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##### CHEM 515 Spectroscopy

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**CHEM 515Spectroscopy**Vibrational Spectroscopy II**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**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.**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.**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.**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”)**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.**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.**Normal Modes in Water Molecule**• For H2O molecule, number of vibrations = 3N – 6 = three vibrations. • Liberation motions are the x, y and z rotations.