gigasecond

Excited-State Processes
+B
kq
A*
Products
Unimolecular Processes:
kp
P
knr
kr
kr: radiative deactivation (emission)
knr: radiationless deactivation
kp: chemical reaction
Bimolecular Processes:
A
kq: bimolecular quenching of A*
(“products” include energy, electron,
and proton transfer between A and B)
The timescale of photochemical events
1s
-3
10 s
ms (milliseconds)
10-6 s
µs (microseconds)-
10-9 s
ns (nanoseconds)
10-12 s
ps (picoseconds)
10-15 s
fs (femtoseconds)
- fs is the lower limit of the chemistry time scale.
- electron motion in molecules takes place in fs.
- photon absorption (excitation) take place in fs.
The time scale
Power
Units
e.g.,
Light travels…
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15
-16
-17
-18
Exasecond
31.7 109 years
age of universe
31.7 billion light-years
Petasecond
31.7 10 years
oligocene
31.7 million light-years
Terasecond
31.7 103 years
entering prehistory
31.7 thousand light-years
Gigasecond
31.7 years
1 human generation
31.7 light-years
Megasecond
11.6 days
1 generation of Drosophila
0.32 light-years
Kilosecond
16.7 min
coffee break
300 million Km
second
heartbeat
300 thousand Km
millisecond
camera shot
300 Km
microsecond
free radicals
300 m
nanosecond
electr. excited molecules
30 cm
picosecond
energy/electron transfer
0.3 mm
6
mol. vibrations
femtosecond
0.3 µm
electron motion in atoms
attosecond
3Å
Excited-State Processes
+B
kq
A*
Products
kp
P
knr
kr
A
Unimolecular Processes:
kr: radiative deactivation (emission)
knr: radiationless deactivation
kp: chemical reaction
Radiative deactivation (Emission)
A*
kr
A + hν
64π 4ν 3
2
kr =
µ
12
3h2
A*
µ12 = ∫ Ψ1µΨ2 dq ∫ S1S 2 dξ ∑ Χ10 Χ 2 n dQ
n
kr
A
Same selection rules as for absorption. In particular,
spin-allowed emission
Fluorescence
spin-forbidden emission
Phosphorescence
Again, Franck-Condon factors do not affect kr, but
determine the shape of the emission band.
Rilassamento vibrazionale (“termalizzazione”) degli stati eccitati
per Franck-Condon, le molecole
elettronicamente eccitate vengono spesso
formate con un eccesso di energia
vibrazionale rispetto all’ambiente circostante
(cioè sono “calde” rispetto alla T del mezzo).
10-12 s
hν
In fase condensata, le molecole perdono il
loro eccesso di energia per collisione con il
mezzo in tempi dell’ordine di pochi
picosecondi (qualche vibrazione).
La maggior parte dei processi fotochimici e
fotofisici di interesse avvengono in tempi >
10-11s . Perciò gli stati eccitati,
indipendentemente dalla loro formazione, si
possono considerare a tutti gli effetti sul
livello v = 0.
Franck-Condon Factors and Absorption/Emission Bandshape
Stokes Shift and Excited-State Distortion
Stokes Shift
0 1 2 3 4 5
0 1 2 3 4 5
1.2
1
em
abs
0.8
0.6
0.4
0.2
0
0.7-10.0
0.6
0.5
-5.0
em
abs
0.0
5.0
10.0
5.0
10.0
5.0
10.0
5.0
10.0
5.0
10.0
wavenumbers (kK)
0.4
0.3
0.2
0.1
0
0.4-10.0
0.3
-5.0
em
abs
0.0
wavenumbers (kK)
0.2
0.1
0
0.4-10.0
0.3
-5.0
em
abs
0.0
wavenumbers (kK)
0.2
0.1
0
-10.0
0.3
0.25
-5.0
em
abs
0.0
wavenumbers (kK)
0.2
0.15
0.1
0.05
0
-10.0
-5.0
0.0
wavenumbers (kK)
CH2
CH
CH3
anthracene
(OH)HC
O
N
quinine
N
Excited-State Processes
+B
A*
Products
kq
kp
P
knr
kr
A
Unimolecular Processes:
kr: radiative deactivation (emission)
knr: radiationless deactivation
kp: chemical reaction
Radiationess Transitions
knr
A*
A*
knr
A
A
2π
2
Ψ1 H ' Ψ2 ρ 2
h
Fermi’s golden rule
k nr =
k nr =
2
2π
0
n
Ψ
S
H
'
Ψ
S
dqd
ξ
X
X
dQ
∫ 1 1
∫ 1 2
2 2
h
H’ is that part of the Hamiltonian responsible for driving the process.
