Radiationless Transitions
• Spin allowed
• Spin forbidden
Chapters 3 & 5
Principles of Molecular Photochemistry: An Introduction
NJT, VR and JCS
Transition Between States
S0 + hn S1 spin allowed absorption
S1 S0 + hn spin allowed emission
(fluorescence)
S1 S0 + ∆
spin allowed radiationless
transition
(internal conversation; IC)
S1 T1 + ∆ spin forbidden radiationless
transition
(intersystem crossing; ISC)
S0 + hn T1 spin forbidden absorption
T1 S0 + hn spin forbidden emission (phosphorescence)
T1 S0 + ∆ spin forbidden radiationless conversion
(intersystem crossing)
]...)[(
][
1
1
Skkk
Sk
iciscf
f
f
+++
=φ
01
11
01
10
SS
TS
hSS
ShS
ic
isc
f
abs
k
k
k
I
!→!
!→!
+!→!
!→!+
ν
ν
Why radiationless transition matters?
Competes with fluorescence and phosphorescence
kisc
krt kqtkqskrs
- hν
T1
S1
S0
- hν '
F0. c0. S0
(F1. c1. S1)*1
(F2. c1. S1)*3
• Changes in electronic, vibrational and spin configurations without the
help of a photon
• Energy redistribution--electronic to vibrational
Radiationless Transitions
Visualization of vibrational levels within an
electronic energy surface
Harmonic Anharmonic
Relative position of energy surfaces
(F1. c1. S1)*1
(F1. c1. S1)*3
F0. c0. S0
Matching vs. Crossing Surfaces
For the same energy gap the rates are different for the two types of surfaces
The S1 and S0 potentials exhibit small
relative displacements. Significant
overlaps between their vibrational
wave functions are obtained only for
small energy separations, ES1−S0.
The IC probability decreases
exponentially with increasing energy
gap. This exponential dependence of
the transition probability on E is
usually dubbed the Energy Gap
Law.
Matching surfaces (e.g., polyaromatics)
Equilibrium geometries similar
S0
Basis of energy gap law during radiationless
transition in nested surfaces: Vibrational overlap
Nested or matching
surfaces:
Extent of vibrational
overlap depends on the
energy gap
f ~ exp-DE
kIC ~ 1013fn
kIC ~ 1013exp-aD
Matching (nested) surfaces
Vibrational overlap can be off-set by density of states
Density of
states large
Density of
states small
Large energy gap favors higher density of states as the vibrational levels that
overlap would be in the region with have higher density. Thus energy gap and
density of states work in opposite direction.
Dependence of rate of kIC (S1 to S0) on energy gap
Dependence of rate of kISC T1 to S0 on energy gap
Overlap between lowest vib level
of T1 and high (degenerate) vib
level of S0)
T1
S0
Conversion of electronic to vibrational energy
Three step process: (i) upper vibrational to lower vibrational level in excited state
(ii) lower vibrational level to upper vibrational of the lower state
(iii) upper vibrational of the lower state to lowest vibrational level
Step 1Step i
Step ii
Step iii
Visualization of
Electronic Energy to Vibrational Energy Transfer
Intramolecular vibrational relaxation (IVR) occurs within 10 to 0.1 ps
Intermolecular vibrational energy transfer (VET) from the
molecule to the solvent occurs in the time range 100 to 10 ps
Crossing surfaces
Equilibrium geometries dissimilar
S0
Weak Coupling
Strong coupling
(F1. c1. S1)*1
(F1. c1. S1)*3
F0. c0. S0
Matching vs. Crossing Surfaces
For the same energy gap the rates are different for the two types of surfaces
Basis of Kasha’s Rule
S2 to S1 IC is fast due to possible
surface crossing and smaller gap
S1 to S0 IC is slow due to
matching surface and larger gap
S2 to S1 IC can be slow if gap is
larger and the surfaces don’t
cross
Kasha’s Rule
All photophysical and
photochemical processes usually
start in S1 or T1, irrespective of
which excited state or vibrational
level is initially produced.
Energy Gap Law and Azulene Anomaly
Fluorescence occurs only from S1 to S0; phosphorescence occurs
only from T1 to S0; Sn and Tn emissions are extremely rare (Kasha's
rule).
