DOCSLIB.ORG

Vibrational Raman Spectroscopy. Selection Rules

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Vibrational Raman Spectroscopy. Selection Rules Subject Chemistry Paper No and Title 8/ Physical Spectroscopy Module No and Title 25/ Vibrational Raman spectroscopy. Selection rules. Mutual Exclusion Principle. Polarization of Raman lines. Module Tag CHE_P8_M25 CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE NO. : 25 (VIBRATIONAL RAMAN SPECTROSCOPY. SELECTION RULES. MUTUAL EXCLUSION PRINCIPLE. POLARIZATION OF RAMAN LINES.) TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction 3. Vibrational Raman Spectroscopy 4. Polarizability ellipsoids 5. Rule of Mutual Exclusion 6. Polarization of Raman Lines 7. Summary CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE NO. : 25 (VIBRATIONAL RAMAN SPECTROSCOPY. SELECTION RULES. MUTUAL EXCLUSION PRINCIPLE. POLARIZATION OF RAMAN LINES.) 1. Learning Outcomes After going through this module, you should be able to: (a) Understand the vibrational Raman spectra (b) Understand the variation of the polarizability ellipsoid of a molecule during a vibration of triatomic molecules. (c) Understand and apply the Rule of Mutual Exclusion. (d) Understand the polarization of Raman lines. 2. Introduction When a beam of monochromatic radiation passes through a liquid or gaseous substance, it might get scattered. Either the frequency of the radiation is unchanged (Rayleigh scattering) or the scattered radiation has lower frequency (Stokes lines) or higher frequency (anti-Stokes lines). Just as for rotational Raman spectroscopy, the important molecular property is the polarizability which must change during the vibration. The polarizability ellipsoid should either change in shape or size during a vibration for it to be Raman active. In this module, we study vibrational Raman spectroscopy. 3. Vibrational Raman Spectroscopy For every vibrational mode one writes: 2 G(u) = we (u +1/ 2) - we c e (u +1/ 2) (u = 0 ,1 , ...) (1) where ωe is the equilibrium vibrational frequency in reciprocal centimetre and c e is the anharmonicity constant. The selection rule is: CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE NO. : 25 (VIBRATIONAL RAMAN SPECTROSCOPY. SELECTION RULES. MUTUAL EXCLUSION PRINCIPLE. POLARIZATION OF RAMAN LINES.) Δυ = 0, ±1, ±2, … (2) which are the same as for Raman and IR spectroscopy. The probability of Δυ = ±2, ±3, … decreases rapidly and may be ignored. Application of the selection rules to equation (1) yields: u = 0 ® u = 1 ~ (3) n = we (1- 2c e ) We restrict ourselves to fundamental transitions only. We would expect Raman lines to appear at distances from the exciting line corresponding to each active fundamental vibration. Therefore, ~ ~ ~ n fundamental =n ex ±n (4) The vibrational Raman spectrum of a molecule will then show a series of reasonably intense lines. The minus represents the situation where the molecule has gained energy (Stokes lines), and the plus indicates when the molecule has lost energy (anti-Stokes lines). Stokes lines refer to the transition υ = 0 → 1 and anti-Stokes lines refer to the υ = 1 → 0 transition (Fig. 1). Since there are very few molecules initially in the excited state at room temperature, anti-Stokes lines are much weaker in intensity. CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE NO. : 25 (VIBRATIONAL RAMAN SPECTROSCOPY. SELECTION RULES. MUTUAL EXCLUSION PRINCIPLE. POLARIZATION OF RAMAN LINES.) Figure 1: Energy level diagram showing the states involved in Raman signal. The line thickness is roughly proportional to the signal strength from the different transitions. Source: http://en.wikipedia.org/wiki/Raman_ spectroscopy 4. Polarizability Ellipsoids In this section we try to show pictorially the polarizability ellipsoids as changed by various vibrational modes. Note that the ellipsoids shown here are only two-dimensional representations. Consider first the hydrogen molecule. Its polarizability ellipsoid is shown in Figure 2. CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE NO. : 25 (VIBRATIONAL RAMAN SPECTROSCOPY. SELECTION RULES. MUTUAL EXCLUSION PRINCIPLE. POLARIZATION OF RAMAN LINES.) Figure 2: Polarizability ellipsoid of the hydrogen molecule As the bond is stretched, the bond becomes more polarizable and the polarizability ellipsoid shrinks in size. Note that here there is a change in size of the polaizability ellipsoid. During compression, it expands in size, and we thus have a means of determining the strengths of bonds of homonuclear