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Learn about the vibrational motions, rotations, and vibrations of polyatomic molecules in this informative guide. Discover the classical picture of molecular vibrations, normal modes of vibrations, and energy levels for molecules like CO2 and H2O.
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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.