- spin orbit coupling operator for spin-forbidden transitions
- nuclear kinetic energy (vibronic coupling) for spin-allowed
ρf(E) is the density of vibrational states of A isoenergetic with A*
k nr =
2π
h
0
n
∫ Ψ1S1H 'Ψ2 S 2dqdξ ∫ X 1 X 2 dQ
2
Electronic factors: Spin Selection Rule
spin-allowed
internal conversion
spin-forbidden
intersystem crossing
El Sayed Rule:
ISC allowed if change of orbital configuration (rotation of charge density)
Franck-Condon factor
2
2π
0 n
Ψ1S1H'Ψ2S2dqdξ Σ n∫ X1 X2 dQ
Radiative case, kr =
∫
h
2
2π
0 n
Radiationless, kr =
Ψ1S1H'Ψ2S2dqdξ ∫ X1 X2 dQ
∫
h
FC factor extremely important in determining knr.
=1
Radiationless transitions.
Role of the Franck-Condon factor
A*
A
A*
A
“Nested” states.
“Crossing” states.
Bad Franck-Condon factor.
Classically, abrupt change in
nuclear kinetic energy.
Good Franck-Condon factor.
Classically, nuclear kinetic
energy is conserved.
Slow process. Rate
decreases with increasing
“energy gap”.
Very fast process
Energy Gap Law
Poor overlap
Better overlap
Deuteration Effect
knr
A*
A
C-H
knr
A*
A
C-D
Kasha’s Rule:
Radiative (and most other intersting) processes always occur from S1 or T1,
independent on the energy of initial excitation
S3
S2
T3
S1
T2
T1
S0
Rationale: Small energy gaps between
excited states, large energy gap between S1
and the ground state. Very fast, 100%
efficient radiationless deactivation from
upper states to S1.
Consequence: Simplified effective Jablonski
diagram
e.g., perylene
So → S2
1.6
S1 → S0
1.4
Abs/em int.
1.2
1.0
So → S1
0.8
0.6
0.4
0.2
0.0
-0.2
excitation
200
300
excitation
400
500
600
λ
Emission = Fluorescence from S1
Independent (constant Φ) on excitation wavelength
700
Excited State Kinetics
+B
A*
Products
kq
[A*]0
kp
P
knr
[ A*] 0
2 .72
kr
τA*
A
−
d [A *]
= (k r + k nr + k p ) [A *] = ∑ik i [A *]
dt
excited-state decay kinetics
efficiency of process i
ηi =
ki
∑ ik i
τ A* =
1
(kr + knr + k p ) =
1
∑iki
excited-state lifetime
Quantum yield of Φ = η (− Α*)η = ki
i
∑i ki
process i
Kinetic Scheme
Dependence of experimental parameters τS, Φf, τT, Φp on rate constants of individual processes
S1
kisc
τS = 1/(kF + kIC + kISC)
T1
kp
kf
kic
Φ f = η f(S 1) = kf/(kf + k ic + kIisc ) = kf τS
τT = 1/(kP + kISC’)
kisc’
Φ p = η isc (S 1) × η r(T1) = η isc (S 1) × [kp/(k p + k isc’)] = η isc (S1) kpτT
η isc (S1) = k isc /(kf + k ic + kIisc ) = k isc τS
S0
Example:
Lowest π−π* state
Example:
Lowest n−π* state
0.9
Organic chromophores
“typical” behavior
Lowest π−π∗ states
Lowest n−π∗ states
− τ(S1), ns
− τ(S1), ps
− ΦF = 0.1-1.0
− ΦF = 0
−ηISC < 1
− ηISC = 1
−ΦF+ ηISC ≈1
−ηIC = 0
− ηIC = 0
− τ(T1), µs-ms
− τ(T1), ms-s
Excited-State Processes
+B
A*
Products
kq
kp
P
knr
kr
Unimolecular Processes:
A
kr: radiative deactivation (emission)
knr: radiationless deactivation
kp: chemical reaction
stati elettronici eccitati
****R
***R
**R
Y
⇒
FOTOCHIMICA
⇒
CHIMICA
X
*R
hν
R
P
stato fondamentale
