Raman excitation spectrum

Equation (6), which expresses the frequency spectrum as the Fourier transform of the time autocorrelation of the initial state, is the central result of this section. It shows how to relate to the observed one-photon spectrum, determined in the frequency domain, to the time evolution of a nonstationary state on the excited electronic state. It is possible to obtain similar results for other spectroscopies. For example, the Raman excitation spectrum is determined by a time cross-correlation function between two different states. This is useful to know because the time autocorrelation function, while quite informative, really only tells us where the initial state is not, while the cross-correlation function tells where the initial state is. Before we turn to these considerations in detail, we should take advantage of what is already implied by the time autocorrelation function itself. 

Figure 17 The Raman excitation spectrum for a transition to the B electronic state of iodo-benzene with one quantum of vibrational excitation in the v, vibrational mode. (Solid line) computed in the harmonic approximation for the motion in the B state. (Dotted line) The maximal entropy fit of this spectrum obtained using Eq. (97). This fit is used to determine the cross-correlation function as shown in Fig. 18. (From Ref. (102).)...

Figure 19 The Raman spectrum and time cross correlation function when the motion on the excited electronic state potential is anharmonic, compare to Figs. 17 and 18, which are for a harmonic approximation. (Top, a) Computed time correlation function using a wide window function (b) The maximal entropy representation of this function, determined from the spectrum. Note the clear separation of time scales due to the anharmonicity (cf. Fig. 20). (Bottom) The Raman excitation spectrum obtained from the computed time correlation function (a). The arrows are the sequence of computations (a) is determined from the dynamics. The spectrum is determined from (a). The maximum entropy cross-correlation function (b) uses only the spectrum as input.

For a properly chosen value of v, the resonance Raman spectrum thus resembles an emission spectrum. However, if we vary v, but keep the frequency difference between incident and scattered light, Vj — Vq, equal to a ground-state band, we can monitor the intensity variation of this band while scanning the absorption spectrum. This Raman excitation spectrum, usually called Raman excitation profile (REP), thus resembles an absorption spectrum for the mode being monitored. If we were to monitor all the scattered Raman light without trying to resolve it, we would observe the Raman analog of a typical absorption spectrum. 

Fig. 12.4 Calculated resonance Raman excitation spectrum solid curves) and homoge-...

The matrix element for resonance Raman scattering thus is proportional to a half-Fourier transform of flie overlap of the final vibrational wavefunction (Xh(g)) with the time-dependent wavepacket X(t) created by exciting the molecule with white light in the ground state. See [6] and [8] for more complete proofs of this relationship, and [10] for a review of some of its extensions and applications. The resonance Raman excitation spectrum is proportional to as explained above. 

Because of the two frequencies, Wj and Wg, that enter into the Raman spectrum, Raman spectroscopy may be thought of as a two-dimensional fomi of spectroscopy. Nomially, one fixes oij and looks at the intensity as a frmction of tOj, however, one may vary tOj and probe the intensity as a frmction of tOj - tOg. This is called a Raman excitation profile. 

Figure 1.14 Raman spectra from a 0.1 wt% Mo03/y-AI203 catalyst obtained by using different (488, 325, and 244 nm) laser excitation energies [108], The UV-Vis absorbance spectrum is reported in the inset to indicate that while the catalyst does not absorb light in the visible region, it does show two UV absorption peaks at 290 and 220 nm. The data clearly illustrate the advantage of using ultraviolet (244 nm) light for Raman excitation, since the spectrum obtained with visible (488 nm) radiation is dominated by the fluorescence of the solid. (Reproduced with permission from Elsevier.)...

Physical Properties Density average and standard deviation Size average and standard deviation Fluorescence Fluorescence excitation spectrum Scattered light spectrum Absorption spectrum (from microwave to UV) Raman spectrum Electrical conductivity, impedance Acoustic properties... 

FIGURE 5. Schematic diagram of low resolution (0.8 nm) Raman scattering spectrum of O3 excited at 266 nm. The spectrum consists of overtones and combination bands in v-] (antisymmetric stretch) and v3 (antisymmetric stretch up to v" = 7 and V3 = 6 No bands with >2 (bending) are evident, suggesting that the bond angle remains the same during the transition. Reproduced from reference (80) with permission from the American Chemical Society. 

Increasing the solvent polarity results in a red shift in the -t -amine exciplex fluorescence and a decrease in its lifetime and intensity (113), no fluorescence being detected in solvents more polar than tetrahydrofuran (e = 7.6). The decrease in fluorescence intensity is accompanied by ionic dissociation to yield the t-17 and the R3N" free radical ions (116) and proton transfer leading to product formation (see Section IV-B). The formation and decay of t-17 have been investigated by means of time resolved resonance Raman (TR ) spectroscopy (116). Both the TR spectrum and its excitation spectrum are similar to those obtained under steady state conditions. The initial yield of t-1 is dependent upon the amine structure due to competition between ionic dissociation and other radical ion pair processes (proton transfer, intersystem crossing, and quenching by ground state amine), which are dependent upon amine structure. However, the second order decay of t-1" is independent of amine structure... 

Figure 2-28 The vi (A symmetry) band of SO in K2SO4 and Na2S04 frozen solutions. Both spectra were measured with 488-nm excitation from an Ar-ion laser at a resolution of 5 cm 1. A-B is the Raman difference spectrum of K2SO4 minus Na2S04. (Reproduced with permission from Ref. 78.)...

Figure 3-21 Comparison of TCNQ - electronic absorption spectrum and resonance Raman excitation profiles, (a) Electronic absorption spectrum from 15,000 to 17,850 cm-1. The extinction coefficient, e, scale is normalized with respect to e at 663.0nm (15,083cm-1) = 3.0 x 103M-Icm-1. (b) Superposition of the v2 (2,192cm-1). v4 (1,389cm-1), v5 (1,195cm-1) and V9 (336 cm-1) excitation profiles. The relative intensity scale has been scaled to 0.00 to lO.Ofor all four spectra. (Reproduced with permission from Ref. 76. Copyright 1976 American Chemical Society.)...

Photo-ions are then detected as a function of interferometer delay. The result is an in-terferogram that upon Fourier transformation yields a Raman spectrum whose resolution does not depend on the bandwidths of the Raman excitation sources but, instead, on the delay range of the interferometer scanned in the experiment. Mass-selective IDSRS and FT-IDSRS have been employed in a number of studies, including one of the benzene dimer (Henson et al., 1991). For examples of IDSRS spectra see Sec. 6.1.4.5. 

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