molecules. The rotational selection rules are the same as those for pure Raman rotations, i.e. ΔJ = 0, ±2, and we observe an OS pattern instead of the PR pattern observed in infrared spectroscopy. Polyatomic Molecules Polyatomic molecules have a larger number of vibrational degrees of freedom as compared to diatomic molecules. An N-atomic molecule has a total of 3N degrees of freedom corresponding to three coordinates required to describe the position of each atom. Three of these correspond to translation of the molecule as a whole. Linear molecules have two rotational degrees of freedom as well, leaving the remaining 3N - 5 degrees of freedom for vibration. Non-linear molecules have three rotational degrees of freedom and consequently there are 3N – 6 vibrational degrees of freedom. CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE NO. : 25 (VIBRATIONAL RAMAN SPECTROSCOPY. SELECTION RULES. MUTUAL EXCLUSION PRINCIPLE. POLARIZATION OF RAMAN LINES.) We first consider a linear triatomic molecule, carbon dioxide, which has four vibrational degrees of freedom. Two of these are degenerate bending modes. The symmetric stretch mode is similar to the stretching mode of a diatomic molecule, and the polarizability ellipsoid varies in size as the molecule vibrates, and this mode of vibration is consequently Raman active (Fig. 3). In fact, the rate of change of polarizability with the normal coordinate is very large and symmetric vibrations are very intense in Raman spectroscopy. Vibrational modes of carbon dioxide -Q Q = 0 +Q Symmetric stretching mode ν1 Bending mode ν2 CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE NO. : 25 (VIBRATIONAL RAMAN SPECTROSCOPY. SELECTION RULES. MUTUAL EXCLUSION PRINCIPLE. POLARIZATION OF RAMAN LINES.) Antisymmetric stretching mode ν3 Figure 3: Changes in the polarizability ellipsoid of the carbon dioxide molecule during its vibrations Consider next the bending mode. Only bending in plane is shown in Figure 3. The molecule changes its appearance from a linear molecule to a bent one during the course of the vibration. Obviously, there is a change in polarizability as the molecule vibrates. In the antisymmetric stretch, too, the polarizability ellipsoid decreases in size during the vibration. However, both these modes are Raman inactive, as we can see from application of Group Theory. Both these vibrations have a symmetric polarizability change and are Raman inactive. We now consider the bent triatomic molecule. The variation of the polarizability ellipsoid (Fig. 4) clearly indicates that all modes are Raman active. Vibrational modes of water -Q Q = 0 +Q Symmetric stretching mode ν1 CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE NO. : 25 (VIBRATIONAL RAMAN SPECTROSCOPY. SELECTION RULES. MUTUAL EXCLUSION PRINCIPLE. POLARIZATION OF RAMAN LINES.) Bending mode ν2 Antisymmetric stretching mode ν3 CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE NO. : 25 (VIBRATIONAL RAMAN SPECTROSCOPY. SELECTION RULES. MUTUAL EXCLUSION PRINCIPLE. POLARIZATION OF RAMAN LINES.) Figure 4: Changes in the polarizability ellipsoid during the normal vibrations of the water molecule 5. Rule of Mutual Exclusion For carbon dioxide, the bending and antisymmetric modes are infrared active, while the symmetric stretch mode is Raman active. This behaviour is typical of all centrosymmetric molecules. Modes that are infrared active are Raman inactive and vice versa. This is the Rule of Mutual Exclusion, which states that no normal mode can be both infrared and Raman active in a molecule that possesses a centre of symmetry. In fact, even for molecules which do not possess a centre of symmetry, symmetric modes are weak in infrared and strong in Raman, whereas bending and asymmetric modes are weak in Raman. If there is no centre of symmetry, then some vibrations will be both Raman and IR active. Hence, if some vibrations are observed to give coincident Raman and IR absorptions, it is certain that the species has no centre of symmetry. Also, all symmetric modes of centrosymmetric molecules are strong in Raman, and this helps in identifying symmetric bands. The symmetric bands can also be identified by studying their polarization. 