Molecular Spectroscopy
Report No. 3
Due: April 27, 2015 Monday
You can get the atomic mass of elements from the reference books available in the library. Do not take average
atomic mass of elements because isotopes should be treated separately.
Problem 1) How many normal modes of vibration does the CO2 molecule have? Describe the motions involved
and comment on their infrared and Raman activity.
Problem 2) Consider the following molecules H2, HCl, CO2, H2O, CH3Cl, CH2Cl2, H2O2, NH3, SF6. Which of
them will give (a) a pure rotational spectrum, (b) a vibrational rotational spectrum, (c) a pure rotational Raman
spectrum and (d) a vibrational Raman spectrum?
Problem 3) In the Raman spectrum of CCl4 obtained by using the mercury arc line at 438.53 nm for excitation,
lines are observed at 440.00, 441.88, and 444.70 nm. Calculate the Raman shift for each of these lines in terms
of wave number.
Problem 4) The infrared and Raman activities of the N2O molecule are listed in Table 4.3 of the text. Answer the
following questions from the data listed in the Table.
a) What is the molecular structure? Describe it based on the spectroscopic data.
b) Identify the vibrational modes of the three bands observed.
c) How to distinguish the symmetric and asymmetric stretching vibrations?
Problem 5) The infrared and Raman spectroscopic data of A2B2 molecule are list in the following table. Deduce
what you can about the structure of the molecule and assign the observed vibrations to particular modes as far as
possible.
Position (cm-1) Infrared spectrum Raman spectrum
2701 inactive strong intensity
2439 strong intensity inactive
1762 inactive strong intensity
537 very strong intensity inactive
505 inactive ?
Problem 6) For a molecule belonging to the D2h point group, deduce whether the following vibrational
transitions, all from the zero-point level, are allowed in the infrared and/or Raman spectrum, stating the
direction of the transition moment and/or the component of the polarizability involved:
a) to the v=2 level of the b1g vibration;
b) to the v=1 level of an au or b2u vibration;
c) to the combination level involving v=1 of a b1uvibration and v=1 of a b3g vibration;
d) to the combination level involving v=2 of an au vibration and v=1 of a b2g vibration.
Problem 7) Consider the molecule CH3Cl.
a) To what point group does the molecule belong?
b) How many normal modes of vibration doer the molecule have?
c) What are the symmetries of the normal modes of vibration for this molecule?
d) Which of the vibrational modes of this molecule are infrared active?
e) Which of the vibrational modes of this molecule are Raman active?
Problem 8) How would you expect the intensities of the C≡C stretching vibration to compare in the infrared and
in the Raman spectrum of these compounds: (a) HC≡CH; (b) HC≡CCl.
Problem 9) For the ICl molecule, the following spectroscopic constants are listed as ωe= 384.293 cm-1, ωeχe=
1.501 cm-1, Be= 0.1141587 cm-1, and αe = 0.0005354 cm-1.
a) Predict the pure rotational Raman spectrum. What will be the Raman shift of the two lines closest to
the exciting laser line?
b) Predict the pattern of the Stokes vibration-rotation Raman spectrum. What will be the Raman shifts of
the S(0) and O(0) lines from the exciting line at 514.5 nm?
ℓαℓα∠λ
ㅢνι여
γ P˘ℓ)㎀ ∠N¿ ,
κ B, Mo끄 α㎕α札.‘ η Zλ 旽 初
● ρ ρ γ
‘
/,/Lρ Δℓυν
ι '〉
½ ℓ¿ ¼
∽z ∠ υ 之‘,N— 으= φ⑿
˛班ι
ㄴ㎔ ℓ ㎕ 羽拗&Δ
¾ μℓ↓
乞α&¸η
“
"μ
ξ
- ε- O
O--¸ H 幼ν
",) R ω㏆ 力㎗枋叱
"κ
↑
½αA꾸竹初 ι
㎕λ R 妃¿¿
ℓ
O - ˛- o
",)工
,
↓ ↓
"0 -ι,o
‘ν
L乞 b (Δ
/H.
