Lectures In Spectroscopy Raman Spectroscopy

Introduction Rotational Raman Vibrational Raman Raman spectrometer Lectures in Spectroscopy Raman Spectroscopy K. Sakkaravarthi Department of Physics National Institute of Technology Tiruchirappalli – 620 015 Tamil Nadu India sakkaravarthi@nitt.edu www.ksakkaravarthi.weebly.com K. Sakkaravarthi Lectures in Spectroscopy 1/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer My sincere acknowledgments to Fundamentals of Molecular Spectroscopy, 4th Ed., C.N. Banwell, McGraw-Hill, New York (2004). Molecular Structure and Spectroscopy, G. Aruldhas, Prentice Hall of India, New Delhi (2002). Introduction to Atomic Spectra, E. H. White, McGraw-Hill, New York (2005). Many other free & copyright internet resources. K. Sakkaravarthi Lectures in Spectroscopy 2/28

Introduction 1 2 3 4 Rotational Raman Vibrational Raman Raman spectrometer Introduction Raman Scattering Rotational Raman spectroscopy Linear Molecules Symmetric Top Molecules Vibrational Raman spectroscopy Vibrational Raman Vibrational Rotational Raman Mutual Exclusion Hyper-Raman scattering Raman spectrometer K. Sakkaravarthi Lectures in Spectroscopy 3/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Scattering in Molecules Interaction of photons (ν0 ) with molecules: (i) Elastic (Rayleigh) scattering: Most molecules. (ii) Inelastic (Raman) scattering: Very few molecules Frequency/Energy shift (1928: CV Raman & KS Krishnan) Raman Scattering Lower freq. (ν ν ν) Stoke’s lines. Higher freq. (ν ν ν) Anti-Stoke’s lines. Raman shift ν (around 10 4, 000 cm 1 ). Original freq. ν Rayleigh lines. K. Sakkaravarthi Lectures in Spectroscopy 4/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Classical Theory: Raman Scattering Molecule in electric field ’E’: Electric field of radiation distorts the electron distribution. Polarization of charged particles P αE, α: Polarizability of the molecule. For an incident radiation of freq. ν0 , change in electric field E E0 cos(2πν0 t). Vibrational motion of the molecule Q Q0 cos(2πνm t), for normal coordinate Q with vibrational freq. νm . Polarizability due to vibrations/rotations α α α0 Q Q · · · H.O. 0 Effective h Polarization: i α P α0 Q Q0 cos(2πνm t) E0 cos(2πν0 t. 0 K. Sakkaravarthi Lectures in Spectroscopy 5/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Classical Theory: Raman Scattering. P α 0 E0 cos(2πν0 t) 1 α 2 Q Q0 E0 [cos 2π(ν0 νm )t cos 2π(ν0 νm )t]. 0 First term: original freq. ν0 (Rayleigh line) Second term: higher freq. ν0 νm (Raman anti-Stokes line) Third term: lower freq. ν0 νm (Raman Stokes line) Change in polarizability for CO2 symmetric stretch bend asymmetric stretch. Symmetric vibrations: Raman active (but IR inactive) Asymmetric vibrations: very weak in Raman (negligibly small) K. Sakkaravarthi Lectures in Spectroscopy 6/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Quantum Theory: Raman Scattering Drawback in classical theory: Gave frequency shifts, but not able to find intensities. Duality: Radiation as particle/photon & wave. Molecules interact with photon/particle hν0 . Moves to virtual state by absorbing some energy. & Return to original state by emitting radiation. No. photon scattering Size of bonds. Mostly, frequency of emitted radiation is same to the frequency of incident radiation: Rayleigh/elastic scattering. Small fraction of radiation with high/low frequency than incident frequency (gains/looses energy): Raman scattering. If molecule gains energy, scattered photon freq. ν0 νm : Stokes lines If molecule looses energy, scattered photon freq. ν0 νm : anti-Stokes lines. K. Sakkaravarthi Lectures in Spectroscopy 7/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Quantum