Introduction to Infrared Spectrometry Chap 16

Infrared Spectral Regions Table 16-1 Most used – 15

Spectral data may be plotted with ordinate as: absorbance (A) percent transmittance (%T) abscissa as: wavenumber (cm -1 ) often called “frequency” wavelength (μm) ordinate abscissa

IR Spectrum of a thin polystyrene film IR Spectrum of a thin polystyrene film Fig. 16-1

Dipole Changes During Vibrations and Rotations Energy of IR photon insufficient to cause electronic excitation But can cause vibrational or rotational excitation To absorb an IR photon, molecule must undergo a net change in dipole moment (gross selection rule) Electric field of molecule (i.e., dipole moment) interacts with electric field of IR photon Both dynamic fields

Dipole Changes During Vibrations and Rotations Magnitude of dipole moment determined by: ( i ) charge (δ+ or δ-) ( ii ) separation of charge (r) Vibration or rotation causes varying separation: Absorption causes increase in vibrational amplitude or rotational frequency

Molecules with permanent dipole moments (µ) are IR active IR active IR inactive Also: all homonuclear diatomics, CH 4 SF 6 C 6 H 6 etc.

Types of Molecular Vibrations Stretching ⇒ change of bond length Fig 16-2 (a)

Bending ⇒ change of bond angle Fig 16-2 (b)

Classical Vibrational Motion Harmonic oscillator model Force required to displace mass, m: F = -ky where k ≡ force constant Potential energy dE = -F dy = ky dy Integrating: E = ½ ky 2

Vibrational Frequency Natural frequency of the classical oscillator: In terms of the reduced mass, μ, of two atoms: where

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:

Potential Energy Curve of Harmonic Oscillator Fig (b)

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