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Unformatted text preview: MOLECULAR VIBRATIONS Melvyn R. Churchill October 01 2009 Degrees of Freedom A molecule composed of n atoms has 3n Degrees of Freedom. (3n coordinates will define the locations of all atoms.) These Degrees of Freedom can factored as follows 3 Degrees of Translational Freedom Translation (movement) of the entire molecule along the x, y & z axes 3 Degrees of Rotational Freedom rotations of the entire molecule about x ( R x ), y ( R y ) & z ( R z ) Therefore: (3n 6) Degrees of Vibrational Freedom Selection Rules IR ACTIVITY : A vibrational mode will be infrared active only if its representation is the same as a first order function ( x , y or z ) RAMAN ACTIVITY : A vibrational mode will be Raman active only when its representation is that of some second order function ( x 2 , xy , x 2 y 2 , etc ) EXCLUSION RULE : a vibrational mode cannot be both infrared active ( ungerade ) and Raman active ( gerade ) in a Centrosymmetric Molecule EXAMPLE #1 trans  FN=NF (which has C 2h symmetry & is centrosymmetric) trans  FN=NF (C 2h ) F F N=N h i (inversion center) at center of N=N bond C 2 perpendicular to screen Character Table for C 2h C 2h E C 2 i h x 2 2 2 trans  FN=NF (C 2h ) F F N=N E 8 vectors in the plane, 4 perpendicular (All vectors remain in place) (E) = 12 trans  FN=NF (C 2h ) F F N=N C 2 8 vectors in the plane, 4 perpendicular All vectors move to different location. (C 2 ) = 0 trans  FN=NF (C 2h ) F F N=N i 8 vectors in the plane, 4 perpendicular All vectors move to different location. ( i ) = 0 trans  FN=NF (C 2h ) F F N=N h 8 vectors in the plane do not move: = 8 4 vectors perpendicular to the plane reverse: =  4 Overall: ( h ) = 4 Vibration Spectrum of transN 2 F 2 The 12 degrees of freedom give rise to the reducible representation dof C 2h E C 2 i h dof 12 0 4 (A g )( dof ) for trans FN=NF C 2h E C 2 i h x 2 2 2 (B g )( dof ) for trans FN=NF C 2h E C 2 i h y z (A...
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This note was uploaded on 12/01/2009 for the course CHE 321 taught by Professor Churchill during the Spring '09 term at SUNY Buffalo.
 Spring '09
 CHURCHILL
 Organic chemistry, Inorganic Chemistry, Atom, Mole

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