Theory: Raman Scattering. Intensity depends on initial population. Power Ps I0 σR (Incident Int. & Raman cross-section) Boltzmann distribution (or) Is Ias )4 (ν0 νm (ν0 νm )4 Is Ias m exp hν kT . m exp hν kT K. Sakkaravarthi Lectures in Spectroscopy 8/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Rotational Raman spectroscopy Linear Molecules Rotational energy changes due to Raman scattering! Rotational energy J BJ(J 1) cm 1 , J 0, 1, 2, . Selection rule J 0, 2 ! Jump in the level due to additional scattered energy. (Symmetry of the polarizability: end-over-end rotations) Rotational energy change ν̄ J J 2 J B(4J 6). When molecules gains energy or scattered photon looses energy Stokes lines with lower frequencies than ν̄0 . Freq. of Stokes spectral lines ν̄ ν̄0 B(4J 6). When molecules looses energy or scattered photon gains energy anti-Stokes lines with higher frequencies than ν̄0 . Freq. of anti-Stokes spectral lines ν̄ ν̄0 B(4J 6). Freq. of Raman spectra ν̄ ν̄0 B(4J 6), J 0, 1, 2, · · · K. Sakkaravarthi Lectures in Spectroscopy 9/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Rotational Raman spectra for Linear Molecules K. Sakkaravarthi Lectures in Spectroscopy 10/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Symmetric Top Molecules Rotational energy JK BJ(J 1) (A B)K 2 cm 1 , Here J 0, 1, 2, ., K 0, 1, 2, . Selection rule K 0 & J 0, 1, 2 !! Jump in the level due to additional scattered energy. (Rotation about molecular axis & its perpendicular axis) Rotational energy change ν̄ R J 1 J 2B(J 1) (for J 1: R branch) ν̄ S J 2 J B(4J 6) (for J 2: S branch) Two Frequency bands for Raman lines: ν̄R ν̄0 2B(J 1) cm 1 . ν̄S ν̄0 B(4J 6) cm 1 . Spectral lines spacing: 2B for R branch Raman lines. Spectral lines spacing: 4B for S branch Raman lines. K. Sakkaravarthi Lectures in Spectroscopy 11/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Rotational Raman spectra for Symmetric Top molecule K. Sakkaravarthi Lectures in Spectroscopy 12/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Vibrational Raman spectroscopy Vibrational Raman spectra Degrees of freedom (normal modes): Anharmonic vibrations. 2 Vibrational energy v v 12 ν̄e v 21 xe ν̄e cm 1 . Here v 0, 1, 2, . (ν̄e equilibrium oscillation freq.) Selection rule v 1, 2, 3, .!!! Jump in the level due to additional scattered energy. Raman spectra are very weak, so only v 1. (overtones, combination & hot bands are negligible) Vibrational energy change 1 0 ν̄e (1 2xe ) cm 1 . Freq. of Raman lines ν̄ ν̄0 ν̄e (1 2xe ) cm 1 . Population in v 1 is very less, so anti-Stokes lines are very weak than Stokes lines. K. Sakkaravarthi Lectures in Spectroscopy 13/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Vibrational Rotational Raman spectra Energy for Raman spectra 2with vibration rotation Jv v 12 ν̄e v 12 xe ν̄e BJ(J 1) cm 1 . Here v 0, 1, 2, . & J 0, 1, 2, . Selection rule v 1 & J 0, 2! For v 1 & J 0: Q branch Stokes lines ν̄e (1 2xe ) cm 1 ν̄Q ν̄0 ν̄e (1 2xe ) cm 1 . For v 1 & J 2: S branch Stokes lines Jv ν̄e (1 2xe ) B(4J 6) cm 1 ν̄S ν̄0 ν̄e (1 2xe ) B(4J 6) cm 1 . For v 1 & J 2: O branch Stokes lines Jv ν̄e (1 2xe ) B(4J 6) cm 1 ν̄S ν̄0 ν̄e (1 2xe ) B(4J 6) cm 1 . K. Sakkaravarthi Lectures in Spectroscopy 14/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Rotational Vibrational structure of Raman Stokes lines of diatomic molecule with vibrational frequency ν̄e (1 2xe ). K. Sakkaravarthi Lectures in Spectroscopy 15/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Mutual Exclusion: Raman spectra Raman scattering & IR: two different processes. Some molecular vibrations are active in both IR & Raman. Several vibrations can be active either in Raman or IR. Molecules with centre