Linear Raman effect

We will first discuss spontaneous Raman spectroscopy with lasers (linear Raman effect) and then briefly some investigations of the nonlinear Raman effect. 

The intensity of Rayleigh scattering and the linear Raman effect is governed by the polarizability tensor apa of a molecule and its derivatives with respect to the normal coordinates. When the electric field of the exciting radiation is very high, further terms in the expression for the induced dipole moment 104)... 

The quantum yield of the classical (or so-called linear) Raman effect is rather poor. Only a fraction of to 10 of the exciting photons are converted into Raman photons. This excludes the detection of low concentration analytes. Moreover, due to the quantum yield of fluorescence, even traces of fluorescent impurities may mask the Raman signal by their fluorescence. Therefore, there has been much scientific effort towards the development of Raman based methods which allow one to overcome this problem. Methods to overcome these problems are Resonance Raman Scattering and Surface Enhanced Raman Scattering. 

The selection rales for SERS are essentially the same as those for the linear Raman effect However, because the local electrical field at the surface is highest in the direction normal to the surface, only vibrations perpendicular to the surface are stron y enhanced. In order to optimise the surface enhancement effect, the laser frequency has to match the frequency of a plasma resonance. A large variety of SERS substrates are reported in the literature. The most common substrates are electrodes, colloids, metal films and silver island metal films. 

Since the coefficients (dp/dq)o are very small, one needs large incident intensities to observe hyper-Raman scattering. Similar to second-harmonic generation (Vol. 1, Sect. 5.8), hyper-Rayleigh scattering is forbidden for molecules with a center of inversion. The hyper-Raman effect obeys selection rules that differ from those of the linear Raman effect. It is therefore very attractive to molecular spectroscopists since molecular vibrations can be observed in the hyper-Raman spectrum that are forbidden for infrared as well as for linear Raman transitions. For example, spherical molecules such as CH4 have no pure rotational Raman spectrum but a hyper-Raman spectrum, which was found by Maker [357]. A general theory for rotational and rotational-vibrational hyper-Raman scattering has been worked out by Altmann and Strey [358]. 

B) THE MICROSCOPIC HYPERPOLARIZABILITY IN TERMS OF THE LINEAR POLARIZABILITY THE KRAMERS-HEISENBERG EQUATION AND PLACZEK LINEAR POLARIZABILITY THEORY OF THE RAMAN EFFECT... 

Na and K azides were detd in solns of varying concns by Petrikalns Ogrins (Ref 12).They also detd the density and refractive index for crystn Na and K azides. The ionic conductance of solid Li azide, as detd by Jacobs Tomkins (Ref 18), obeyed the general equation log k = log A - (E/2.303RT) where k is the specific conductivity in ohm-1 cm"1 A is a constant and E is activation energy in kcal/ mol. For Li azide log A 0.840, E is 19.1 and T, the temp range 300 370°K. The Raman Effect of crystn Li azide was detd by Kahovec Kohlrausch (Ref 14/, the observed frequency, 1368.7 cm-1, corresponded to the oscillation in a linear triatomic molecule. 

Sr(N3)j is not discussed by Sax (Ref 24) but its effects should be considered similar to those of the alkali and alkaline earth azides Sr azide was first prepd in 1898 by Dennis Benedict (Ref 1) and in the same year by Curtius Rissom (Ref 2) by the action of HNj on the oxide, hydroxide or carbonate of Sr. Its prepn has also been described by Mellor (Ref 7), Gmelin (Ref 9), Audrieth (Ref 10) and others (Refs 11, 15, 18, 19 25). The cryst structure of Sr(N3)2 was investigated to a limited extent by A.C.Gill (cited in Ref 1) and in detail by Llewellyn Whitmore (Ref 15) who established its orthorhmb nature as ionic, with a linear sym azide ion, N N 1.12A, and Sr to N distance of 2.63 to 27lX. Kahovec Kohlrausch (Ref 16) detd, from the Raman Effect, both on cryst powd and in soln, frequencies which corresponded to sym. oscillation in a linear triatomic molecule. 

Non-linear optical effect An effect brought about by electromagnetic radiation the magnitude of which is not proportional to the irradiance. Non-hnear optical effects of importance to photochemists are harmonic frequency generation, lasers, Raman shifting, upconversion, and others. 

If coherent radiation with a very high intensity is applied continuously or as pulse, non-linear effects can be observed which produce coherent Raman radiation. This is due to the quadratic and cubic terms of Eq. 2.4-14, which describe the dipole moment of a molecule induced by an electric field. Non-linear Raman spectroscopy and its application are described in separate chapters (Secs. 3.6 and 6.1), since this technique is quite different from that of the classical Raman effect and it differs considerably in its scope. 

The importance of the hyper Raman effect as a spectroscopic tool results from its symmetry selection rules. These are determined by products of three dipole moment matrix elements relating the four levels indicated in Fig. 3.6-1. It turns out that all infrared active modes of the scattering system are also hyper-Raman active. In addition, the hyper Raman effect allows the observation of silent modes, which are accessible neither by infrared nor by linear Raman spectroscopy. Hyper Raman spectra have been observed for the gaseous, liquid and solid state. A full description of theory and practice of hyper-Raman spectroscopy is given by Long (1977, 1982). 

Nonlinear vibrational spectroscopy provides accessibility to a range of vibrational information that is hardly obtainable from conventional linear spectroscopy. Recent progress in the pulsed laser technology has made the nonlinear Raman effect a widely applicable analytical method. In this chapter, two types of nonlinear Raman techniques, hyper-Raman scattering (HRS) spectroscopy and time-frequency two-dimensional broadband coherent anti-Stokes Raman scattering (2D-CARS) spectroscopy, are applied for characterizing carbon nanomaterials. The former is used as an alternative for IR spectroscopy. The latter is useful for studying dynamics of nanomaterials. 

Since the Raman effect involves two spin-one photons, the angular-momentum selection mle becomes A J = 0, 2. This gives rise to three distinct branches in the rotation-vibration spectra of diatomic and linear molecules the 0-branch (A / = —2), the Q-branch (A J = 0) and the S-branch (A J = - -2). All diatomic and linear molecules are Raman active. Raman spectroscopy can determine rotational and vibrational energy levels for homonuclear diatomic molecules, which have no infrared or microwave spectra. 

---