, is given by the convolution of the true radiant flux spectrum (as it would be recorded by a perfect instrument) with the spectrometer response function. In absorption spectroscopy, absorption lines typically appear superimposed upon a spectral background that is determined by the emission spectrum of the source, the spectral response of the detector, and other effects. Because we are interested in the properties of the absorbing molecules, it is necessary to correct for this background, or baseline as it is sometimes called. Furthermore, we shall see that the valuable physical-realizability constraints presented in Chapter 4 are easiest to apply when the data have this form. 

Owing to aberrations, grating defects, and so on, it may not be adequate to approximate the response function by formulas based on idealized models. If a line source could be found having the spectrum that approximates a 8 function, then perhaps the measurement of such a line would adequately determine the response function. We have learned, however, that the spatial coherence of the source plays an important part in the shape of the response function. This precludes the use of a laser line source to measure the response function applicable to absorption spectroscopy. Furthermore, we... 

In the response function formalism developed by Mukamel [1], all four wave-mixing spectroscopies are described by four response functions, R, ..., i 4, and their complex conjugates. Double-sided Feynman diagrams are shown in Fig. 12 representing these response functions. The response functions in turn are described by a single line shape function g t) given by... 

Prof. Fleming, the expressions you are using for the nonlinear response function may be derived using the second-order cumulant expansion and do not require the use of the instantaneous normal-mode model. The relevant information (the spectral density) is related to the two-time correlation function of the electronic gap (for resonant spectroscopy) and of the electronic polarizability (for off-resonant spectroscopy). You may choose to interpret the Fourier components of the spectral density as instantaneous oscillators, but this is not necessary. The instantaneous normal mode provides a physical picture whose validity needs to be verified. Does it give new predictions beyond the second-order cumulant approach The main difficulty with this model is that the modes only exist for a time scale comparable to their frequencies. In glasses, they live much longer and the picture may be more justified than in liquids. 

TNP-ATP complex obtained by the single-molecule time-resolved spectroscopy, together with a fluorescence decay curve of TNP-ATP obtained by a bulk measurement. Both curves were well fitted to biexponential functions. The instrument-response function in 195-ps fwhm is also displayed. (B) Representative fluorescence spectrums of two individual enzyme-TNP-ATP complexes showing different emission peaks. A fluorescence spectrum of TNP-ATP obtained from a bulk measurement is also displayed for comparison. All spectrums were normalized to unity at their maximum. (From Ref. 18.)... 

A successful X-ray spectroscopy of the quality required for the pionic hydrogen experiment is based on a narrow and well understood response function of the crystals. An energy calibration or an optimization can not be achieved with ffuorescence X-rays produced with X-ray tubes. Their width is an order of magnitude broader than the resolution of the crystals. The line shape is moreover influenced by poorly determined satellite lines. 

In resonant infrared multidimensional spectroscopies the excitation pulses couple directly to the transition dipoles. The lowest order possible technique in noncentrosymmetrical media involves three-pulses, and is, in general, three dimensional (Fig. 1A). Simulating the signal requires calculation of the third-order response function. In a small molecule this can be done by applying the sum-over-states expressions (see Appendix A), taking into account all possible Liouville space pathways described by the Feynman diagrams shown in Fig. IB. The third-order response of coupled anharmonic vibrations depends on the complete set of one- and two-exciton states coupled to thermal bath (18), and the sum-over-states approach rapidly becomes computationally more expensive as the molecule size is increased. 

In this chapter we surveyed the theoretical analysis of resonant multidimensional spectroscopies generated by the interaction of 3 fs pulses with a Frenkel exciton system. Closed expressions for the time-domain third-order response function derived by solving the NEE are given in terms of various exciton Green functions. Alternatively, the multidimensional time-domain signal can be calculated starting from the frequency domain the third-order... 

Competing processes are another concern in real experiments. These processes result from interactions with different time orderings of the pulses and with perturbation-theory pathways proceeding through nonresonant states. They correspond to the constant nonresonant background seen in CARS and other frequency-domain spectroscopies. These nonresonant interactions are only possible when the excitation and probe pulses are overlapped in time, so they add an instantaneous component to the total material response function... 

To demonstrate the potential of two-dimensional nonresonant Raman spectroscopy to elucidate microscopic details that are lost in the ensemble averaging inherent in one-dimensional spectroscopy, we will use the Brownian oscillator model and simulate the one- and two-dimensional responses. The Brownian oscillator model provides a qualitative description for vibrational modes coupled to a harmonic bath. With the oscillators ranging continuously from overdamped to underdamped, the model has the flexibility to describe both collective intermolecular motions and well-defined intramolecular vibrations (1). The response function of a single Brownian oscillator is given as,... 

It is important to note that the two electric fields that lead to a Raman transition can have different polarizations. Information about how the transition probability is affected by these polarizations is contained within the elements of the many-body polarizability tensor. Since all of the Raman spectroscopies considered here involve two Raman transitions, we must consider the effects of four polarizations overall. In time-domain experiments we are thus interested in the symmetry properties of the third-order response function, R (or equivalently in frequency-domain experiments... 

In order to investigate solids or polymer systems with free carriers by IR spectroscopy, it is very convenient to measure the reflectivity instead of absorbance or transmittance. Thus, the problems to be discussed in this context are usually described by a linear response formalism. In its simplest form, this means that the response function (dielectric function) s(u ) of a damped harmonic oscillator is used to describe the interaction between light and matter. The complex form of this function is... 

As pointed out in Section 3.3, Raman spectroscopy is usually a singlebeam method, and the observed spectrum is the product of the actual Raman scattering and an instrument response function. Correction of relative intensities across a Raman spectrum is possible, although not common, using the techniques described in Chapter 10. For quantitative analysis, however, one must be concerned about the reproducibility of the observed magnitude... 

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