《仪器分析 Instrumental Analysis》课程教学资源（教材讲义）06 Infrared Spectrometry

Infrared Spectrometry (Chapter 16 17) 750-3000nm Region Energy Wavenumber Wavelength (kJ/mol) (cm-1) (um) Near IR 150-50 12,800-4000 0.78-2.5 Mid IR 50-2.5 4000-200 2.5-50 Far IR 2.5-0.1 200-10 50-1000 Energy of IR photon insufficient to cause electronic excitation but can cause vibrational or rotational excitation Molecule electric field(dipole moment)interacts with IR photon electric field (both dynamic) Magnitude of dipole moment determined by (i)charge (ii)separation of charge Vibration or rotation causes varying separation +尺 +)( CEM 333 page 6.1

Infrared Spectrometry (Chapter 16 & 17) ~750-3000 nm Region Energy (kJ/mol) Wavenumber (cm-1) Wavelength (µm) Near IR 150-50 12,800-4000 0.78-2.5 Mid IR 50-2.5 4000-200 2.5-50 Far IR 2.5-0.1 200-10 50-1000 Energy of IR photon insufficient to cause electronic excitation but can cause vibrational or rotational excitation Molecule electric field (dipole moment) interacts with IR photon electric field (both dynamic) Magnitude of dipole moment determined by (i) charge (ii) separation of charge Vibration or rotation causes varying separation + - + - + - CEM 333 page 6.1

Molecule must have change in dipole moment due to vibration or rotation to absorb iR radiation Absorption causes increase in vibration amplitude/rotation frequency Molecules with permanent dipole moments (u)are IR active 0-0 十 No dipole moment HCI.H2O.NO Atoms,O2,H2,Cl2 IR active IR inactive u measured in debye (D) 1D=3.33x10-30Cm 10 D equivalent to +1 and-1 charge separated 1A CEM 333 page 6.2

Molecule must have change in dipole moment due to vibration or rotation to absorb IR radiation Absorption causes increase in vibration amplitude/rotation frequency Molecules with permanent dipole moments (µ) are IR active H - Cl d+ d￾O - O No dipole moment HCl, H2O, NO Atoms, O2, H2, Cl2 IR active IR inactive µ measured in debye (D) 1 D = 3.33x10-30 C·m 10 D equivalent to +1 and -1 charge separated 1 Å CEM 333 page 6.2

Types of Molecular Vibrations: Stretch Bend change in bond length change in bond angle symmetric scissoring asymmetric wagging rocking twisting/torsion CEM 333 page 6.3

Types of Molecular Vibrations: Stretch Bend change in bond length change in bond angle symmetric scissoring asymmetric wagging rocking twisting/torsion + + - - + ns nas r s w t CEM 333 page 6.3

Only some modes may be IR active: Example CO2 O=C=O linear ○O0 26+ No net dipole moment change 2δ+ Net dipole moment change 28 Net dipole moment change Vs not IR active Vas,bend IR active CEM 333 page 6.4

Only some modes may be IR active: Example CO2 O=C=O linear 2d + d d - - No net dipole moment change 2d + d d - - Net dipole moment change 2d + d d - - Net dipole moment change ns not IR active nas, bend IR active CEM 333 page 6.4

Classical vibrational motion: -V Mass Displacement y m Force required to displace m is F=-k.y Hooke's Law spring constant (N/m) CEM 333 page 6.5

Classical vibrational motion: Mass m -y +y Displacement y Force required to displace m is F = -k× y Hooke's Law spring constant (N/m) CEM 333 page 6.5

Energy is force x distance dE=-Fdy dE=kydy Total Energy ∫dE=k∫ydy 0 0 1. B=2为2 Parabolic E vs.displacement curve of harmonic oscillator 0 Displacement y- (Fig16-3) CEM 333 page 6.6

Energy is force ´ distance dE = -Fdy dE = kydy Total Energy dE 0 E ò = k ydy o y ò E = 1 2 ky2 Parabolic E vs. displacement curve of harmonic oscillator (Fig 16-3) CEM 333 page 6.6

Classical vibrational frequency: 1k Vclassical= 2元Vm v independent of energy Two masses? 4= mm2 Velassical reduced mass 2πVu m1+m2 What about quantum mechanics? (1) E=v+2)2元Vu Vibrational quantum number(0,1,2.) EhVdrscl Ground vibrational state (v=0) 3 E1hVclassical First excited state(v=1) △E=hVclassical Calculated AE often agrees quite well with experiment Vealeulated (C=O)=1600 cm-1 Vexperiment(C=O)=1600-1800 cm-1 See example 16-1 (2)△V=±1 Vibrational Selection Rule Since levels equally spaced-should see one absorption frequency CEM 333 page 6.7

