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Unformatted text preview: CHEM*3440 Chemical Instrumentation Topic 10 Infrared Spectroscopy Infrared is Rovibrational Spectroscopy Wavelengths between 0.8 μm to 1 mm. Associated with changes in nuclear motion (vibrations and rotations). In gas phase, rotational transitions are resolved; in liquid phase, they are broadened. Usually only focus on vibrational character. Energy is usually reported in wavenumbers (cm-1 ); also proportional to frequency. ! = 1 " ! = c ! Near IR 0.8 - 2.5 ! m 12800 - 4000 cm-1 Mid-IR 2.5 - 50 ! m 4000 - 200 cm-1 Far IR 50 - 1000 ! m 200 - 10 cm-1 most commonly studied region Types of Vibrations molecular dipole moment must change during a vibration to be IR active. this oscillating dipole interacts with the oscillating E-M Feld of the photon, leading to absorption. Stretching Vibrations Bending Vibrations Changes in bond length Changes in bond angle symmetric anti-symmetric wagging twisting scissoring rocking + + + – – Simple Harmonic Oscillator vibrations are successfully modeled as simple harmonic oscillator. based on Hooke ! s Law: restoring force is proportional to displacement ¡ = - k x Displacement from Equilibrium Potential Energy U ( x ) = 1 2 k x 2 SHO more realistic potential Sinusoidal Motion in SHO By comparing Newton ! s Second Law with Hooke ! s Law, we obtain a differential equation. F = ma = ! kx a = d 2 x d t 2 m d 2 x d t 2 = ! kx " d 2 x d t 2 = ! k m x A solution to this equation can be written as x ( t ) = A cos 2 ! t ( ) ! = k m = k μ ! is called the angular frequency. It is related to the frequency " by ! = 2 #" . The μ is reduced mass and is used when both ends of the bond can move (always). Quantum Vibrational Motion molecular motion is quantized which leads to vibrational quantum levels indexed by a quantum number “v”. E v = v + 1 2 ! " # $ h % = v + 1 2 ! " # $ h & h = h 2 ’ % = 2 ’ & & = 1 2 ’ k μ energy absorbed is energy difference between two levels. In the SHO, the spacing is same between ALL adjacent levels ! E v " v + 1 = h # = h $ = h 1 2 % k μ selection rules: " v = ±1 for electric dipole transitions (i.e. infared transitions) Anharmonic Oscillator real molecules, vibrations “close to being” harmonic. relaxes the selection rules (overtones and combination bands) distorts the intensities of the transitions changes spacings so that they are not all the same, but come closer together as you go up the vibrational ladder. bond can “break”; not so with SHO. Typical Spectra spectra are usually presented as %transmittance against wavenumber. Mid-IR is usual scan range. Widely used as an aid in organic molecule identiFcation. Sinusoidal Motion in SHO By comparing Newton ! s Second Law with Hooke ! s Law, we obtain a differential equation....
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This note was uploaded on 05/15/2010 for the course CHEM 3440 taught by Professor Danthomas during the Fall '06 term at University of Guelph.
- Fall '06