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Xi. Raman Spectroscopy Raman spectroscopy XI XI RAMAN SPECTROSCOPY References DC Harris o ch MD Bertolucci Symmetry and Sp ectroscopy Oxford University Press J M Hollas Mo dern Sp ectroscopy Wiley Chichester Handb o ok of vibrational sp ectroscopy J M Chalmers P R Griths Eds Wiley G Herzb erg Infrared and Raman Sp ectra Van Nostrand K P Hub er o ch G Herzb erg Constants of Diatomic Molecules Van Nostrand PW Atkins Molecular Quantum Mechanics Oxford University Press LA Wo o dward Intro duction to the Theory of Molecular Vibrations and Vibrational Sp ectroscopy Clarendon Press EB Wilson JC Decius o ch PC Cross Molecular Vibrations McGrawHill En ny upplaga Dover S Califano Vibrational States Wiley EFH Brittain WO George o ch CHJ Wells Academic Press MD Harmony Intro duction to Molecular Energies and Sp ectra Holt Winston CRC Handb o ok of Sp ectroscopy T Hase Sp ektrometriset taulukot Otakustantamo CRC Press B Schrader Ramaninfrared atlas of organic comp ounds VCH Weinheim D A Long The Raman eect A unied treatment of the theory of Raman scattering by molecules Wiley Chichester XI Molecular spectroscopy XI The Raman phenomenon The Raman sp ectroscopy measures the vibrational motions of a molecule like the infra red sp ectroscopy The physical metho d of observing the vibrations is however dierent from the infrared sp ectroscopy In Raman sp ectroscopy one measures the light scat tering while the infrared sp ectroscopy is based on absorption of photons A summary of the scattering theory is given in App endix I Scattering is also discussed in advanced textb o oks in quantum mechanics The Raman phenomenon was detected in by the Indian physicist Sir Chandrasekhara Venkata Raman and Kariamanikkam Srinivasa Krishnan Indep endently of this work the phenomenon was also rep orted by Grigory Landsb erg and Leonid Mandelstam However the phenomenen was predicted theoretically even earlier by using the classical mo del After the end of s the metho d was forgotten for several decades b ecause the signal is very weak Raman sp ectro copy exp erienced a renaissance in the s when the lasers were invented and started to b e used as light sources in sp ectroscopy The basics of the Raman scattering can b e explained using classical physics but a more comprehensiv theory requires quantum mechanical treatise Both the classical and quan tum mechanical formulations are schetched b elow Classical description of the Raman phenomenon Consider a molecule for the sake simplicity one without a p ermanent dip ole moment The eect of a p ermanent dip ole moment can b e easily incorp orated An oscillating electric eld F F cos t XI induces a dip ole moment F cos t XI The quantity is the p olarizability of the molecule The p olarizability is not a constant but varies with every vibrational motion of the molecule Let the fundamental vibration C V Raman and K S Krishnan Nature A new typ e of secondary radiation C V Raman and K S Krishnan Indian Journal of Physics A new class of sp ectra due to secondary radiation I C V Raman was made a knight in and received the Nob el pro ce for his invention in G Landsb erg and L Mandelstam Naturwiss A Smekal Naturwiss Raman spectroscopy XI frequences of the molecule b e k M Then k M X cos t XI k k k k A phase factor has b een included in the formula The induced dip ole moment is k M X p F cos t F cos t cos k k k k F cos t XI M X F cos t cos t k k k k k k The classical theory of electromagnetism states that an oscillating dip ole emits radiation of the intensity jpj XI I c A simple insertion gives the result 4 0 I F cos t Rayleigh 3 c 0 P M F f cos t anti Stokes 3 k k k k k c XI 0 cos t g Stokes k k k An oscillating dip ole moment emits therefore with the frequency of the incident eld Ray leigh scattering in phase with the incident eld In addition the molecule radiates with two frequencies that are mo dulated by the frequency of the excited normal vibration and phase shifted Raman scattering The Raman scattered light has a lower frequency than the incident light Stokesraman scattering or a higher frequency antiStokes Raman scattering One of the failures of the classical picture is that the ratio of the Stokes and antiStokes intensities should theoretically b e I Stokes k XI I anti Stokes k which is not the case exp erimentally XI Molecular spectroscopy The quantum mechanical description of the Raman eect The relevant quantum mechanical system is the molecule plus the eld Usually the time dep endent Schrdinger equation of the system is solved by using p erturbation theory basically in the same way the Einstein transition rate is calculated but in this case to second order The