CEM 882 Lectures 5

Rotational t Vibrational

Motion

we likey

Molecular rotation ,

in gas phase µ←2r→9 Rotation By M

←H-- H-> Vibration nuclear

↳ Capital letters formass

nuclear parameters,small letters for e

-

parameters

TT = Mf I -- Rtxp L -- MR#nih

Mr -_ 1,33, ...

RI ao ne-- nr

-

- I

Maov = MaoVK -

¥=⑤ .io#=i@4Ybooprpn-meimerconstant)

[ nuclear rotational velocity2-

electron orbital velocity

E.EMV -

- Inmate Em)MT froth

"

Eelec To"Microwaved-

RT Erotdr Far infrared- 10cm

"

maov = M RV

¥ -

- tmall.fi{ME EMILIE)%

= Enix" Jg n

MT,Erotd RY froth

D' ÷: →

÷ 8→ →

O

he

£3a

o

ro

IEre

''

gD=UN

BI

-n¥f÷¥da

1970 ⇒ detection with

a microwave telescope

of an emission signalat 90 GHz I 3cm

' '

-

Hypothesis that signalis due to Hcot⇒

isoelectronic with HCN

1975 ⇒ discharge of

Azt co ⇒ observed

microwave spectrum ⇒

Very clear signal at

correct w ⇒ Hoot1St1980

outside earth ⇒ poly atonymolecule

HE ¥¥ detectedin space =HE t co → Hat HootNH

,TT ( exothermic)universal )protaotnator Microwave

astronomy

Vibration ansesdisplacement equilibrium→ X. = R- Ree lowestToad lengths beonnedros'S

spring -= bond restoring force length← •fleet → t F KxH H angles) ⇐ force constant←RT

from e-InucleiDZX -

z= ) x electrostatics

xEeEssiioslF@ehE.o:S:c't.intX

←I→1¥, *angular frequencyHarmonic

oscillator

vibrational= "fk×dx=tzkx VPotential Energy Tox

Hypothesize tzkao - bond energy- Eye.KK heeled-

- Rydbergaf& I Goo Na= 105cm"

• 11h. -molecularLiem F-spring

-- Fgravity electronic spectra

w -- HIM = JEEMag

Teen ¥K2 2Eelec

= 27T Eeiec -2

Tn to ntocm "

Guess Evib - Trw = 2E 72000

like a → Cni'

photonX. E. rib Eviblz

Eel. ¥eEa=K2=⑨mIbthis - x' news

""

see KZ Separate→ → independent

C-elect C-ribs> C-rot motions← Born -Oppen

Vela 's> Vvibs> Vrot heimer

Approximation

normal mode

bond springsGas phase time - coordinated

fo I motion of masses

BE single0 0 Vibrational normal modes mess thee.

singleboutta ←o asymmetric springangle o

stretch

spring →

symmetricin Rotational

stretch O O bend motion is÷.O Oo O (smallest also excitedC y → ←

center- of -mass K) and is

is fixed basis forlineshapes

{→

ftp.rons.euin

Czwpoint

groupsymmetry

Infection model Electron microscopy

J. AIDS 1990, 3, 965

HIV/target cellmembrane fusion

Hgtv spike proteinHIV →

membrane

→

targetimmunecell

membrane

150 nm-

Electron micrograph ofSARS viruses fusing witha cell

SARS

viruses MM

cell

D

Membrane-associated viral fusion peptideTwo different peptides

helixb sheethelixb sheet

Biochemistry, 2000, 39, 1826-1833Secon

d derivative s

pectraquit:IogIo.✓ C-Nr

Residues I -33 of 'H

Hiv spike Residues1- 16

protein µsubunit d

d

9 "deconvolution"

gaussian fittingfunction

d

d d

16 33'

heel

B sheet helix