6. Polarization of Raman Lines We consider a beam of light incident in the x-direction. Assume that this is linearly polarized and all its electric vectors point in the y-direction. Let the direction of observation of the scattered radiation be z (see Fig. 5). CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE NO. : 25 (VIBRATIONAL RAMAN SPECTROSCOPY. SELECTION RULES. MUTUAL EXCLUSION PRINCIPLE. POLARIZATION OF RAMAN LINES.) Figure 5: Polarization of Raman lines Let us first consider a molecule, such as CH4, whose polarizability ellipsoid is isotropic, i.e. spherical in shape. The scattered radiation will then have the same polarization as the incident radiation, since the molecule’s polarizability has no preferred direction. What happens if the molecule’s polarizability ellipsoid is anisotropic? As an example, take CH3Cl. The molecule is more polarizable along the C-Cl bond direction and rotates the plane of polarization of the radiation along the C-Cl bond direction. However, in a sample of gaseous chloroform
Load more

Recommended publications
  • Surface-Enhanced Raman Scattering (SERS)
    Focal Point Review Applied Spectroscopy 2018, Vol. 72(7) 987–1000 ! The Author(s) 2018 Surface-Enhanced Raman Scattering Reprints and permissions: sagepub.co.uk/journalsPermissions.nav (SERS) in Microbiology: Illumination and DOI: 10.1177/0003702818764672 journals.sagepub.com/home/asp Enhancement of the Microbial World Malama Chisanga, Howbeer Muhamadali, David I. Ellis, and Royston Goodacre Abstract The microbial world forms a huge family of organisms that exhibit the greatest phylogenetic diversity on Earth and thus colonize virtually our entire planet. Due to this diversity and subsequent complex interactions, the vast majority of microorganisms are involved in innumerable natural bioprocesses and contribute an absolutely vital role toward the maintenance of life on Earth, whilst a small minority cause various infectious diseases. The ever-increasing demand for environmental monitoring, sustainable ecosystems, food security, and improved healthcare systems drives the continuous search for inexpensive but reproducible, automated and portable techniques for detection of microbial isolates and understanding their interactions for clinical, environmental, and industrial applications and benefits. Surface-enhanced Raman scattering (SERS) is attracting significant attention for the accurate identification, discrimination and characteriza- tion and functional assessment of microbial cells at the single cell level. In this review, we briefly discuss the technological advances in Raman and Fourier transform infrared (FT-IR) instrumentation and their application for the analysis of clinically and industrially relevant microorganisms, biofilms, and biological warfare agents. In addition, we summarize the current trends and future prospects of integrating Raman/SERS-isotopic labeling and cell sorting technologies in parallel, to link genotype-to-phenotype in order to define community function of unculturable microbial cells in mixed microbial communities which possess admirable traits such as detoxification of pollutants and recycling of essential metals.
    [Show full text]
  • Complementary Vibrational Spectroscopy
    Complementary Vibrational Spectroscopy Kazuki Hashimoto1,2, Venkata Ramaiah Badarla3, Akira Kawai1 and Takuro Ideguchi*3,4 1 Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan 2 Aeronautical Technology Directorate, Japan Aerospace Exploration Agency, Tokyo 181-0015, Japan 3 Institute for Photon Science and Technology, The University of Tokyo, Tokyo 113-0033, Japan 4 PRESTO, Japan Science and Technology Agency, Saitama 332-0012, Japan *[email protected] Vibrational spectroscopy, comprised of infrared absorption and Raman scattering spectroscopy, is widely used for label-free optical sensing and imaging in various scientific and industrial fields. The group theory states that the two molecular spectroscopy methods are sensitive to vibrations categorized in different point groups and provide complementary vibrational spectra. Therefore, complete vibrational information cannot be acquired by a single spectroscopic device, which has impeded the full potential of vibrational spectroscopy. Here, we demonstrate simultaneous infrared absorption and Raman scattering spectroscopy that allows us to measure the complete broadband vibrational spectra in the molecular fingerprint region with a single instrument based on an ultrashort pulsed laser. The system is based on dual-modal Fourier-transform spectroscopy enabled by efficient use of nonlinear optical effects. Our proof-of-concept experiment demonstrates rapid, broadband and high spectral resolution measurements of complementary spectra of organic liquids for
    [Show full text]
  • Infrared and Raman Spectroscopy UNIT II: Infrared and Raman Spectroscopy
