Rotational and Vibrational Spectroscopy pdf

Rotational and Vibrational Spectroscopy Lecture Date: January 30th, 2008 Vibrational and Rotational Spectroscopy  Core techniques: – Infrared (IR) spectroscopy – Raman spectroscopy – Microwave spectroscopy The Electromagnetic Spectrum  The basic!  Microwave  Infrared (IR) The History of Infrared and Raman Spectroscopy  Infrared (IR) Spectroscopy: – First real IR spectra measured by Abney and Festing in 1880’s – Technique made into a routine analytical method between 19031940 (especially by Coblentz at the US NBS) – IR spectroscopy through most of the 20th century is done with dispersive (grating) instruments, i.e monochromators – Fourier Transform (FT) IR instruments become common in the 1980’s, led to a great increase in sensitivity and resolution  Raman Spectroscopy: – In 1928, C V Raman discovers that small changes occur the frequency of a small portion of the light scattered by molecules The changes reflect the vibrational properties of the molecule – In the 1970’s, lasers made Raman much more practical NearIR lasers (1990’s) allowed for avoidance of fluorescence in many samples W Abney, E R Festing, Phil Trans Roy Soc London, 1882, 172, 887-918 Infrared Spectral Regions  IR regions are traditionally sub-divided as follows: Region Wavelength Wavenumber (), m (), cm -1 Frequency (), Hz Near 0.78 to 2.5 12800 to 4000 3.8 x 1014 to 1.2 x 1014 Mid 2.5 to 50 4000 to 200 1.2 x 1014 to 6.0 x 1012 Far 50 to 1000 200 to 10 6.0 x 1012 to 3.0 x 1011 After Table 16-1 of Skoog, et al (Chapter 16) What is a Wavenumber?  Wavenumbers (denoted cm-1) are a measure of frequency – For an easy way to remember, think “waves per centimeter”  Relationship of wavenumbers to the usual frequency and wavelength scales:  Converting wavelength () to wavenumbers:  cm 1  10000  Image from www.asu.edu Rotational and Vibrational Spectroscopy: Theory  Overview: – Separation of vibrational and rotational contributions to energy is commonplace and is acceptable – Separation of electronic and rovibrational interactions  Basic theoretical approaches: – Harmonic oscillator for vibration – Rigid rotor for rotation  Terminology: – Reduced mass (a.k.a effective mass):  m1m2 m1  m2 See E B Wilson, Jr., J C Decius, and P C Cross, “Molecular Vibrations”, Dover, 1955 Rotational Spectroscopy: Theory  Rotational energy levels can be described as follows:  ( J )  ( J  1) B  ( J  1)3 D For J = 0, 1, 2, 3… The rotational constant: B  h / 8 r02 c The centrifugal distortion coefficient: D  B /  c2 c  Where: c is the speed of light k is the Hooke’s law force constant r0 is the vibrationally-averaged bond length Example for HCl: B0 = 10.4398 cm-1 D0 = 0.0005319 cm-1 r0 = 1.2887 Å k 2c u  is the reduced mass h is Planck’s constant 0 = 2990.946 cm-1 (from IR) k = 5.12436 x 105 dyne/cm-1 R Woods and G Henderson, “FTIR Rotational Spectroscopy”, J Chem Educ., 64, 921-924 (1987) Vibrational Spectroscopy: Theory  Harmonic oscillator – based on the classical “spring” m  2 k u E  v  h m m is the natural frequency of the oscillator (a.k.a the fundamental vibrational wavenumber) k is the Hooke’s law force constant (now for the chemical bond) v is the vibrational quantum number h is Planck’s constant Note – all E are potential energies (V)!  Since v must be a whole number (see Ex 16-1, pg 386): E  h m  h 2 k  and   5.3 10 12 (wavenumbers) k   The potential energy function is: E HO (r )  k ( r  re ) 2 or E HO ( r )   (2c m ) (r  re ) 2 r is the distance (bond distance) re is the equilibrium distance Vibrational Spectroscopy: Theory  Potential energy of a harmonic oscillator: Figure from Skoog et al Anharmonic Corrections  Anharmonic motion: when the restoring force is not proportional to the displacement – More accurately given by the Morse potential function than by the harmonic oscillator equation – Primarily caused by Coulombic (electrostatic) repulsion