chem 515 spectroscopy vibrational spectroscopy ii
Post on 19-Dec-2015
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CHEM 515Spectroscopy
Vibrational Spectroscopy II
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Vibrations of Polyatomic Molecules
• N particles have 3N degrees of freedom (x, y and z for each).
• Three degrees of freedom are translations.
– TX = X1 + X2 +…+XN
– TY = Y1 + Y2 +…+YN
– TZ = Z1 + Z2 +…+ZN
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Vibrations of Polyatomic Molecules
• N particles have 3N degrees of freedom (x, y and z for each).
• Three degrees of freedom are rotations about x, y and z axes. RX, RY, and Rz .
• For linear molecules, only two rotational axes will represent degrees of freedom.
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Vibrations of Polyatomic Molecules
• N particles have 3N degrees of freedom (x, y and z for each).
• The rest of degrees of freedom are vibrations. Number of vibrations are:– 3N – 6 for nonlinear
molecules.– 3N – 5 for linear
molecules.
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Classical Picture of Vibrational Motions in Molecules
• Classically, polyatomic molecules can be considered as a set of coupled harmonic oscillators.
• Atoms are shown as balls connected with each other by Hooke’s law springs.
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Classical Picture of Vibrational Motions in Molecules
• Stronger forces between O and H atoms are represented by strong springs (resistance to stretching the bonds).
• Weaker force between H atoms is represented by weaker spring (resistance to increase of decrease of the HOH angle “bending of the angle”)
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Normal Modes of Vibrations
• The collective motion of the atoms, sometimes called Lissajous motion, in a molecule can be decomposed into normal modes of vibration within the harmonic approximation.
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Normal Modes of Vibrations
• The normal modes are mutually orthogonal. That is they represent linearly independent motions of the nuclei about the center-of-mass of the molecule.
• For CO2 molecule, number of vibrations = 3N – 5 = four vibrations.
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Normal Modes in Water Molecule
• For H2O molecule, number of vibrations = 3N – 6 = three vibrations.
• Liberation motions are the x, y and z rotations.
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Vibrational Energy levels for H2O
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