Ch1b09Lecture06

Ch1b09Lecture06 - 1 Molecular Vibrational Spectroscopy 1 E...

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2 Li-F δ + - δ - Li - F δ + - δ - µ = dipole moment = charge x distance Molecular Vibrational Spectroscopy Li-F δ + - δ - E time Molecules can absorb or emit light at their frequencies of vibration What if molecular vibration doesn’t change dipole moment? ν −1
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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
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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 ∫∫ + = = b kx kxdx dx x F 2 2 1 ) (
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6 ΕΨ = Ψ + Ψ 2 2 2 2 2 1 2 kx dx d µ h Molecular Vibrational Spectroscopy H vib Ψ = E vib Ψ 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
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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,… ω e or ν e = vibrational frequency (tricky!!)
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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,… ω e or ν e = vibrational frequency (tricky!!) E( ν e or ω e ) = h ν e ( v +1/2) Vibrational Energy Levels:
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9 h = 6.626E-34 J·s (kg m 2 s -1 ) = Planck’s constant E( ν e or ω e ) = h ν e ( v +1/2) Vibrational Energy Levels: ν e = 1/2 π (k/ µ ) 1/2 The vibrational frequency, or energy of vibration, is: k = bond force constant (spring constant from Hooke’s Law) µ = reduced mass
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ΕΨ = Ψ + Ψ 2 2 2 2 2 1 2 kx dx d µ h Molecular Vibrational Spectroscopy H vib Ψ = E vib Ψ ν = 1,2,3 ν e (the vibrational frequency) is determined by the stiffness of the spring
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11 Molecular Vibrational Spectroscopy ν = 1,2,3 Note that v =0 is NOT at the bottom of the potential energy well
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