as atoms approach EMorse (r )  hcDe (1  e  a ( r  re ) ) a De is the dissociation energy  (2c m ) 2hcDe  Effects: at higher quantum numbers, E gets smaller, and the ( = +/-1) selection rule can be broken – Double ( = +/-2), triple ( = +/-3), and higher order transitions can occur, leading to overtone bands at higher frequencies (NIR) Vibrational Coupling  Vibrations in a molecule may couple – changing each other’s frequency – In stretching vibrations, the strongest coupling occurs between vibrational groups sharing an atom – In bending vibrations, the strongest coupling occurs between groups sharing a common bond – Coupling between stretching and bending modes can occur when the stretching bond is part of the bending atom sequence – Interactions are strongest when the vibrations have similar frequencies (energies) – Strong coupling can only occur between vibrations with the same symmetry (i.e between two carbonyl vibrations) Vibrational Modes and IR Absorption  Number of modes: – Linear: 3n – modes – Non-linear: 3n – modes  Types of vibrations: – Stretching – Bending Symmetric No change in dipole IR-inactive Asymmetric Change in dipole IR-active  Examples: – CO2 has x – = normal modes Scissoring Change in dipole IR-active  IR-active modes require dipole changes during rotations and vibrations! Vibrational Modes: Examples  IR-activity requires dipole changes during vibrations!  For example, this Inactive Active Active Active is Problem 16-3 from Skoog: Inactive Active Inactive IR Spectra: Formaldehyde  Certain types of vibrations have distinct IR frequencies – hence the  chemical usefulness of the spectra The gas-phase IR spectrum of formaldehyde: (wavenumbers, cm-1)  Tables and simulation results can help assign the vibrations! Formaldehyde spectrum from: http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/InfraRed/infrared.htm#ir2 Results generated using B3LYP//6-31G(d) in Gaussian 03W Rayleigh and Raman Scattering  Only objects whose dimension is ~1-1.5  will scatter EM radiation  Rayleigh scattering: – occurs when incident EM radiation induces an oscillating dipole in a molecule, which is re-radiated at the same frequency  Raman scattering: – occurs when monochromatic light is scattered by a molecule, and the scattered light has been weakly modulated by the characteristic frequencies of the molecule  Raman spectroscopy measures the difference between the wavelengths of the incident radiation and the scattered radiation The Raman Effect  The incident radiation excites “virtual states” (distorted or polarized states) that persist for the short timescale of the scattering process  Polarization changes are necessary to form the virtual state and hence the Raman effect  This figure depicts “normal” (spontaneous) Raman effects Virtual state Virtual state hv1 hv1 hv1 – hv2 Anti-Stokes line hv1 – hv2 Stokes line Excited state (vibrational) Scattering timescale ~10-14 sec (fluorescence ~10-8 sec) Ground state (vibrational) H A Strobel and W R Heineman, Chemical Instrumentation: A Systematic Approach, 3rd Ed Wiley: 1989 More on Raman Processes  The Raman process: inelastic scattering of a photon when it is incident on the electrons in a molecule – When inelastically-scattered, the photon loses some of its energy to the molecule (Stokes process) It can then be experimentally detected as a lower-energy scattered photon – The photon can also gain energy from the molecule (anti-Stokes process)  Raman selection rules are based on the polarizability of the molecule  Polarizability: the “deformability” of a bond or a molecule in response to an applied electric field Closely related to the concept of “hardness” in acid/base chemistry P W Atkins and R S Friedman, Molecular Quantum Mechanics, 3rd Ed Oxford: 1997 More on Raman Processes  Consider the time variation of the dipole moment induced by incident radiation (an EM field):  (t )   (t ) (t ) Induced dipole moment EM field polarizability  If the incident radiation has frequency  and the polarizability of the molecule changes between min and max at a frequency int as a result of this rotation/vibration:  (t )     cos int t  cos t  = max - min mean polarizability  Expanding this product yields:  (t )   cos t   cos(  int )t  cos(  int )t  Anti-Stokes line Rayleigh line Stokes line P W Atkins and R S Friedman, Molecular Quantum Mechanics, 3rd Ed Oxford: 1997 The Raman Spectrum of CCl4 Rayleigh line (elastic scattering) 0 = 20492 cm -1  = 488.0 nm Stokes lines (inelastic scattering) Observed in “typical” Raman experiments Anti-Stokes lines (inelastic scattering) 459 314 218 -218 -314 -459 400 200 -200 -400 cm-1 Raman shift  = ( s - 0) Figure is redrawn from D P Strommen and K Nakamoto, Amer Lab., 1981, 43 (10), 72 10 Raman Spectrometers  The basic design dispersive Raman scattering system: Sample Wavelength Selector Detector (photoelectric transducer) (90° angle) Radiation source  Special considerations: – Sources: lasers are generally the only source strong enough to scatter lots of light and lead to detectable Raman scattering – Avoiding fluorescence: He-Cd (441.6 nm), Ar ion (488.0 nm, 514.5 nm), He-Ne (632.8), Diode (782 or 830), Nd/YAG (1064) Modern Raman Spectrometers  FT-Raman spectrometers – also make use of Michelson interferometers – Use IR (1 m) lasers, almost no problem with fluorescence for organic molecules – Have many of the same advantages of FT-IR over dispersive – But, there is much debate about the role of “shot noise” and whether signal averaging is really effective  CCD-Raman spectrometers – dispersive spectrometers that use a CCD detector (like the ICP-OES system described in the Optical Electronic lecture) – Raman is detected at optical frequencies! – Generally more sensitive, used for microscopy – Usually more susceptible to fluorescence, also more complex  Detectors - GaAs photomultiplier tubes, diode arrays, in addition to the above 17 More on Raman  Raman can be used to study aqueous-phase samples – IR is normally obscured by H2O modes, these happen to be less intense in Raman – However, the water can absorb the scattered Raman light and will damp the spectrum, and lower its sensitivity  Raman has several problems: – Susceptible to fluorescence, choice of laser important – When used to analyze samples at temperatures greater than 250C, suffers from black-body radiation interference (so does IR) – When applied to darkly-colored samples (e.g black), the Raman laser will heat the sample, can cause decomposition and/or more black-body radiation Applications of Raman Spectroscopy  Biochemistry:   water is not strongly detected in Raman experiments, so aqueous systems can be studied Sensitive to e.g protein conformation Inorganic chemistry: also often aqueous systems Raman also can study lower wavenumbers without interferences Other unique examples: – Resonance Raman spectroscopy: strong enhancement (102 – 106 times) of Raman lines by using an excitation frequency close to an electronic transition (Can detect umol or nmol of analytes) – Surface-enhanced Raman (SERS): an enhancement obtained for samples adsorbed on colloidal metal particles – Coherent anti-Stokes Raman (CARS): a non-linear technique using two lasers to observe third-order Raman scattering – used for studies of gaseous systems like flames since it avoids both fluorescence and luminescence issues 18 Applications of Raman Spectroscopy  Raman in catalysis research (see C&E News, Oct 13, 2006, pg 59): – Useful for the study of zeolite interiors – Fluorescence can be a problem, but one approach is to use UV light (257 nm) which avoids it just like switching to the IR (but at the risk of decomposition) – See work from the Stair group at Northwestern – For uses of SERS: Catal Commun 547 (2002)  Raman microscopy: offers sub-micrometer