2. Molecular photophysics

62

Kasha's rule In the electronic excited state, molecules quickly relax to the lowest vibrational level (Kasha-Vavilov's rule), and from there can decay to the lowest electronic state via photon emission or non-radiative processes.

(π, π*)(n, π*)

n

π*

π

S0 S1 S2

220 260 300 340 380 0

0.2

0.4

0.6

0.8

O

(π, π*)

(n, π*)

Wavelength / nm

Abs

orba

nce

Example of benzophenone

S0

S1

S2

2.1 Excited state deactivation pathways

63

Jablonski's diagram

S0

S1

S2

T1

VR

ISC

IC

fluor

esce

nce

abso

rptio

n

T-T absorption

phosphorescence

VR

VR

ISC

IC

abso

rptio

n (1

0–16

s)

VR

(~

10–1

2 s)

fluorescence (10–9-10–6 s)

phosphorescence (10–4-102 s)

internal conversion IC (10–9-10–6 s)

intersystem crossing ISC (10–9-10–6 s)

{radiative decay pathways

non-radiative pathways

T2

{vibrational relaxation VR (10–13-10–12 s)

C O

64

Spin correlation effect

ΔE1,3

(n, π*)

T1S1

S0

(π, π*)

T1

S1

S0

ΔE1,3

E

nπ*

π

In addition to Coulombic interaction, magnetic interaction causes the repulsion between two electrons occupying different orbitals to be maximal when their spins are parallel.

In a triplet excited state, the two single electrons sitting on the HOMO and the LUMO, respectively, tend to adopt a configuration maximizing their spatial separation and, thus, the transient dipole moment. This results in a lower energy level for T1 compared to S1 state. This spin correlation effect is more pronounced for spatially overlapping HOMO and LUMO orbitals, such as in (π, π*) state, and is less important for (n, π*) state, for instance.

S1

65

Internal conversion (IC) implies the transformation of electronic excitation into vibrational energy. This process takes place through nuclear tunneling from the excited state potential surface to that of the ground state. Strong overlap of vibrational wave functions is necessary.

Since back-tunneling can also readily occur, fast vibrational relaxation (VR) is an important condition for this deactivation pathway.

nuclear coordinate

E

VR

S0

Non-radiative deactivation processes

hν

hν'

ICIC

T1

66

Intersystem crossing (ISC) is a special case of internal conversion, w h i c h t a ke s p l a c e between an electronic e x c i t e d s t a t e a n d another excited state charac ter i zed by a different spin multiplicity (S1 → T1, for instance). This process involves a simultaneous spin flip.

Vibrational relaxation is also necessary to avoid crossing back to the initial system.

nuclear coordinate

E

S0

ISC

hν

S1

Non-radiative deactivation processes

T1

S0

S1

hν''hν'hν

E

67

Radiat ive deact ivat ion (photo-emission) processes are electronic transitions. They are submitted to the same selection rules as the light absorption. Fluorescence is the radiative deactivation pathway taking place between two states of identical spin multiplicity. This transition is spin-allowed.

Phosphorescence, by definition, is a spin-forbidden radiative deactivation process taking place between two states of different spin multiplicities.

According to Kasha's rule, radiative processes usually occur from the lowest vibronic excited state at a given spin multiplicity. This is not a strict rule and there are exceptions.

Radiative deactivation processes

fluorescence

phosphorescence

68

Emission spectrum

E

nuclear coordinate hν

The applicability of the Franck-Condon p r i n c i p l e i n b o t h a b s o r p t i o n a n d fluorescence, along with Kasha's rule leads to an emission spectrum appearing as the approximate mirror image of the absorption.

The 0-0 vibronic transition, common to both spectra, corresponds to their crossing point.

69

Stokes shift

//wavelength

//

fluorescence

phosphorescence

0-0

Stokes shift is the difference (in wavelength or frequency units) between positions of the band maxima of the absorption and emission spectra of the same electronic transition. A small Stokes shift is indicative of a rigid molecule, with little change in the equilibrium nuclear configuration in the ground- and excited states.

Systems characterized by large Stokes shift have important applications, such as optical brighteners and invisible inks, which absorb UV light and emit in the visible.

70

Solvation dynamics

Solvent dipoles have then to rearrange around the excited molecule. This process involves the rotation of solvent molecules and depends on the viscosity. It is fast enough to take place prior to the fluorescence, whose spectrum is, thus, red shifted in a polar medium.

In addition to internal nuclear coordinates, solvation coordinate has also to be considered when a molecule dissolved in a polar solvent absorbs light. Upon photoexcitation, the dipole moment of a solvated chromophore is modified.

hν M

solvent dipoles relaxation

solvent dipole

chromophoresolvation coordinate

E

71

Kinetics of excited state's radiative decay

Radiative decay of an excited state is a random process, therefore following a first order rate law:

M + hν   →  M* →   M + hν'

−ddt [M*] = kr

0 ⋅[M*]   ∫⎯ →⎯   [M*]t  = [M*]0 ⋅ exp (–kr0 ⋅ t)

kr is the (natural) radiative rate constant. It is identical to the Einstein coefficient A0←1 for spontaneous emission.

kr0

is called the period or lifetime of the excited state and should not be confused with the half-life time .

τ r0

t1/2

τ r0  =  1

kr0 t1/2  = 

ln2kr0≠

Inte

nsity

(co

unts

)

101

102

103

Time / ns0 1 2 3 4 5

TCSPC data

2.2 Kinetics of photophysical processes

72

Kinetics of excited state's radiative decay

τ r0  =  1

kr0  = 

3.417 ⋅108

ν 2nm ⋅n

2 ⋅ A =  2.210 ⋅108

ν 2nm ⋅n

2 ⋅ εmax ⋅ Γ

Single-peak Lorentzian absorption band

ν

ε

Γ

εmax

νmax ε(ν) dν∫ = A

transition intensity

The probabilities of a transition occurring between the ground state (0) and an excited state (1) and vice versa in the processes of light absorption and spontaneous emission, respectively, are linked together by Einstein's expression of coefficients A1←0 (absorption) and A1→0 (emission):

τ r0  ≈ 10

−4  [mol-1 ⋅ l ⋅ cm-1 ⋅ s]εmax  [mol

-1 ⋅ l ⋅ cm-1]

[cm-1] ε(ν ) dν∫   [mol-1 ⋅ l ⋅ cm–2 ]refractive index

In the UV :

kr0  = A0←1  = 

8π ⋅ c ⋅ ln(10) ⋅105

NA

 ⋅ ν  2 ⋅ n2 ⋅ A

73

Radiative lifetime of organic fluorophores

  calculated experimental

benzene 407 414

benzylic alcohool 237 362

toluene 174 200

ethyl-benzene 185 172

p-xylene 92.5 75

phenol 29 26

anthracene 12.9 13.8

9,10-dichloro anthracene 10.4 15.5

perylene 4.7 6.8

τ r0 [ns]

M

Allowed transition

Symmetry forbidden transition

ƒ1,0 = 1 Γ = 3'000 cm–1

= 35'000 cm–1 ( max 290 nm)

= 1.2 ns

ƒ1,0 = 2·10–4 Γ = 3'000 cm–1

= 35'000 cm–1 ( max 290 nm)= 6 µs

ƒ1,0 = 2·10–7 Γ = 3'000 cm–1

= 35'000 cm–1 ( max 290 nm)

= 6 ms

Spin forbidden transition(phosphorescence)

τ r0

τ r0

τ r0

νmax

νmax

νmax