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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