k
R
P
E
transition state
reactants
∆G #
∆G 0
MR
k = (kBT/h) exp(-∆G#/RT)
products
TS
reaction coordinate
MP
e.g.,
k = (k BT/h) exp(-∆G#/RT)
HCHO → H2 + CO
H
C O
H
H
C O
H
H
H
+C O
Excited states are short-lived
⇓
to be efficient, excited-state reactions must be
very fast: i.e., activationless or downhill
prototype reaction:
breaking (stretching) of a σ bond
Stretching of a σ Bond
e.g., H-H, CH3-CH3
Correlation of states:
- Same spin
-Same symmetry
-No state crossing between states of
same spin&symmetry
Rules for the correlation of states
between different molecular geometries
- must have the same spin
- must have the same symmetry
- states of same symmetry and spin can never cross
Ψ = c1Ψ10 + c2Ψ20
( E1 − E2 ) 2 − 4 H 12
E1 + E2
m
E=
2
2
c1 (E1 − E ) + c2 H12 = 0 


(
)
c
H
c
E
E
+
−
=
0
 2 12 2 2

2
1
0.8
alf
0.6
a%
% AB
%A+B-
0.4
0.2
0
-20
-10
0
10
20
30
40
Stretching of a σ Bond
e.g., H-H, CH3-CH3
S2
Z2
Z1
S1
T1
3
D
D
1
S0
Schematic State Correlation
prototype reaction:
twist around a double bond
(cis-trans isomerization)
A
A
B
A
B
B
A
B
State correlation diagram
(no inforamtion)
S2(π∗2)
S2(π∗2)
S1(ππ∗)
S1(ππ∗)
T1(ππ∗)
T1(ππ∗)
S0(π2)
S0(π2)
A
B
A
B
cis
A
B
B
A
trans
S 2(π∗2 )
S2 (π∗ 2 )
S1 (ππ∗)
S1(ππ∗)
T1(ππ∗)
T1 (ππ∗)
S0(π 2 )
S 0(π 2 )
A
B
A
B
cis
A
B
B
A
trans
orbital correlation
A
A
B
A
B
B
B
state correlation
A
π∗
S 2(π∗2 )
S2 (π∗ 2 )
S1 (ππ∗)
S1(ππ∗)
T1(ππ∗)
T1 (ππ∗)
S0(π 2 )
S 0(π 2 )
π∗
π
π
A
A
A
B
B
B
A
B
A
A
B
B
A
B
B
A
A
B
cis
A
B
A
B
B
A
trans
cis
trans
S 2(π∗2 )
S2 (π∗ 2 )
S1 (ππ∗)
S1(ππ∗)
T1(ππ∗)
T1 (ππ∗)
S0(π 2 )
S 0(π 2 )
A
B
A
B
cis
A
B
B
A
trans
state correlation
real potential energy
S 2 (π∗2 )
S 2 (π∗2 )
S 1 (ππ∗)
S 1 (ππ∗)
T1 (ππ∗)
T1 (ππ∗)
S 0 (π 2 )
S 0(π 2 )
A
B
A
B
cis
A
B
B
A
trans
Photochromic Diarylethenes
e.g.,
1 .5
R
R
N
O
hν (430 nm)
N
O
O
0 .9
A
O
1 .2
R'
R'
S
S
R'
hν (530 nm)
S
S
R'
closed
open
0 .6
0 .3
0 .0
300
400
500
nm
600
Cylobutene → Butadiene
CONROT
DISROT
Ground vs excited states: different reactivity?
Answer: correlation of MOs and states between reactant and products.
CONROT
Relevant
symmetry
element:
C2
C2
DISROT
σv
C
Relevant
symmetry
element:
σv
C2
σv
C
C2
σv
C
Symmetry must be maintained along the reaction coordinate
Cyclobutene – Butadiene
conrotatory ring opening/closure
CH3
CH3
H
H
Orbital Correlation:
State Correlation:
φ4∗
σ∗
π∗
φ3∗
π
φ2
σ
φ1
-thermally allowed
-photochemically forbidden
σπ2σ∗
Φ1Φ22Φ4∗
Cyclobutene – Butadiene
disrotatory ring opening/closure
CH3
CH3
H
H
σv
σv
Orbital Correlation:
State Correlation:
σ∗
φ4∗
π∗
φ3∗
σ2 π∗2
π
φ2
σ
φ1
-thermally forbidden
-photochemically allowed
Φ1 2Φ3∗2
conrotatory
disrotatory
Hexatriene-Cyclohexadiene
disrotatory ring closure/opening
Hexatriene-Cyclohexadiene
disrotatory ring closure/opening
H
CH3
H H
H
CH3
CH3 CH3
σv
σv
- thermally allowed
- photochemically
forbidden
H
CH3
H H
C2
CH3
CH3
CH3 H
C2
- thermally forbidden
- photochemically
allowed