Introduction to Infrared Spectrometry Chap 16

Quantum Mechanical Treatment of Vibrations Required to include quantized nature of E From solving the wave equations of QM: Selection rule for vib. transitions

Quantum Mechanical Treatment of Vibrations Interatomic distance, r → hv res Plot of potential energy: where level spacings: All vib levels spaced equally for HO only

Anharmonic Oscillator (AHO) Problems with Harmonic Oscillator (HO) Model Real vib levels coalesce as v levels increase Real vib levels coalesce as v levels increase Does not allow for dissociation of bond Repulsion is steeper at small r Appears as if atoms can pass through each other during vibrational amplitude Solution:

Anharmonic Oscillator (AHO) Fig. 16-3

Anharmonic Oscillator (AHO) Three consequences: (1) Harmonic at low v levels (2) ΔE becomes smaller at high v levels (3) Selections rule fails: Δv = ±1 and ± 2... referred to as overtones

Vibrational Modes Approach: Each atom in a molecule can be located with three coordinates (degrees of freedom) A molecule with N atoms then has 3N DOF Translational motion defined by center-of- mass coordinates (COM)

Linear Molecules 3 DOF to define translation 2 DOF to define rotation 3N – 5 ≡ number of vibrational modes Nonlinear Molecules 3 DOF to define translation 3 DOF to define rotation 3N – 6 ≡ number of vibrational modes

Examples N2N2 CO 2 H2OH2O CH 3 -C(O)-CH 3

Vibrations of CO 2 No dipole changeDipole change } 667 cm cm cm -1 Fig Doubly degenerate

Vibrations of H 2 O 1595 cm cm cm -1

IR Sources and Transducers Sources (1200 – 2200 K)

Spectral emission from a Nernst glower at ~ 2200 K Fig 16-16

IR Sources and Transducers Sources (1200 – 2200 K)

Transducers IR beam W, ΔT at transducer mK-µK

IR Instrumentation Dispersive Grating IR Instruments: Fig 16-11

IR Instrumentation Dispersive Grating IR Instruments:   Similar to UV-Vis spectrophotometer   BUT sample after source and before monochromator in IR   Sample after monochromator in UV- Vis - less incident light   Grating blazes per mm   Single beam and double beam (DB in time and space)   DB eliminates atmospheric gas interference

Fig Single- and Double-Beam Spectra of the Atmosphere

Fourier Transform IR Instruments: FTIR has largely displaced dispersive IRs A multiplex instrument (e.g., diode array) Beam is split and pathlength is varied to produce interference patterns Signal converted from frequency domain to time domain Fourier transform then converts “clean” signal back to frequency domain

Fourier Transform Instruments (Section 7-I) have two advantages: (1) (1) Throughput (or Jaquinot) advantage Few optics, no slits, high intensity Usually, to improve resolution, decrease slit width but less light makes spectrum "noisier" i.e., signal-to-noise ratio (S/N) decreases (p ):

S/N improves with more scans (noise is random, signal is not!) Fig. 5-10

(2) Multiplex (or Fellget) advantage Simultaneously measure entire spectrum Components of Fourier Transform Instruments Based on Michelson Interferometer frequencytime Converts frequency signal to time signal

Fig (p 207) Frequency domain Time domain

Fig (p 207) Time Domain Signal of a Source Made Up of Many Wavelengths

Frequencies of IR photons ~ 100 THz No detector can respond on s time scale Need to modulate high freq signal → lower freq without loss of P(t) relationships Interferometer: Splits beam equally in power Recombines them such that variations in power can be measured as P(δ) δ ≡ retardation, difference in pathlengths of the two beams

Single Frequency Source Michelson Interferometer Fig (p 208)

Computer needed to turn complex interferogram into spectrum: Single Frequency: Fig (p 188)

Two Frequencies: Many Frequencies:

High S/N ratios - high throughput Rapid (<10 s) Reproducible High resolution (<0.1 cm -1 ) Inexpensive (relatively!) Advantages to FT Instruments