    CORE COURSE-VIII (CC-VIII) PHYSICAL METHODS IN CHEMISTRY II UNIT II: Infrared and Raman Spectroscopy UNIT II: Infrared and Raman Spectroscopy Vibrations in simple molecules (H2O, CO2) and their symmetry notation for molecular vibrations – group vibrations and the limitations – combined uses of IR and Raman spectroscopy in the - – structural elucidation of simple molecules like N2O, ClF3, NO3 , ClO4 effect of coordination on ligand vibrations – uses of groups vibrations in the structural elucidation of metal complexes of urea, thiourea, cyanide, thiocyanate and dimethyl sulfoxide. Effect of isotopic substitution on the vibrational spectra of molecules – vibrational spectra of metal carbonyls with reference to the nature of bonding – geometry and number of C-O stretching vibrations (group theoretical treatment) – applications of Raman spectroscopy – resonance Raman spectroscopy. Vibrations in simple molecules (H2O, CO2) Molecular Vibrations There are two types of molecular vibrations, stretching and bending. A molecule consisting of n atoms has a total of 3n degrees of freedom, corresponding to the Cartesian coordinates of each atom in the molecule. In a nonlinear molecule, 3 of these degrees are rotational and 3 are translational and the remaining corresponds to fundamental vibrations; in a linear molecule, 2 degrees are rotational and 3 are translational. The net number of fundamental vibrations for nonlinear and linear molecules is therefore: Molecule degrees of freedom: (nonlinear 3n– 6) (linear 3n– 5) The fundamental vibrations for water, H2O, are given in Figure. Water, which is nonlinear, has three fundamental vibrations. Carbon dioxide, CO2, is linear and hence has four fundamental vibrations (Figure). The two scissoring or bending vibrations are equivalent and therefore, have the same frequency and are said to be degenerate, appearing in an IR spectrum at 666 cm–1.
    [Show full text]
  • Time Resolved Raman Spectroscopy for Depth Measurements Through
    VU Research Portal Time-Resolved Raman Spectroscopy for depth analysis in scattering samples Petterson, I.E.I. 2013 document version Publisher's PDF, also known as Version of record Link to publication in VU Research Portal citation for published version (APA) Petterson, I. E. I. (2013). Time-Resolved Raman Spectroscopy for depth analysis in scattering samples. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. E-mail address: [email protected] Download date: 30. Sep. 2021 Chapter 1. Introduction Concepts of Raman spectroscopy 11 1.1 Light scattering and the Raman effect Types of electromagnetic scattering When photons from a monochromatic light source such as a laser illuminate a material, the light can be transmitted, absorbed or scattered. In the case of scattering, the majority of this light is elastically scattered by the material with the same photon energy as the incident beam.
    [Show full text]
  • Basic Principles
    CHAPTER 2 Basic Principles 1. ELECTROMAGNETIC RADIATION All light (including infrared) is classified as electromagnetic radiation and consists of alter- nating electric and magnetic fields and is described classically by a continuous sinusoidal wave like motion of the electric and magnetic fields. Typically, for IR and Raman spectros- copy we will only consider the electric field and neglect the magnetic field component. Figure 2.1 depicts the electric field amplitude of light as a function of time. The important parameters are the wavelength (l, length of 1 wave), frequency (v, number cycles per unit time), and wavenumbers (n, number of waves per unit length) and are related to one another by the following expression: n 1 n ¼ ¼ ðc=nÞ l where c is the speed of light and n the refractive index of the medium it is passing through. In quantum theory, radiation is emitted from a source in discrete units called photons where the photon frequency, v, and photon energy, Ep, are related by Ep ¼ hn À where h is Planck’s constant (6.6256 Â 10 27 erg sec). Photons of specific energy may be absorbed (or emitted) by a molecule resulting in a transfer of energy. In absorption spectros- copy this will result in raising the energy of molecule from ground to a specific excited state E + + – – Time FIGURE 2.1 The amplitude of the electric vector of electromagnetic radiation as a function of time. The wavelength is the distance between two crests. 7 8 2. BASIC PRINCIPLES E 2 Molecular E energy p ( ) levels E E E p = 2 – 1 E 1 FIGURE 2.2 Absorption of electromagnetic radiation.
