Molecular Spectroscopy chemistry homework

L - b H=TtV T -- III.milVip -- LIE

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define mass- weighted coerel Gi = (Imi)" ki - Xie)

T -- IEEE inn M mechanics

. . I is a column Veeder cheek -7 ad T= Ipi

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a- KEEFE.EE#iEitEEiEIEet.i.?.io .

at bottenTV(Ii-01=0 of thepotential teen

vaI÷⇒¥⇒¥¥o E.F. kij LiEj

U=IE '

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Lagrangian mechanics to solve theme E-AM ." define ⇐ TCI;) - Hei) Lagrange's equated

date)a→. - Rated o single particle case L='zmx'2- thx) Ex -- mi 3¥ = -2¥ dafcmx

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) +31×-0 ma = m = -Ex = F -

for polyatomic vibrations ↳ T- V -- t.EE?-I?.?gkijEiGj 2L

⇐i )si? Ii

IIT. )%= - ftp.Ekijkj his gonej due to double E.AM→ Ii 1- 3- kijqj =o

counting .

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general solution is Ei= Ai Ces Hkt to,

sub Gj into E - O - M

O = -NAicos#¥)t.fkijajceslxkt.io#O=-dAitZjkijAj "

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iii.Ii: -

: : - -

ti :÷÷f.\ , I

ksn.tl "

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KSN ,3N -X

det (E -RE)-o ⇒ detlktxdee do diagonalize k . aset efs.ee# solute en d 3.N solutions ← eigenvalue . 3. N- 516) often are allowed crib freq . di = 4172022 Thi i. angular freq Vi is frequency

find some diagonalize k . →Normalmeet.es WIFEY.fr

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Qk= ↳ Ej linear asnperpoaiten. a-= .co/umveeee-.E--EEE-- EE I i

i

. I' is he

transposeof E

Ei -- Et

aye . . . . EtkE=o⇒E + EEE-0

- - row EEE EE + EEEE-0 ✓eeer

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Ekmatrix IE =L: t E-o

V

E-Koi . .

) e find Etta can mark F as a diagonal matrix .

eigenvalue .

*=f÷÷: Et EE-0

E.am + ai -0 Ii onlydepend on Qi

all meteors are decoupled . Cnormal modes? 2T=E"EYE' '(EAT =

'EEE -- a''ai

zu = I'EIETTFE.IE#aT=ETEEE'a Risk.IE?Ialiud--eTEE---zxiQEnooffdigtijmso

Example : a linear molecule . O C O

0=0-0 MA MB me I

. I, T's ← see a Sz

2V= kisitkzsfsi-xz-XT.SE#-xI = k, (Xi -Xz)

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t kzlxz -XD -

= k , Xftk

, XE- 2K , Xixztkzxztkzxz

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-2kHz Ii = MikeXz

3V=¥aEtmCktkdEEt¥eE5 -

- 214 ¥3 Ii Iz

- 2kg

calculate ¥

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- - M 1213

i e 2Ii2Gj

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Ehs III -X

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-d -¥

• ¥*. ÷::! consider 0=0--0 MaeMe

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