S2 to S1 rate vs Energy Gap
Role of vibrational level (nn) on radiationless process
Bond Type Vibrational Frequency
Type
C=C stretch 2200 cm-1
C=O stretch 1700 cm-1
C=C stretch 1600 cm-1
N=N stretch 1500 cm-1
C-H bend 1000 cm-1
C-C stretch 1000 cm-1
C-C bend 500 cm-1
C-H stretch 3000 cm-1
C-D stretch 2100 cm-1
Electronic to Vibrational Energy Transfer
High frequency vibrations are important in radiationless transitions.
Vibrational level to match the gap is of lower # with high frequency vibrations.
C-H stretch 3000 cm-1
C-D stretch 2100 cm-1 Higher vibrational
level needed to
match; poor
overlap, slow
decay, large FP
Isotope Effect on
Rate of T1 to S0
T1
S0
Effect of deuteration on radiationless process (T1 to S0)
Birks book
perprotonated
q perdeuterated
Mikkel Bregnh.j, Michael Westberg, Frank
Jensen and Peter R. Ogilby, Phys. Chem.
Chem.Phys., 2016, 18, 22946
Decay of singlet oxygen depends
on solvent and deuteration
Vibrational effects on singlet oxygen lifetime
In aromatics because of the large S1 to S0 energy gap internal
conversion does not compete with kISC and kF
(exception)
For large aromatic molecules the sum of the quantum yields of
fluorescence and ISC is one i.e., rate of internal conversion is very slow
with respect to the other two (Ermolaev’s rule).
(F1. c1. S1)*1
(F1. c1. S1)*3
F0. c0. S0
Internal conversion in matching vs. crossing surfaces
For the same energy gap the rates are different for the two types of surfaces
Breakdown of Born-Oppenheimer Approximation
Mixing of surfaces
For the same nuclear configuration
there are two electronic configurations
with identical energies. Under
favorable conditions this would lead
to mixing resulting in avoided
crossing.
Two surfaces with different
electronic or spin configurations
Energy is fine, but
orbitals don’t overlap
Breakdown of Born-Oppenheimer Approximation
Vibronic mixing enables surface mixing
Intersystem crossing in
carbonyl compounds (np*)
Intersystem crossing in aromatic molecules (pp*)
and and olefins (pp*)
Intersystem Crossing in
Diradicals and Radical Pairs
Spin forbidden transitions
R(S0) + hν → *R(S1)
R(S0) + hν → *R(T1)
*R(T1) → R(S0) + hν
*R(T1) → R(S0) + heat
*R(S1) → R(T1) + heat
T1
S1
S0
kisc
kisc kP
Intersystem crossing in
molecules with np* and pp* states
O
Singlet-Triplet Transitions
Role of Spin-Orbit Coupling
T1
S1
S0
T1 + λ S1
Spin-Orbit coupling mixes the states,
no longer pure states
S1
S0
Breakdown of Born-Oppenheimer Approximation
Spin-Orbit coupling enables surface mixing
For the same nuclear configuration
there are two spin configurations.
Coupling between the two surfaces
could lead to mixing and result in
avoided crossing.
Two surfaces with different spin
configurations.
Breakdown of Born-Oppenheimer Approximation
Spin-orbit coupling facilitated by vibronic mixing enables surface mixing
Two spins of ½: S = 1
Spin multiplicity= 2S+1 = 3
a
b
MS=0
αβ−βα
a
a
b
b a
b
MS=1 MS=-1 MS=0
Ms1
Ms1
Ms1
Ms2
Ms2
Ms2
αα ββ αβ+βα
Two spins of ½: S = 0
Spin multiplicity = 2S+1 = 1
Angular momentum vector representations of two
electron system: Singlet and Triplet
Spin interconversion in one spin system
Sz
a
q
Sz
b
q
Sz
a
Sz
b
q
q
z
S1a
Hi
z
S1a
Hi
z
S1a
Hi
S1 and Hi
uncoupuled
S1 and Hi coupuled to
yield the resultant S1 + Hi
S1 and Hi precess about
resultant
z
S1a
Hi
z
S1b
Hi
Hx or Hy
Zero Field a b a b
High Field b
a
b
a
D-
D+
D-
D+
Spin interconversion in one spin system in zero and
high magnetic field
Spin interconversion in two spin system
High Field
X
T-
T0
T+
S
X
T+
S
T-
T0
T+
S
Spin interconversion in two spin system
High Field
T-
T0
T+
T-
T+
ST0 S
S1
S2
S1
S2 S2
S1
triplet,T0 singlettorques producing
a rotation of S2 about z
Z axis Z axis
S1
S2
tightly coupled loosely coupled tightly coupled
Hz
Spin interconversion in two spin system (Spin rephasing)
S1 S2
S1 S2
S2
S1
triplet,T+ singlet,Storques producing a
rotation of S2 about x or y
S1 S2
tightly coupled loosely coupled tightly coupled
Hx (or Hy)
X, Y axis
Spin interconversion in two spin system: Spin flipping
Available Internal Magnetic Fields
An external magnetic fields cannot be responsible for the singlettriplet
transition, because it would act equally on both spins.
