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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