    [Show full text]
  • Complementary Vibrational Spectroscopy
    ARTICLE https://doi.org/10.1038/s41467-019-12442-9 OPEN Complementary vibrational spectroscopy Kazuki Hashimoto1,2, Venkata Ramaiah Badarla3, Akira Kawai1 & Takuro Ideguchi 3,4* Vibrational spectroscopy, comprised of infrared absorption and Raman scattering spectro- scopy, is widely used for label-free optical sensing and imaging in various scientific and industrial fields. The two molecular spectroscopy methods are sensitive to different types of vibrations and provide complementary vibrational spectra, but obtaining complete vibrational information with a single spectroscopic device is challenging due to the large wavelength 1234567890():,; discrepancy between the two methods. Here, we demonstrate simultaneous infrared absorption and Raman scattering spectroscopy that allows us to measure the complete broadband vibrational spectra in the molecular fingerprint region with a single instrument based on an ultrashort pulsed laser. The system is based on dual-modal Fourier-transform spectroscopy enabled by efficient use of nonlinear optical effects. Our proof-of-concept experiment demonstrates rapid, broadband and high spectral resolution measurements of complementary spectra of organic liquids for precise and accurate molecular analysis. 1 Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan. 2 Aeronautical Technology Directorate, Japan Aerospace Exploration Agency, Tokyo 181-0015, Japan. 3 Institute for Photon Science and Technology, The University of Tokyo, Tokyo 113-0033, Japan. 4 PRESTO, Japan Science and Technology Agency,
    [Show full text]
  • LASER-BASED MOLECULAR SPECTROSCOPY for CHEMICAL ANALYSIS-RAMAN SCATTERING PROCESSES (IUPAC Recommendations 1997)
    Pure & Appl. Chem., Vol. 69, No. 7, pp. 1451-1468, 1997. Printed in Great Britain. 0 1997 IUPAC INTERNATIONAL UNION OF PURE AND APPLIED CHEMISTRY ANALYTICAL CHEMISTRY DIVISION COMMISSION ON SPECTROCHEMICAL AND OTHER OPTICAL PROCEDURES FOR ANALYSIS* Nomenclature, Symbols, Units, and their Usage in Spectrochemical Analysis-XVIII LASER-BASED MOLECULAR SPECTROSCOPY FOR CHEMICAL ANALYSIS-RAMAN SCATTERING PROCESSES (IUPAC Recommendations 1997) Prepared for publication by B. SCHRADER' AND D. S. MOORE2 'Institut fur Physikalische und Theoretische Chemie, Universitat-GH-Essen,D-45 117 Essen, Germany 2Chemical Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87544, USA *Membership of the Commission during the period 1987-1995 in which the report was prepared was as follows: Chairman: 1987-1991 J.-M. M. Mermet (France); 1991-1995 T. Vo-Dinh (USA); Secretary: 1987-1989 L. R. P. Butler (South Africa); 1989-1993 A. M. Ure (UK); 1993-1995 D. S. Moore (USA); TituZar Members: G. Gauglitz (Germany, 1991-95); W. H. Melhuish (New Zealand, 1985-89); J. N. Miller (UK, 1991-95); D. S. Moore (USA, 1989-93); N. S. Nogar (USA, 1987-1991); N. Omenetto (Italy, 1989-91); B. Schrader (Germany, 1989-95); C. SCn6maud (France, 1987-89); N. H. Velthorst (Netherlands, 1993-95); T. Vo-Dinh (USA, 1989-91); M. Zander (Germany, 1987-89); Associate Members: F. Adams (Belgium, 199 1-95); A. M. Andreani (France, 1991-95); J. R. Bacon (UK, 1993-95); H. J. Coufal (USA, 1989-95); G. Gauglitz (Germany, 1989-91); G. M. Hieftje (USA, 1983-93); T. Imasaka (Japan, 1993-95); W. Lukosz (Switzerland, 1993-95); J.
