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Symmetry Analysis for

Vibrational Modes of BrF3using Group Theory

Lam Vo – CHM 354 16 SP

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The Molecule

SymmetryElements• E•

C2• σ v(xz

• σ v!(yz

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Point Group and Character Tab

Po"nt #ro$% C2v 2

C2v E C2 σ v σ v!

 & 1 1 1 1 1 z

x2'y2'

z

2

 & 2 1 1 1 1 ) z xy

*1 1 1 1 1 x' )  y xz

*2 1 1 1 1  y' ) x  yz

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Reducible Representations fo

 Vibrational Modes

χ(E) 3+6 6χ(C2

)

(+C2

(1,2-os./o /χ(σ v ) 4 4

χ(σ v) 2 2

C2v  E C2 σ v 

 ! " 1 1 1

 ! 2 1 1 1

#" 1 1 1

#2 1 1 1

$ vib % & '

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rreducible Representations of

• )e0$-t"on orm$la

• a &1  6 x 1 , / x 1 , 4 x 11*

• a &2  6 x 1 , / x 1 , 4 x

1&• a*1  6 x 1 , / x 1 , 4 x

12

• a*2  6 x 1 , / x 1 , 4 x 1"

 vib + *! " , 2#" ,

•  C2v E C2 σ v σ v! & 1 1 1 1 1

 & 2 1 1 1 1

*1 1 1 1 1

*2 1 1 1 1

 vib % & ' 2

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#asis -unctions for the .or/a

Modes

d "s t8e stret-8"n9 0"stan-ea "s t8e :en0"n9 an9leb "s t8e o$to%lane :en0"n9an9le

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The 0tretches

C2v E C2 σ v σ v!

Symmetry

stretch 

d"1d2 2 & 2 &  ! " , #"stretch 

d* " " " "  ! "

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The #ends

C2v E C2 σ v σ v!

Symmetry

bend 

a"1a2 2 & 2 &  ! " , #"bend 

a* " " " "  ! "

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The ut3of3Plane #end

• ;rom a%%ly"n9 C2v symmetry o%erat"ons

to t8e 0s an0 as'

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0!4Cs fro/ Pro5ection perato

) E ) C2 ) σ v ) σ v! P &1  P &2  P*1  P

01 (02 01 02 01 02 6(d" ,

d2)/ 6(d" 3

d2)

03 03 03 03 03 6d* / /

a1 (a2 a1 a2 a1 a26(a" ,

a2)/

6(a" 3

a2)

: : : : : / / /

 

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.or/ali7ation of 0!4Cs

 

+ normal"zat"on -onstant - -oeB"-"ent "n S&LC

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Theoretical and E8peri/ental !-re9uencies'1:

Modes R (R) ;ave<

(;ebM)

 ;ave<(bserve

d)

 & 1 :en0 )') 216 242

*2 :en0 )') 23. 242

*1 :en0 )') 324 35/ & 1 

stret-8)') 514 552

*1stret-8

)') 5D/ 612

 & 1stret-8

)') 64/ 65

A8e t?o ta?ell on n%eaFs "n s%e-tr$m' are t?o %ea

"n t8e )aman s%e-A8e vareG$en-"eso:serva:le ty%"-ally ?3/ -m1' reasona:ly

 

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References

1@ C8em"stry Learners@

8tt%II???@-8em"strylearner@-omI:rom"netr"J$or"0e@8tml (a--esse0 /4I2DI2/16

2@ Cotton' ;@ &@ Chemical Applications in Group Theory 3rd edition. Kxor0 n"ver+e? orF' 2//6@

3@ C Nav"s C8emO"F"@8tt%II-8em?"F"@$-0av"s@e0$ICoreIP8ys"-alC8em"stryIS%e-tros-o%yIV":rat"onals-o%yIV":rat"onalMo0esISymmetry&0a%te0L"nearCom:"nat"onsQ+ormal"zat" (a--esse0 /4I2DI2/16@

4@ Sel"9 H@' Claassen H@' Hollo?ay R@ H@ nrare0 an0 )aman S%e-tra o Cl;3 an0 *

Chem. Phys. "=>&1 52 (>)?

5@ Oe:MK

http://www.chemistrylearner.com/bromine-trifluoride.htmlhttp://chemwiki.ucdavis.edu/Core/Physical_Chemistry/Spectroscopy/Vibrational_Spectroscopy/Vibrational_Modes/Symmetry_Adapted_Linear_Combinations#Normalizationhttp://chemwiki.ucdavis.edu/Core/Physical_Chemistry/Spectroscopy/Vibrational_Spectroscopy/Vibrational_Modes/Symmetry_Adapted_Linear_Combinations#Normalizationhttp://chemwiki.ucdavis.edu/Core/Physical_Chemistry/Spectroscopy/Vibrational_Spectroscopy/Vibrational_Modes/Symmetry_Adapted_Linear_Combinations#Normalizationhttp://chemwiki.ucdavis.edu/Core/Physical_Chemistry/Spectroscopy/Vibrational_Spectroscopy/Vibrational_Modes/Symmetry_Adapted_Linear_Combinations#Normalizationhttp://www.chemistrylearner.com/bromine-trifluoride.html