intensities are then according to App endix I e nm j njm jm j XI I k i i c with the matrix elements of the induced dip ole moment X X nj jr r j F jm i i j njm jm f i h r m r j XI nj F jr r j jm i i j g nr The momentaneous dip ole moment is determined also here by the p olarizability The i meaning of this expression is illustrated in Fig XI In addition to the free molecules eigenstates somewhat p erturb ed the system also has an innite numb er of virtual states r Very schematically one can say that the molecule is excited to a virtual state where a photon has transferred from the electric eld to the molecule dressed molecule and then go es back to one of the initial states In the gure it is also shown that the energy of the incident photon must not b e equal to any of the electronic excitation energies of the molecule b ecause the photon is absorb ed in that vase The upp ermost whole line in the gure indicates an electronically excited state hν hν hν hν hν hν 0 0 0 UVvis absorption ν k ν ν ν ν ν ν ν ν h = h 0 h = h 0 - h k h = h 0 + h k Rayleigh scattering Stokes scattering Anti-Stokes scattering Fig XI Schematic representation of the Raman eect Raman spectroscopy XI In the quantum mechanical mo del the intensity dep ends on the o ccupation of the initial state This is determined by the Boltzmann distribution Thus the intensity ratio is I Stokes k hc k T k e XI I anti Stokes k This ratio dep ends on the temp erature T Therefore one can determine the temp erature of the sample by measuring the intensities of b oth the Stokes line and the corresp onding antiStokes line The temp erature is given by the formula k XI T I antiStokes 0 k lnf g lnf g I Stokes 0 k An example of the Raman sp ectrum is shown in Fig XI 22479 22624 22720 Raman intensity -> 23156 22148 22176 23252 23397 22938 23700 23728 -800 -400 0 400 800 Raman frequency (cm-1) 218 218 314 314 459 459 762 762 790 790 Fig XI An example of a Raman sp ectrum Carb on tetrachloride Intensity of the scattered light The most common pro cess in light scattering is that the photon do es not interact at all with the sample but simply passes through it Only one photon of or is scatteted XI Molecular spectroscopy An overwhelming ma jority of the scattered photons show Rayleigh scattering where the frequency of the scatteted light is the same as that of the incident light Only one of a thousand or ten thousand scattered photons will have a mo dulated frequency ie will b e Raman scattered Therefore the intensity of the Rayleigh signal is a thousandth of the intensity of the incident light and intensity of the Raman signal is a millionth of the intensity of the incident light In the ab ove gure the Rayleigh band is shown in the middle Its frequency is used as the origin of the Raman sp ectrum The p ositions of the Raman bands are Their k displacements from give the frequencies of the normal vibrations The Rayleigh band is very intense as compared to the Raman bands on b oth sides of it The StokesRaman bands on the lowenergy side are stronger than the antiStokesRaman bands on the highenergy side of the central Rayleigh band but their distances from the central band are the same as those of the StokesRaman bands In practical measurements one wishes to remove the strong rayleigh band in order to b e able to observe the Raman signals Therefore only the StokesRaman part of the sp ectrum is usually shown The infrared and Raman sp ectra of carb on tetrachloride are shown in Fig XI 2000 1500 1000 500 Fig XI Infrared and Raman sp ectra of carb on tetrachloride The intensity of the signal is determined by the scattering cross section by the frequency of the incident light and by the Boltzmann factor The scattering cross section dep ends on the molecular p olarizability tensor see App endix I From this follow the selection rules in the Raman sp ectroscopy The eect of the incident light is imp ortant b ecause the intensity dep ends on the fourth p ower of the frequency If the wavelength is Raman spectroscopy XI halved eg from to nm the intensity of the scattered light will increase by a factor XI Molecular spectroscopy XI The Raman sp ectrometer The light source The light source of a Raman sp ectrometer must give very intense radiation for the scattered light to b e strong enough to b e observed In addition the light should b e as mono chromatic as p ossible so that the Raman bands would b e as narrow as p ossible In the old instruments a mecury vap or lamp is commonly used It has several strong emission bands and nm If one do es not use a lter to select one of the bands all of them will generate a sp ectra that may partly overlap The emission bands
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