lateral resolution combined with depth-profiling (when combined with confocal microscopy) Comparison of IR and Raman Spectroscopy  Advantages of Raman over IR: – Avoids many interferences from solvents, cells and sample preparation methods – Better selectivity, peaks tend to be narrow – Depolarization studies possible, enhanced effects in some cases – Can detect IR-inactive vibrational modes  Advantages of IR over Raman: – Raman can suffer from laser-induced fluorescence and degradation – Raman lines are weaker, the Rayleigh line is also present – Raman instruments are generally more costly – Spectra are spread over many um in the IR but are compressed into several nm (20-50 nm) in the Raman  Final conclusion – they are complementary techniques! 19 Interpretation of IR and Raman Spectra  General Features: – Stretching frequencies are greater (higher wavenumbers) than corresponding bending frequencies  It is easier to bend a bond than to stretch it – Bonds to hydrogen have higher stretching frequencies than those to heavier atoms  Hydrogen is a much lighter element – Triple bonds have higher stretching frequencies than double bonds, which have higher frequencies than single bonds  Strong IR bands often correspond to weak Raman bands and vice-versa Interpretation of IR and Raman Spectra Characteristic Vibrational Frequencies for Common Functional Groups Frequency (cm-1) Functional Group 3200-3500 alcohols (O-H) Broad amine, amide (N-H) Variable alkynes (CC-H) Sharp 3000 Comments alkane (C-C-H) alkene (C=C-H) 2100-2300 alkyne (CC-H) 1690-1760 carbonyl (C=O) ketones, aldehydes, acids 1660 alkene (C=C) Conjugation lowers amide frequency nitrile (CN-H) imine (C=N) amide (C=O) 1500-1570 nitro (NO2) 1300-1370 1050-1300 alcohols, ethers, esters, acids (C-O) See also Table 17-2 of Skoog, et al More detailed lists are widely available See R M Silverstein and F X Webster, “Spectrometric Identification of Organic Compounds”, 6th Ed., Wiley, 1998 20 IR and Raman Spectra of an Organic Compound O OH The IR and Raman spectra of flufenamic acid (an analgesic/antiinflammatory drug): CF3 FT-IR Flufenamic acid Aldrich as recd 0.30 0.25 Abs 0.20 0.15 0.10 0.05 FT-Raman Flufenamic acid Aldrich as recd 60 50 Int 40 30 20 10 3500 3000 2500 2000 1500 1000 500 Raman shift (cm-1) IR and Raman Spectra of an Organic Compound O OH The IR and Raman spectra of flufenamic acid (an analgesic/antiinflammatory drug): CF3 FT-IR Flufenamic acid Aldrich as recd 0.30 0.25 Note – materials usually limit IR in this region Abs 0.20 0.15 0.10 0.05 FT-Raman Flufenamic acid Aldrich as recd 60 50 Int 40 30 20 10 1600 1400 1200 1000 800 600 400 200 Wavenumbers (cm-1) 21 IR and Raman Spectra of an Organic Compound The IR and Raman spectra of tranilast: Tranilast Form I FV101031-171A1 FTIR 0.6 0.5 Abs 0.4 0.3 0.2 0.1 Tranilast Form I FV101031-171A1 FT-Raman 500 O3 C4 O 400 C5 C3 C2 Int N1 C16 C11 C15 300 C18 C14 H3 C C10 C8 C9 C12 C13 C7 O 200 O O5 O2 C17 H3 C 100 3500 C6 C1 N H O OH O1 O4 3000 2500 2000 1500 1000 500 Wavenumbers (cm-1) IR Frequencies and Hydrogen Bonding Effects  IR frequencies are sensitive to hydrogen-bonding strength and geometry (plots of relationships between crystallographic distances and vibrational frequencies): G A Jeffrey, An Introduction to Hydrogen Bonding, Oxford, 1997 22 Applications of Far IR Spectroscopy  Far IR is used to study low frequency vibrations, like those between metals and ligands (for both inorganic and organometallic chemistry) – Example: Metal halides have stretching and bending vibrations in the 650-100 cm -1range – Organic solids show “lattice vibrations” in this region  Can be used to study crystal lattice energies and semiconductor properties  The Far IR region also overlaps rotational bands, but these are normally not detectable in condensed-phase work Terahertz Spectroscopy  A relatively new technique, addresses an unused portion of