Classical vibrational frequency: nclassical = 1 2p k m n independent of energy Two masses? nclassical = 1 2p k m m = m1 ×m2 m1 + m2 reduced mass What about quantum mechanics? (1) E = n + 1 2 æ è ö ø h 2p k m = n + 1 2 æ è ö ø h ×nclassical Vibrational quantum number (0, 1, 2. ) E0 = 1 2 hnclassical Ground vibrational state (n = 0) E1 = 3 2 hnclassical First excited state (n = 1) DE = hnclassical Calculated DE often agrees quite well with experiment ncalculated (C=O) = 1600 cm-1 nexperiment (C=O) = 1600-1800 cm-1 See example 16-1 (2) Dn = ±1 Vibrational Selection Rule Since levels equally spaced - should see one absorption frequency CEM 333 page 6.7

Anharmonic oscillator: Must modify harmonic oscillator potential for (i)electron repulsion(steeper at small distances) (ii)dissociation (bond breaks at large distances) New E-y curve: r1 11 Dissociation energy -2 y=6 v=5 v=4 v=3 Energy level/ vibrational y=2 quantum number =1 v=0 Interatomic distance r Fig 16-3 Three consequences (1) Harmonic at low v (2) AE becomes smaller at high v(broadens band) (3) Selection rule fails△v=±land△v=±2.(overtones) CEM 333 page 6.8

Anharmonic oscillator: Must modify harmonic oscillator potential for (i) electron repulsion (steeper at small distances) (ii) dissociation (bond breaks at large distances) New E-y curve: Fig 16-3 Three consequences (1) Harmonic at low n (2) DE becomes smaller at high n (broadens band) (3) Selection rule fails Dn = ±1 and Dn = ±2. (overtones) CEM 333 page 6.8

How many vibrational modes? 2 atoms(H2)-1 vibration (stretch v) 3 atoms (H2O)-3 vibrations (vs,Vas,o) 3 atoms(CO2)-4 vibrations (Vs,vas,o, 4 atoms (H2CO)-6 vibrations(vs,vas,p(CH2)v(C=O)) 5 atoms. 3N-6 Non-linear molecule 3N-5 Linear molecule "Normal modes" Coupling of different vibrations shifts frequencies Coupling likely when: (1)common atom in stretching modes (2)common bond in bending modes (3)common bond in bending+stretching modes (4)similar vibrational frequencies Coupling not likely when (1)atoms separated by two or more bonds (2)symmetry inappropriate Example v(C-O)in methanol 1034cm-1 ethanol 1053cm-1 butanol 1105cm-1 CEM 333 page 6.9

How many vibrational modes? 2 atoms (H2) - 1 vibration (stretch n) 3 atoms (H2O) - 3 vibrations (ns, nas, s) 3 atoms (CO2) - 4 vibrations (ns, nas, s, w) 4 atoms (H2CO) - 6 vibrations (ns, nas, s, w, r(CH2) n(C=O)) 5 atoms . 3N - 6 Non - linear molecule 3N - 5 Linear molecule "Normal modes" Coupling of different vibrations shifts frequencies Coupling likely when: (1) common atom in stretching modes (2) common bond in bending modes (3) common bond in bending+stretching modes (4) similar vibrational frequencies Coupling not likely when (1) atoms separated by two or more bonds (2) symmetry inappropriate Example n(C-O) in methanol 1034 cm-1 ethanol 1053 cm-1 butanol 1105 cm-1 CEM 333 page 6.9

Instrumentation: Sources Nernst Glower heated rare earth oxide rod 1-10 um (1500K) Globar heated SiC rod (~1500 K) 1-10μm W filament lamp 1100K 0.78-2.5μm Hg arc lamp plasma >50um CO2 laser stimulated emission lines 9-11um Transducers Thermocouple thermoelectric effect- cheap,slow, dissimilar metal junction insensitive Bolometer Ni.Pt resistance highly thermometer(thermistor)at sensitive 1.5K <400cm-1 Pyroelectric triglycine sulfate fast and piezoelectric material sensitive (mid IR) Photoconducting PbS,HgCdTe light sensitive fast and resistance thermometer at sensitive 77K IR beam 10-7-10-9 W,AT at transducer mK-uK CEM 333 page 6.10

Instrumentation: Sources Nernst Glower heated rare earth oxide rod (~1500 K) 1-10 µm Globar heated SiC rod (~1500 K) 1-10 µm W filament lamp 1100 K 0.78-2.5 µm Hg arc lamp plasma >50 µm CO2 laser stimulated emission lines 9-11 µm Transducers Thermocouple thermoelectric effect - dissimilar metal junction cheap, slow, insensitive Bolometer Ni, Pt resistance thermometer (thermistor) at 1.5 K highly sensitive <400 cm-1 Pyroelectric triglycine sulfate piezoelectric material fast and sensitive (mid IR) Photoconducting PbS, HgCdTe light sensitive resistance thermometer at 77 K fast and sensitive IR beam 10-7-10-9 W, DT at transducer mK-µK CEM 333 page 6.10