½仰ι
ιλ
"ℓ
)工 R η夕㎕
O — C・一 O
¼ ι奴 竹 ‥㎁ 跛 Λ 竹 工R 婉 脇 苾
← ← -⇒
ν
”
쩠;L唆 笏 雜ξ
㎘
*㎍#虔懸 ZL j往
Z,/ㅏ L,‘ [,ι I,・
” ')
''ㅢ
‘
lO/砂Δℓ
ℓ吼
(ω P〃 ㄴZ Jto充 υAρ ℓC尤 乞ℓ 1; Hα , Hγ 0, εH¸ α , ˛H½ α z,N杓
⌒” ℓ以
ιι 走⅞Δ Hz
〔 ¿
b) ι ㅏ㎭ ˇ
φℓ
"ι
赫 ,
"γ
; t」 E"Lf〉 nㄴ
ιω ρ嫩 ˘ι,'I:. R㏂ 翊
'ㅏ
,ι
쌕 ㎕
㎐ 侁 ; ιι ” ,I'I:
(J⇒ ㄵ¿ η
水Rλ〃αη
ιℓppIλ η; α ’
"γ
"
ηB)
Iℓ η
T ㎂Δ
7'γ
μ,8˚ Ξ3 '” 깍
n = φBB. n = 之 I803 '” [' ,3xIσ
牛午O,OO η仰 = ψ O, OOK Iσ = ㅗ2 ,그 ? ˛ ˛
枾「')
-') "i-' (4 = ?6
ψμ g' "・‘ㄲ = 21ι
I˛
“ 3 ∫
"”
ηj-'’(Δ = I7그 ¼
ι
ㅣ‘Δ= 3Iι ι —
ψφ˛l.,O어 〓 그之φ8? ια√ 枋 ')
‘
“
”
∫ ㅑ
孜ι˛
)、 ?γ나 )
‘
’‘ (α ) αn’ ㎘㎂ N〓 N=0 /ι υ ㄴι ι ℓ
˛¿侁ℓㅋ 쇼 {協 ι ℓ"Λ˛
’ ∠ P- 亦̆化ωo(ι¼ αιλ
孔θ 녀ℓ P- ωη
必 ι ㅅ ∠
˛“αΔ 尺αργ
ℓ ιαΠι
娥 I υψ 魄 ε ∠ 嫩 ㎈ 叛 妨 ㎖ 亡翊 幽 ℓℓ
“
'・
˛b) ,B 우( ˘¿녁νγ ¾ ι
uo˛ ι ¿υ
¿ 住
ιι ν
I乏 λγL) Pι (’ ￢R、 ㅋ仁化Δνκκν仁˛Δ
½
;:::
∠μ 九
ι
('q,,'I」 "'Jκ
㎁
" 'ν
) P¨ Mι ρ㏊ Δ
M￠粒
-
"℡ "
˛
ω 位3ε ˛cφ杻↓˘ ㎕1¸乳) R"解 ㏂ 0∠
ρ Ψ
L:≥ I"￠
τ 〈 η¸
L,κ η ㎕"妬
机 ω&λ ) R翊 翊 oℓ
仰 Ψ
˛ Ξ)
‰ 小ℓ
"1
R仍竹ι α脇 ㎐ ㏊ λ ∠九η
˛札ℓι ˛˛枋
"孔 "'노
→ α妙 拉札⅜Δ η 劤 "
密— ¾
一⇒A 一
B —B— A A抄 ˛I尨ι
Λα
乞A- β-β -A ,色 ι
Γ夕 ικι侁ℓ I〉
一⇒ BN- ι= ¿ φκ#겼 뇨ι
3N-ζ = η φ 拉 Δ ⅞伐 Λ ηι免札 ι机 〃 Zι磁
” —
2’ OI AΨn. Aλ ㄴℓ
」ι A, IR"η
I— B— B— -〉
cλ ” ok¸ ZZλ Λ
ι)
’
2φ B" αι ～B- 8-A, 1R αι¼ι乞
YΛ ‘ ’ㄴ λ , A●-> (-¨
A莎 tㄷ 化)
-’
‘
Iη , (㎍ h 沈 , A— B一 B— A, IR ι牝 α∠Z¿ )
˛
"咤
˛ ˘
α △ℓ
αι ¼ㅔ -B-¼ ,
"".,"k」I,
← -⇒
E3?‘f
1R α
cλι
私ℓ )
夕O夕 ℓ勻'‖
η ¼ Δ' '—
t‘
"η
ψ
尤λ˛
7ι ℓ꼬α αι拉Ψ ‘ o?ι ㎕Z¸ ㎕ℓ㎀ι
νι化
αZ⅞ ¿
,˛ ∂
⅞oι ⊂D.