the EM spectrum (the “terahertz gap”): – 50 GHz (0.05 THz) to THz (1.2 cm-1 to 100 cm-1)  Made possible with recent innovations in instrument design, accesses a region of crystalline phonon bands P F Taday and D A Newnham, Spectroscopy Europe, , www.spectroscopyeurope.com G Winnewisser, Vibrational Spectroscopy (1995) 241-253 23 Applications of Near IR Spectroscopy  Near IR – heavily used in process chemistry  Amenable to quantitative analysis usually in conjunction with chemometrics (calibration requires many standards to be run)  While not a qualitative technique, it can serve as a fast and useful quantitative technique especially using diffuse reflectance  Accuracy and precision in the ~2% range  Examples: – On-line reaction monitoring (food, agriculture, pharmaceuticals) – Moisture and solvent measurement and monitoring  Water overtone observed at 1940 nm – Solid blending and solid-state issues Near IR Spectroscopy Figure from www.asdi.com For more information see: Ellis, J.W (1928) “Molecular Absorption Spectra of Liquids Below m”, Trans Faraday Soc 1928, 25, pp 888-898 Goddu, R.F and Delker, D.A (1960) “Spectra-structure correlations for the Near-Infrared region.” Anal Chem., vol 32 no 1, pp 140-141 Goddu, R.F (1960) “Near-Infrared Spectrophotometry,” Advan Anal Chem Instr Vol 1, pp 347-424 Kaye, W (1954) “Near-infrared Spectroscopy; I Spectral identification and analytical applications,” Spectrochimica Acta, vol 6, pp 257-287 Weyer, L and Lo, S.-C (2002) Spectra-Structure Correlations in the Near-infrared, In Handbook of Vibrational Spectroscopy, Vol 3, Wiley, U.K., pp 1817-1837 Workman, J (2000) Handbook of Organic Compounds: NIR, IR, Raman, and UV-Vis Spectra Featuring Polymers and Surfactants, Vol 1, Academic Press, pp 77-197 24 Near IR Spectrum of Acetone  NIR taken in transmission mode (via a reflective gold plate) on a Foss NIRsystems spectrometer  Useful for quick solvent identification Near IR Spectrum of Water (1st Derivative)  1st derivative (and 2nd derivative) allows for easier identification of bands 25 Photoacoustic Spectroscopy  First discovered in 1880 by A G Bell  The IR “version” of photoacoustic sampling is generally applied to two types of system (UV-Vis spectrometry can also be performed): IR Radiation Gas:  All gas (or all-liquid) systems: IR Radiation  The solid-gas system: IR-Transparent Gas Solid A G Bell, Am J Sci 20 (1880) 305 A G Bell, Philos Mag 11 (1881), 510 The Photoacoustic Effect for Solid-Gas Systems  The photoacoustic effect is produced when intensitymodulated light hits a solid surface (or a confined gas or liquid) Psurface  (1  R) P0  e Modulated IR Radiation  ( +  ) x R  surface reflectivity P0  incident IR beam power PA Cell Gas (Psurface)  - absorption coefficient  - thermal diffusion length Microphone P0 x Solid P(x) Thermal Wave (attenuates rapidly) IR is absorbed by a vibrational transition, followed by non-radiative relaxation J F McClelland Anal Chem 55(1), 89A-105A (1983) M W Urban J Coatings Technology 59, 29 (1987) 26 The Thermal Diffusion Length  The thermal diffusion length  is:   2a  The thermal diffusivity a is: k C k  thermal conductivity   density C  specific heat 0.15 cm/sec IR 1.2 cm/sec IR PVF2 PET a   - thermal diffusion length =/2 The variable , the modulation frequency of the IR radiation, is directly proportional to interferometer mirror velocity, and is defined as:   4  M   IR Frequency (wavenumbe rs)  M  Mirror vel ocity of Michelson interferom eter (cm/sec) Urban, M W J Coatings Technology 1987, 59, 29 Quintanilla, L., Rodriguez-Cabello, J C., Jawhari, T and Pastor, J M Polymer 1993, 34, 3787 The Thermal Diffusion Length   The mirror velocity is therefore inversely related to the thermal diffusion length, and therefore can be used to control the maximum sampling depth Typical thermal diffusion lengths for the carbonyl band (~1750 cm-1) of poly(ethylene