6 - Vibrational Spectroscopy

# 6 Vibrational - 1 Molecular Vibrational Spectroscopy = dipole moment = charge x distance E time Li-F Li F Li-F Molecules can absorb or emit light

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2 Li-F G + - G - Li - F G + - G - P = dipole moment = charge x distance Molecular Vibrational Spectroscopy Li-F G + - G - E time Molecules can absorb or emit light at their frequencies of vibration What if molecular vibration doesn±t change dipole moment? Q ±²
3 Some Vibrations that we might or might not be able to see using absorption or emission spectroscopy S =C= O S = C = O Symmetric stretch O=C= O O = C = O Symmetric stretch

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4 Some Vibrations that we might or might not be able to see using absorption or emission spectroscopy S =C = O S = C= O As ymmetric stretch O =C = O O = C= O As ymmetric stretch
5 Hooke's Law says that the restoring force due to a spring is proportional to the length that the spring is stretched, and acts in the opposite direction. F =-kx , where F is the force, k is the spring constant, and x is the amount of particle displacement. The model for molecular vibrations: Hooke±s Law Integrate Hooke±s force Law to get the potential energy ³³ ± ² b kx kxdx dx x F 2 2 1 ) (

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6 (< < ± < ² 2 2 2 2 2 1 2 kx dx d P ! Molecular Vibrational Spectroscopy H vib < = E vib < Li F The molecule is modeled as two atoms connected together by a spring Potential energy term from Hooke±s Law (remember high school physics) Kinetic E + Potential E Pot E r (bond length) r e f(x) = potential energy = kx 2
7 New Parameter: The vibrational quantum #: v h = 6.626E-34 J·s (kg m 2 s -1 ) = Planck±s constant v = 0,1,2,3,² Z e or Q e = vibrational frequency (tricky!!) so use different colors!

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8 New Parameter: The vibrational quantum #: v h = 6.626E-34 J·s (kg m 2 s -1 ) = Planck±s constant v = 0,1,2,3,² Z e or Q e = vibrational frequency (tricky!!) E( Q e or Z e ) = h Q e ( v +1/2) Vibrational Energy Levels:
9 h = 6.626E-34 J·s (kg m 2 s -1 ) = Planck±s constant E( Q e or Z e ) = h Q e ( v +1/2) Vibrational Energy Levels: Q e = 1/2 S (k/ P ) 1/2 The vibrational frequency, or energy of vibration, is: k = bond force constant (spring constant from Hooke±s Law) P = reduced mass

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(< < ± < ² 2 2 2 2 2 1 2 kx dx d P ! Molecular Vibrational Spectroscopy H vib < = E vib < Q = 1,2,3 Q e (the vibrational frequency) is determined by the stiffness of the spring
11 Molecular Vibrational Spectroscopy Q = 1,2,3 Note that v =0 is NOT at the bottom of the potential energy well

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12 Q e = (1/2 S )(k/ P ) 1/2 What are units of k? Equating both sides of the equation, s -1 = (k/kg) 1/2 So s -2 = k/kg and kg s -2 = k = Newton m -1 Because the spring constant has units of (Force/unit length), we often call it a force constant . The vibrational force constant