Fermis golden rule Lecture 3 excitations and molecular ... · Lecture 3 excitations and molecular vibrations Fermis golden rule Selection rule external field (light wave) ... requirement

Lecture 3 excitations and molecular vibrations

Ferm

is golden rule

Selection rule

external field (light wave)polarization

of incoming

light

antisymm

etric operator

http://chemw

iki.ucdavis.edu/Core/P

hysical_Chem

istry/Q

uantum_M

echanics/Quantum

_States_of_A

toms_and

_Molecules/4.

wikipedia: A

uswahlregel

el. dipole transistion:

electronic dipole selection rule for aromatics

Exam

ple: Benzenepolarization along y

requirement for transition

mom

ent non-zero

note: in z direction, all orbits are antisymm

etric, therefore no transition dipole perpendicular to m

olecular plane

example: pentacene

transition only along short axislong axis along beam

Molecular vibrations

antracene

pentacene

normal m

odes

each mode:

all atoms sam

e frequency (like spring w

ith masses)

harmonic oscillation in norm

al coordinates

(6 needed for translation and rotation)

IR &

Ram

an are complem

entary methods to m

ap out m

olecular vibrations

polarization of a vibrational mode

a real molecule: superposition of norm

al-modes:

note: energy distributed among all m

odes equally:

IR spectrom

eters in spacespectrom

eters in the lab

conventional spectrometer: dispersive

IR spectrom

eters

FT

IR fourier transform

infrared spectrometer

Michelson interferom

eter

for FT

IR, w

e use broad incoherent IR source

(something hot)

for each mirror position, w

e measure the

incoherent sum of all w

avelength, each in its special interference condition

this way w

e measure the F

T of the transm

itted intensity. if w

e sample a large am

ount of mirror

positions, we can calculate back the original

spectrum

C. W

estermeier,... C

. Liewald, F

. Keilm

ann, BN

, Nature C

omm

unications (2014)

Ram

an

relative to HeN

e