    [Show full text]
  • 1 Raman Spectroscopy
    Light Scattering Chem 325 Raman Spectroscopy • Incident light beam interacting with a collection of molecules • Some elastic ‘collisions’ occur, light scattered • Energy of the scattered light is identical with the incident light • RAYLEIGH scattering • Very small amount undergoes inelastic scattering • There has been some energy transfer to or from the molecules! Light Scattering Raman Scattering • Incident light of frequency νννº • Elastically scattered light of frequency νννº Incident light has Incident light has LOST energy GAINED energy Vibrational Raman Energy Scattering 1 Raman Scattering Raman Scattering Rayleigh • Most of the light is transmitted, very little is scattered Stokes • >99% scattered light is Rayleigh • Very weak Stokes scattering • Very , very weak anti-Stokes scattering ν1 • ν 2 Stokes, anti-Stokes due to transfer of vibrational ν quantities of energy 3 ν 4 º A vibrational spectrum! ν Raman Scattering Raman Spectrometer • A vibrational spectrum generated by Raman scattering of light. • Scattering is more efficient if higher ννν light CW or FT is used for excitation. • Use visible light. • Need very high intensity: the Raman effect is weak! Need sensitive detector. • Historically: high-intensity Hg arc lamp • Now: lasers (visible, Near-IR) 2 Raman Spectroscopy • The Raman intensities may be quite O different than those of the IR spectrum IR C • Often the opposite to those of IR H3C CH3 • Some IR bands may be ‘missing’ from the Raman, and vice versa Raman Band Intensities Raman Activity Rule : • Polarizability For a vibrational mode to be IR active the vibrational – The ease with which the electron cloud of the motion must cause a change in the dipole moment of molecule can be distorted by an electric field.
    [Show full text]
  • Principles of Raman Spectroscopy
    Principles of Raman Spectroscopy Salvatore Amoruso Lectures for the course of Atomic and Molecular Physics and Laser Spectroscopy 1 Raman scattering Raman Spectroscopy is based on Raman scattering Raman effect was first observed in 1928 and was used to investigate the vibrational states of many molecules in the 1930s. Raman discovered that a very small fraction of the scattered light was present at wavelength different from the incident one (Raman shift), and got the Nobel prize in 1931. Raman Inelastic scattering Initially, spectroscopic methods based on the phenomenon were used in research on the structure of relatively simple molecules. However, the development of laser sources and new generations of monochromators and detectors has made possible the application of Raman spectroscopy to the solution of many problems of scientific and technological interest. Scattering We already studied the Rayleigh (elastic scattering) at the very beginning of the course. We discussed it as due to the re-emission of light from the molecular dipole induced by the incoming beam! Linear medium Pt 0 Et Molecule induced electronic dipole pt q r t E expik r t e e 0 0 pt E 0 exp it From the Lorentz model we got Rayleigh (elastic) scattering formula 1 I 4 s 4 Raman Scattering: classical description Consider now molecular vibrations at v pt qere t r0 cosvt v Vibrating molecular dipole v r rr0 To make the formula easier cos t cos t 0 r v v 0 v v pt Et cos tE cost 0 v v 0 E E E cost v 0 cos t v 0 cos t 0 0 2 v 2 v Raman Scattering: classical description 2 2 4 2 2 4 2 2 4 2 E E E I p 0 0 v 0 v v 0 v s 2 8 8 Rayleigh Raman Stokes Anti-Stokes Typically Raman scattering << Rayleigh scattering -5 -6 -2 -3 Is(10 -10 ) Iinc Is (10 -10 ) Iinc v r rr0 Raman scattering depends on induced changes of polarizability, i.e.
    [Show full text]
  • Practical Group Theory and Raman Spectroscopy, Part I: Normal Vibrational Modes
    ELECTRONICALLY REPRINTED FROM FEBRUARY 2014 ® Molecular Spectroscopy Workbench Practical Group Theory and Raman Spectroscopy, Part I: Normal Vibrational Modes Group theory is an important component for understanding the fundamentals of vibrational spectroscopy. The molecular or solid state symmetry of a material in conjunction with group theory form the basis of the selection rules for infrared absorption and Raman scattering. Here we investigate, in a two-part series, the application of group theory for practical use in laboratory vibrational spectroscopy. David Tuschel n part I of this two-part series we present salient polarization selection rules in both data acquisition and and beneficial aspects of group theory applied to interpretation of the spectra. Ivibrational spectroscopy in general and Raman spec- There are so many good instructional and reference troscopy in particular. We highlight those aspects of materials in books (1–11) and articles (12–15) on group molecular symmetry and group theory that will allow theory that there did not seem to be any good reason readers to beneficially apply group theory and polariza- to attempt to duplicate that work in this installment. tion selection rules in both data acquisition and inter- Rather, I would like to summarize and present the most pretation of Raman spectra. Small-molecule examples salient and beneficial aspects of group theory when it are presented that show the correlation between depic- is applied to vibrational spectroscopy in general and tions of normal vibrational modes and the mathemati- Raman spectroscopy in particular. cal descriptions of group theory. The character table is at the heart of group theory and contains a great deal of information to assist vibra- Why Would I Want to Use Group Theory? tional spectroscopists.
