Methods Sensitive toFree Radical Structure

• Resonance Raman

• Electron-Spin Resonance (ESR) or Electron Paramagnetic Resonance (EPR)

Motivation

• Absorption spectra of free radical and excited states are generally broad and featureless

• Conductivity is not species specific

• Conductivity is additive with respect to ionic content of the cell

Specific Vibrations?

• Now have vibrational spectroscopy in laser flash photolysis, usually in organic solvents

• Water is a good filter of infrared and masks vibrational features of free radicals

• Raman is weak, second-order effect

• What about Resonance Enhanced Raman?

Medium

Emergent light+-

EiIncident light

s = 0

0

s = 0 mn

s Scattered light

RamanRayleigh

LIGHT SCATTERING

Pi = αij Ej

P = Induced electric dipole momentE = Electric field of the electromagnetic

radiation αij = Elements of polarizability tensor

G.N.R. Tripathi

Imn = Const. I0 (0 mn)4 I( ) mn I2

( ) mn = (1/h) MmeMen / (em 0 + i e) e + non-resonant terms

e

n

m

mn

em0

ENHANCEMENT OF RAMAN SCATTERING

(via αij )

Probability

Amplitude

G.N.R. Tripathi

RESONANCE RAMAN

em >> 0 Normal Raman

em - 0 ~ 0 Resonance Raman

|( ) mn 2 = Const. × (MmeMen)2 / 2

Enhancement up to 107-108

Pulse radiolysis time-resolved resonance Raman

Identification, structure, reactivity and reaction mechanism of short-lived radicals and excited electronic states in condensed media

Relevance: Theoretical chemistry, chemical

dynamics, biochemistry, ,paper and pulp-industry, etc.

G.N.R. Tripathi

1000 1200 1300 1400

Raman shift (cm-1)

[Ru(bpy)2dppz]2+ bound to DNA

NODNA present

DNA present

2,2’- bipyridyldppz = dipyridophenazine

http://www.lot-oriel.com/site/site_down/cc_appexraman_deen.pdf

Two-slit experiment

Selection Rulesfor the Amplitudes of Transitions

Electronic Transition Elements

(Dipole allowed)

Franck-Condon Factor

For Resonance enhancement bothmust be non-zero

http://www.personal.dundee.ac.uk/~tjdines/Raman/RR3.HTM

Relationship to Radiationless Transitions and Absorption

dP(nm)/dt = (42/h) |Vmn|2 FC (Em)

This is a probability. Quantum mechanics usually calculates amplitudeswhich are “roughly the square root” (being careful about complex numbers)

Taking the square root, shows that the amplitudes forradiationless transitions are first-order in the interaction V

Likewise, simple absorption and spontaneous emission are first-orderprocesses with regard to an interaction Vrad

Connection to Wavefunctions

- abb )(),(),( dxafabKtx

So we can use the path integral to see how onenon-stationary state (f) at time ta propagates into another

at time tb

abfor,0),( ttabK

In terms of the stationary states of the system

ababa*

b1

for,)(exp)()(),( ttttEi

xxabK nnn

n

Expansion of part of exponential for small potentials

22

),(!2

1),(1),(exp

b

a

b

a

b

a

t

t

t

t

t

tdttxV

idttxV

idttxV

i

),(),(),(),( )2()1(0V abKabKabKabK

Putting this back into the Amplitude Kv(b,a) gives aperturbation expansion

of thepath integral

Interpretation of First Term

)(2

exp),( 20 tDxdtx

miabK

b

a

t

t

b

a

Represents propagation of a free particle from (xa,ta) to (xb,tb)with no scattering by the potential

V

a

b

Second Term

)(),(2

exp),( 2)1( tDxdsssxVdtxmii

abKb

a

b

a

t

t

b

a

t

t

Interpretation of Second Term

b

a

b

a

t

t

b

a

t

tdstDxssxVdtx

miiabK )(),(

2exp),( 2)1(

x

t

tb

tc

ta a

c

b

c0- cc02 ),(),(),()(),(

2exp dxacKtxVcbKtDxssxVdtx

mib

a

t

t

b

a

Particle moves from a to c as a free particle.At c it is scattered by V[x(s),s] = Vc.After it moves as a free particle to b.The amplitude is then integrated over xc,namely over all paths.

Physical Meaning of 2nd Term

Represents propagation of a particle from (xa,ta) to (xb,tb)that may be scattered once by the potential at (xc,tc)

V

a

b

b

a

t

tdtdxacKtxVcbK

iabK cc0- cc0

)1( ),(),(),(),(

c

Interpretation of Third Term

Represents propagation of a particle from (xa,ta) to (xb,tb)that may be scattered twice by the potential,

once at (x(s),s) and once at (x(s),s)

)(),(),(2

exp2

1),( 2)2( tDxsdssxVdsssxVdtx

miabK

b

a

b

a

b

a

t

t

t

t

b

a

t

t

V

a

b

Selection Rules (A-term)

A-term:  Condon approximation - the transition polarizability is controlled by                the pure electronic transition moment and vibrational overlap                integrals

The A-term is non-zero if two conditions are fulfilled: (i)    The transition dipole moments []ge0 and []eg0 are both non-zero.

(ii)   The products of the vibrational overlap integrals, i.e. Franck-Condon         factors, <ng|e><e|mg> are non-zero for at least some values of

        the excited state vibrational quantum number .

Consideration ofFranck-Condon

Factors

<ne|g> = 0orthogonal

<ne|g> 0Non-symmetricOr Symmetric

TotallySymmetricVibrationalMode

TotallySymmetricVibrationalMode

<ne|g> 0<ne|g> 0

http://www.personal.dundee.ac.uk/~tjdines/Raman/RR4.HTM

Why must these modes totally symmetric vibrations?

Hg(Q) = Qg + (k/2)Q2

He(Q) = Qg + Q + (k/2)Q2

All terms in the Hamiltonian must be totally symmetric,Therefore, the displacement Q must also be totally symmetric

G.N.R. Tripathi

G.N.R. Tripathi

G.N.R. Tripathi