terephthalate): Mirror Speed (cm/sec) 0.15 0.30 0.60 0.90 1.20 Thermal Diffusion Length (microns) 8.9 6.3 4.5 3.6 3.1 The thermal diffusivity was taken to be 1.3 * 10-3 cm2/sec, and the absorption coefficient of the carbonyl band was assumed to be 2000 cm-1 Urban, M W and Koenig, J L Appl Spec 1986, 40, 994 Quintanilla, L., Rodriguez-Cabello, J C., Jawhari, T and Pastor, J M Polymer 1993, 34, 3787 27 A Typical Photoacoustic FTIR Spectrum A PA-FTIR Spectrum of a silicone sealant: IR Modulation frequency is high IR Modulation frequency is low  The spectrum shows peaks where the IR radiation is being absorbed due to vibrational energy level transitions  Differences between a PA-FTIR spectrum and a regular IR spectrum: – IR modulation frequency effects (weak CH3 and CH2 bands) – Saturation of strong bands in the spectrum Paroli, R M., Delgado, A H., and Cole, K C Canadian J Appl Spectr 1994, 39, Photoacoustic Saturation  Strong bands in PA-FTIR spectra often A Saturated Band show saturation  Saturation occurs when the vibrational transition is being pumped to its excited state faster than it can release energy  A high absorption coefficient coincides with faster saturation Rosencwaig, A Photoacoustics and Photoacoustic Spectroscopy Wiley: New York, 1980 Paroli, R M., Delgado, A H., and Cole, K C Canadian J Appl Spectr 1994, 39, 28 Depth-Profiling Studies with PA-FTIR   Thermal diffusion length allows for IR depth profiling with PA-FTIR Example: a layer of poly(vinylidine fluoride (PVF2) on poly(ethylene terephthalate) (PET) 0.15 cm/sec IR 1.2 cm/sec IR PVF2 PET PVF2 top layer is micrometers thick  - thermal diffusion length =/2 The carbonyl band, due to the PET, is marked with a red dot () Data acquired with a Digilab FTS-20E with a home-built PA cell Urban, M W and Koenig, J L Appl Spec 1986, 40, 994 Crocombe, R A and Compton, S V Bio-Rad FTS/IR Application Note 82 Bio-Rad Digilab Division, Cambridge, MA, 1991 Applications of FT Microwave Spectroscopy  Under development for: real-time, sensitive monitoring of gases evolved in process chemistry, plant and vehicle emissions, etc… – Current techniques have limits (GC, IR, MS, IMS) – Normally use pulsed-nozzle sources and high-precision FabryPerot interferometers (PNFTMW) Compound Detection Limit (nanomol/mol) Acrolein 0.5 Carbonyl sulfide Sulfur dioxide Propionaldehyde 100 Methyl-t-butyl ether 65 Vinyl chloride 0.45 Ethyl chloride Vinyl bromide Toluene 130 Vinyl cyanide 0.28 Acetaldehyde Diagram from http://physics.nist.gov/Divisions/Div844/facilities/ftmw/ftmw.html For more information, see E Arunan, S Dev And P K Mandal, Applied Spectroscopy Reviews, 39, 131-181 (2004) 29 Hybrid/Hyphenated Techniques: Interfaces  Interfaces between vibrational spectrometers and other analytical instruments  GC-FTIR: gaseous column effluent passed through light pipes  Similar Technique: TGA-IR, for identification of evolved gases from thermal decomposition Figure from Skoog et al Homework Problems Chapter 16: 16-7 Chapter 18: 18-2 30 Further Reading L J Bellamy, Advances in Infrared Group Frequencies, Methuen and Co., 1968 R M Silverstein and F X Webster, Spectrometric Identification of Organic Compounds, 6th Ed., Wiley, 1998 P W Atkins and R S Friedman, Molecular Quantum Mechanics, 3rd Ed., Oxford, 1997 31 ... crystalline phonon bands P F Taday and D A Newnham, Spectroscopy Europe, , www.spectroscopyeurope.com G Winnewisser, Vibrational Spectroscopy (1995) 241-253 23 Applications of Near IR Spectroscopy ... frequency and wavelength scales:  Converting wavelength () to wavenumbers:  cm 1  10000  Image from www.asu.edu Rotational and Vibrational Spectroscopy: Theory  Overview: – Separation of vibrational. .. Near-infrared, In Handbook of Vibrational Spectroscopy, Vol 3, Wiley, U.K., pp 1817-1837 Workman, J (2000) Handbook of Organic Compounds: NIR, IR, Raman, and UV-Vis Spectra Featuring Polymers and Surfactants,