of symmetry: Raman active (polarizability), IR inactive (no change in dipole moment) Mutual exclusion Molecules without centre of symmetry shall be active in both IR & Raman. K. Sakkaravarthi Lectures in Spectroscopy 16/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Comparison: IR and Raman transitions! K. Sakkaravarthi Lectures in Spectroscopy 17/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer IR and Raman offers complementary techniques! K. Sakkaravarthi Lectures in Spectroscopy 18/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Hyper-Raman scattering (HRS) effect A modified version of Raman scattering! Inelastic second harmonic scattering of photons. Sum frequency generation: A coherent process involving two incident fields (with frequencies ν1 & ν2 and wave vectors k1 & k2 ) produce a single field with frequency ν1 ν2 and wave vector k1 k2 . Hyper-Rayleigh scat.: Elastic scat. for ν1 ν2 & k1 k2 . Hyper-Raman scattering: Inelastic form of Hyper-Rayleigh scattering!! K. Sakkaravarthi Lectures in Spectroscopy 19/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Hyper-Raman scattering (HRS) effect. Hyper-Raman scattering: Inelastic scattering of incident photons (with frequency ν1 ν2 ν) into photons of two different frequencies 2ν ν!! HRS Stokes lines: νS ν1 ν2 ν. HRS anti-Stokes lines: νAS ν1 ν2 ν. ν depends on the usual scattering of molecular vibrations. HRS effect is usually very weak, but has aspects which make it interesting for Raman spectroscopy. HRS can provide vibrational information on molecules where ordinary Raman Scattering is suppressed due to symmetry issues. K. Sakkaravarthi Lectures in Spectroscopy 20/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Basic Raman spectrometer K. Sakkaravarthi Lectures in Spectroscopy 21/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Schematic: Basic Raman spectrometer K. Sakkaravarthi Lectures in Spectroscopy 22/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Schematic: Basic Raman spectrometer K. Sakkaravarthi Lectures in Spectroscopy 23/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Basic Raman spectrometer K. Sakkaravarthi Lectures in Spectroscopy 24/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Raman spectrometer Several variants of Raman spectrometers. To enhance the sensitivity (ex. surface-enhanced Raman), improve the spatial resolution (Raman microscopy), very specific information (resonance Raman), etc. Spontaneous Raman spectroscopy Surface-enhanced Raman spectroscopy (SERS) Resonance Raman spectroscopy Surface-enhanced resonance Raman spectroscopy (SERRS) Angle-resolved Raman spectroscopy Transmission Raman spectroscopy Tip-enhanced Raman spectroscopy (TERS) Stand-off remote Raman Many hand-held Raman spectrometers! K. Sakkaravarthi Lectures in Spectroscopy 25/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Few Applications of Raman spectra K. Sakkaravarthi Lectures in Spectroscopy 26/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Summary From the present series of lectures, we have learned the principle, explicit description and detailed analyses of transitions in molecules due to Raman scattering by including the vibrational and rotational effects! K. Sakkaravarthi Lectures in Spectroscopy 27/28

Introduction Rotational Raman Vibrational Raman Raman spectrometer Thank You K. Sakkaravarthi Lectures in Spectroscopy 28/28

Introduction Rotational Raman Vibrational RamanRaman spectrometer Lectures in Spectroscopy Raman Spectroscopy K.Sakkaravarthi DepartmentofPhysics NationalInstituteofTechnology Tiruchirappalli-620015 TamilNadu India sakkaravarthi@nitt.edu www.ksakkaravarthi.weebly.com K. Sakkaravarthi Lectures in Spectroscopy 1/28