    [Show full text]
  • Vibrational Spectroscopic Characterization of Form II Poly(Vinylidene Fluoride)
    Indian Journal of Pure & Applied Physics Vol. 43, November 2005, pp. 821-827 Vibrational spectroscopic characterization of form II poly(vinylidene fluoride) P Nallasamy Department of Physics, Bharathidasan Govt. College for Women, Pondicherry 605 003 and S Mohan Raman School of Physics, Pondicherry University, Pondicherry 605 014 Received 28 December 2004; revised 20 June 2005; accepted 8 September 2005 The Fourier transform Raman (FT-Raman) and infrared absorption (FTIR) spectra of form II poly(vinylidene fluoride) have been recorded and analysed. A complete spectral analysis, assignments to observed bands, normal coordinate analysis and discussion of the spectra are presented. The computed spectrum is in excellent agreement with experiment. The poten- tial energy distribution (PED) is evaluated from respective potential constants to analyse the purity of the modes. Keywords: Infrared and Raman spectra; Normal coordinate analysis, Poly(vinylidene fluoride), Vibrational spectroscopy IPC Code: G01J3/00 1 Introduction carried out a vibrational analysis of two forms (α and Vibrational spectroscopy has significant contribu- β) of PVDF using Urey-Bradley type force field. tions towards the studies of structure and physico– Boerio and Koenig9 reported the Raman spectra of chemical properties of crystals and molecular sys- form II PVDF and observed some unique bands that tems1-3. Raman spectroscopy—among spectroscopic are not observed in the IR spectra. Cortili and Zerbi10 techniques that provided detailed information about discussed the chain conformation of PVDF by analys- molecular structure—is the most appropriate tool be- ing the infrared spectra of form I and form II. Infrared cause it is simple, quick and powerful to perform the and Raman spectra of form I PVDF have been studied vibrational assignment and to elucidate the structure extensively by Boerio and Koenig11, Cessac and 12 13 14 and conformation of the molecule.
    [Show full text]
  • Symmetry and Molecular Vibrations
    Spectroscopic Selection Rules E 0 v = 4 v = 3 v = 2 v = 1 v = 0 d • For a vibrational fundamental ( ∆v = ±1), the transition will have nonzero intensity in either the infrared or Raman spectrum if the appropriate transition moment is nonzero. • If the transition moment for infrared absorption or Raman scattering is nonzero for a particular normal mode, the mode is said to be allowed or active in the associated kind of spectrum (i.r. or Raman). • If the transition moment for infrared absorption or Raman scattering is zero for a particular normal mode, the mode is said to be forbidden or inactive in the associated kind of spectrum (i.r. or Raman). Spectroscopic Selection Rules Symmetry Analysis of Transition Moment Integrals • An integral of the product of two functions, IfAfBdτ, can be nonzero only if it is invariant under all operations of the molecule’s point group. • This can occur only if the direct product of f AfB is or contains the totally symmetric representation of the point group. • In terms of the symmetry of fA and fB, the direct product of f AfB is or contains the totally symmetric representation only if fA and fB belong to the same symmetry species. Only the direct product of a symmetry species with itself is or contains the totally symmetric representation. Spectroscopic Selection Rules Infrared Activity • For infrared absorption to occur, the normal mode must have an oscillating molecular dipole moment with the same frequency as the oscillating electric field of the radiation. • The transition moment for the fundamental of a normal mode ( v = 0 6 v = 1) can be written M(0,1 ) = Iψ0µψ 1dτ where ψ0 and ψ1 are wave functions for the ground and excited vibrational states, and µ is the oscillating electric dipole moment vector as a function of the normal coordinate , Q, for the normal mode.
    [Show full text]