{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

CHEM321 FILE 15B GROUP THEORY & MOLECULAR VIBRATIONS - trans-F-N=N-F + BCl3

CHEM321 FILE 15B GROUP THEORY & MOLECULAR VIBRATIONS - trans-F-N=N-F + BCl3

Info iconThis preview shows pages 1–14. Sign up to view the full content.

View Full Document Right Arrow Icon
MOLECULAR VIBRATIONS Melvyn R. Churchill October 01 2009
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Background image of page 2
Selection Rules IR ACTIVITY : A vibrational mode will be infra-red 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 infra-red active ( ungerade ) and Raman active ( gerade ) in a Centrosymmetric Molecule
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
EXAMPLE #1 trans - F-N=N-F (which has C 2h symmetry & is centrosymmetric)
Background image of page 4
trans - F-N=N-F (C 2h ) σ h i (inversion center) at center of N=N bond C 2 perpendicular to screen
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Character Table for C 2h C 2h E C 2 i σ h
Background image of page 6
trans - F-N=N-F (C 2h ) E 8 vectors in the plane, 4 perpendicular (All vectors remain in place) Χ (E) = 12
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
trans - F-N=N-F (C 2h ) C 2 8 vectors in the plane, 4 perpendicular All vectors move to different location. Χ (C 2 ) = 0
Background image of page 8
trans - F-N=N-F (C 2h ) i 8 vectors in the plane, 4 perpendicular All vectors move to different location. Χ ( i ) = 0
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
trans - F-N=N-F (C 2h ) σ h 8 vectors in the plane do not move: Χ= 8 4 vectors perpendicular to the plane reverse: Χ = - 4 Overall: Χ h ) = 4
Background image of page 10
Vibration Spectrum of trans-N 2 F 2 The 12 degrees of freedom give rise to the reducible representation Γ dof C 2h E C 2 i σ h Γ dof 12 0 0 4
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
(A g )( Γ dof ) for trans- F-N=N-F C 2h E C 2 i σ h x 2 2 2
Background image of page 12
(B g )( Γ dof ) for trans- F-N=N-F C 2h E C 2 i σ h y z
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 14
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}