'=
τ
κ
I〉角
小ι竹ι
˛ )
F九 ˛Λη χ
t kㅅ 亡̧
泌∠ ι7心 αp'
之⅜ ρ2力 poj)● ˛
'η ^ㅆ
㈌ ν= o →z "½˛比ℓ⅜ IAℓ br’ ν
¿ 化ακ ¿
ιη
b'θ
x
¸ χι"≒"λ多') ㅗR ¿κα˛劤
'" = /l"
R-- ω(χ
"ι私ℓ
ι
‘ χ, "'多 —˛θ
따˛
φρ的ωη )
"Δ
‘
b) ν= 0 →I I¿ I
¾ααAφ㎘α劤γ
A“ ;"ι 1R , R“ κ柳 λ Δκ¿
Π 孑년 ;ν
→I Iℓ小㎕⅜bz“ A形 ㎗狄¿h7 “
ν
'= O
8z“ (’ ) j IR 仍
ι仇˛ ("-
㏊ b‘ι )
; Rα ''κ
〃
ι麻 αcI乞υ名
'(,α
˛) '=o --, '=' ⅜ br“ x '=' 여 b多
b'“ ㅅb'】 〓Δ )α
B)“ (’ ) ; 1R 枷 ’¿Λι
-oι
e"ι I -’ ?ι )
, R ιΛ
φ
,ιιη?t 'ι λ¿ λ
η˛
t,ι /e’ e느
''ν
‘
ω υ=0 → 之⅜αα
"’
'ψ
η ’ ㎚ 力L"
느
Ψ xI oι bυ 仰
ααx ααx b그 "ιχ多 1R κ牝 Iι ¿ 叱
, = b,, "느
R α 力oι θ
/νι ⅸιι倂˛
¿
” ”
‘ χou9“I ' Cρ ㎛ 〉
多 √φψ癌 )
㎙ ㎕肋η7) ‘
ιㅏ
I〕 α 」
￠) ˛,ν po¸ ㄾ
"守
:’ I⌒
b) ,N-6 = g ηψιι
"
˛) α, ( ν ν½ν,), e (¼ ≠, 〉쯩,νι’
', "
)
1) A' (μ〉' ㅆκ
누 ,1)
˙
"ξ, : IR ι
ν ν¿,ν ㏓
'"
E (μ χ
"μ
ㅆχ
生 χ χ ,λ
,
'
J'
ν≠,"'쌍 , ‘ ¿: 1fξ ι
ι
e) ㎕ 赫 嫩 「ι λ
ν赫
Zι oηt」 ?ι
P札 υ¿ι
υ肛8)
(/α
) HC ≡˛H, H— C ΞC ㅡ H
-' — ・
-〉 (- ξ¨
乞
α
㎘ ㏊
Δλα玖χ ∂ι ™ 痂 L九 ι
(b) HC≡ ⊂α C Ξ ε 一 Cι 'φ
" Hㅡ
—) --〉 (- ←—
"f
Tυ ˛
ω¿ℓη?' e)
Ro尤 αℓ¿ tℓ札
ψt㎕ ℓα ⅜ ι
∠ㅛαI砂π虎 oI-∠ ¿υ
'肌 .ι ½
'丁
¿ 〓B 丁'""
丁+ ') ∽√ '
仍?ι ι α/η Λℓ
∠R ∽/”ι ℓ¿χ
ιZ●夕
∠ ι
ιΛιℓ之⊥υ
‘
A丁 = 0, m ± z "η
衫
㈁ Γ哄 p㎶ 肋 九赫 ㎕ R㏂ ι"L, I/η
'J'γ
A 丁= + Z α ιI AE = ¿ - εJ = B μ丁+¿ )
'γ
Bν = Be - ㅆ ν+¼ )
= 0˚ IIψ
',g?・
θ θoΞ βΞ e θ +¼ 〓
- 0, υ ‘
多 g?I ●I' ) . II˙
‘
Λε= 0, I/多 8?I 牛χO + ¿) = 0˚ ι8 ,, μιη ‘
‘ "-'
ν = )花 士 O,ι B33ψ ¿o√ '
‘
‘
乞
ρ
Γ˘ ¨ㄴ λ“ηℓ
免 I˜ ,丈
j˜
” ¿= ι
υι ζ
+ ½ ∵
κ j"+½ (伊 ) -' )ㅗ
½ ι'+½ )Z
따 9 ¸ισ+½ 〉- I,,o'
= 58
¨ -= O
= ∫
eI, ηηI2Γ η
ι '
½ρ乞ν
= Ξ
η3.o‘ z,,'ⅱ”尸⅞侁 ν= I
7Λ〃α 0‘ υ) = "4τ χ-)ι - B H丁 +ι
〓∫
η￥3 ι¿ ψΞφ
? ι̃Γ'-
'β 38I, 'z? /oo o〃 ', 0‘ ι
BB多 "ι '㎋
’
'
‘
= oΞ∫
φ 나. B● / ι끄Eη √ '
0) = 〉
s ι 4多 κ
・
-)ι + 8 牛丁+ ι)
= Iη O,,o ?B8,2 ˛η√
‘ '
½˛ ¸
(o) 0(0)→
( ζIψ ξ勿●) 沕깍
‘ 多婉〃
㎕珝/¼
”
