Chem 24 Lectures 6 and 7 Molecular Vibrational Spectroscopy

Chem 24 Lectures 6 and 7 Molecular Vibrational Spectroscopy...

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1 Thurs, Jan 18 Vibrational Spectroscopies (2.5-3 lectures)
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2 Vibrational Spectroscopy (IR and Raman) a Fourier Transform Infrared Spectrometer molecular vibrations; gross selection rule, the basis of quantum mechanical selection rules fingerprint IR
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3 -1.5 -1 -0.5 0 0.5 1 1.5 1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113 The nature of Fourier transforms and frequency space -1.5 -1 -0.5 0 0.5 1 1.5 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 -1.5 -0.5 0 0.5 1 1.5 1 5 9 1 31 72 12 5 2 frequencies 2 frequencies 2 frequencies
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4 -1.5 -1 -0.5 0 0.5 1 1.5 1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113 -1.5 -1 -0.5 0 0.5 1 1.5 1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113 -1.5 -1 -0.5 0 0.5 1 1.5 1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113 The nature of Fourier transforms and frequency space The two frequencies beat against each other to produce a 3 rd frequency
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5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 109 115 4 frequencies added together a Fourier transform approach says that any function can be represented by a series of sin and cos functions, each with their own amplitude
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6 This very sharply defined spectral feature is effectively a high-Q oscillator absorption spectrum Fourier transform of absorption spectrum
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7 This broadened spectral feature is effectively a low-Q oscillator absorption spectrum Fourier transform reveals multiple frequencies
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8 Fourier Transform IR: An interferogram The sin and cos functions that add up to make this function represent the IR absorption spectrum of the molecule
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9 At a deeper scale, this picture of adding frequencies together to generate additional frequencies, or for getting destructive and constructive interference of wavefunctions, is something that we will touch on later. -1.5 -1 -0.5 0 0.5 1 1.5 1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113
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10 Vibrational Spectroscopy of Diatomic Molecules rot N tot rot N b b a a E r U m m , , 2 2 2 2 ) ( 2 2 kinetic energy operators for nuclei a and b Pot Energy function (incl. nuclear repulsion) for nuclear motion (found by solving the electronic Schr. eqtn) wave function for nuclear motion total energy of molecule (including translational energy) Make a couple of assumptions (not approximations) int , , , E E E trans tot rot N trans N rot N we do this because R, the internuclear separation distance, is only a function of the relative positions of the two atoms PLUS we can consider the molecule as a center of mass that rotates and vibrates about a set of coordinates that stay fixed with respect to the molecule. That center of mass translates
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11 Vibrational Spectroscopy of Diatomic Molecules N N E r U ) ( 2 2 2 is reduced mass Pot Energy function (incl. nuclear repulsion) for nuclear motion (found by solving the electronic Schr. eqtn) total energy of molecule (excluding translational energy) The assumptions allow for some simplifications int , , , E E E trans tot rot N trans N rot N r Non-Rigid Rotor If we solve this Hamiltonian, we get the rotational
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Chem 24 Lectures 6 and 7 Molecular Vibrational Spectroscopy...

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