External and Internal Magnetic Fields
spin orbital
Angular momentum
Magnetic moment
Precession and Spin-Orbit coupling
Besides an external magnetic field another source of coupling is
the spin-orbit coupling: if L is coupled to S, they both precess
around their resultant. The rate of precession about an axis is
proportional to the strength of the coupling of the spin to the new
magnetic field.
The power of the magnetic field generated is proportional to the
rate of precession.
When L and S are strongly coupled it is difficult for other forces to
break the coupling
• The strength or energy (ESO) of spin-orbit coupling is directly
proportional to the magnitude of the magnetic moment due to electron
orbital motion, µL (a variable quantity depending on the orbit), and the
electron spin, µS (a fixed quantity).
• Spin-orbit coupling in organic molecules will be effective in inducing
transitions between different spin states if one (or both) of the electrons
involved approaches a “heavy” atom nucleus that is capable of causing
the electron to accelerate and thereby create a strong magnetic moment
as the result of its orbital motion for a one electron atom, zSO ~ Z4).
• For maximum effect of the nuclear charge, the electron must be in an
orbital that approaches the nucleus closely, i.e., an orbital with some scharacter,
since s-orbitals have a finite probability of being located near
or even in the nucleus!
More on Spin-Orbit Coupling
S
µS
z
S
µS
z
The electron possesses a spin magnetic moment due to its charge and spin.
The magnetic moment µs is quantized in magnitude and orientation as the
angular momentum S from which it arises
Magnetic moment due to spin
Magnetic moment of an orbiting electron
An electron in a Bohr atom is modeled as a point charge rotating
about a fixed axis centered in the nucleus. Then it possesses an
orbital magnetic moment:
µL= -(e/2m) L
nucleus
spin
Field at a molecular level is generated from the orbital motion of
the electron around the nucleus.
€
ˆHSO = ζl⋅ s
ζn,l ∝
Z4
n3
l(l +1/2)(l +1)
The Spin-Orbit coupling constant depends on the fourth power of
the atomic number and its effect is very large for heavy atoms.
Spin-Orbit Coupling and Heavy Atom Effect
Spin-orbit coupling energies for selected atoms
Spin-orbit coupling parameter is related
to atomic number
The heavy atom effect on spin transitions
The “heavy atom” effect is an “atomic number” effect that
is related to the coupling of the electron spin and electron
orbital motions (spin-orbit coupling, SOC).
Most commonly, the HAE refers to the rate enhancement
of a spin forbidden photophysical radiative or
radiationless transition that is due to the presence of an
atom of high atomic number, Z.
The heavy atom may be either internal to a molecule
(molecular) or external (supramolecular).
Internal Heavy Atom Effect: Spin forbidden absorption
I
I
Cl
Cl
CCl4
Pure liquid
C2H4Br2
C2H5I
External Heavy Atom Effect: Spin forbidden absorption
400
λ (nm)
ε
0.15
350
CH3
CH2
Ι solvent
450 500
T1(π, π*)S0
High pressure
of xenon
Cl
0.10
0.05
External Heavy Atom Effect: Spin forbidden absorption
Influence of Heavy Atom Effect on ISC and phosphorescence
F. Wilkinson in Organic molecular physics, J. B. Birks (ed.), Wiley, 1975. p. 126
Turro et. al., JACS, 93, 1032, 1971
Non-Radiative decay from T1
Radiative decay from T1
M Zander, G Kirsch - Zeitschrift für Naturforschung A, 1989, 205
Intersystem crossing
in carbonyl compounds and others with np*)
Spin-orbit coupling in organic molecules will be effective in
inducing transitions between states of different spin if a “px ®
py” orbital transition on a single (the same) atom is involved in
the electronic transition. This orbital transition provides both a
means of conserving total angular momentum during the
transition and also a means of generating orbital angular
momentum that can be employed in spin-orbit coupling. This
works in the case of np* state.
Conservation of energy and angular momentum
(spin & orbit coupling)
Spin change will occur at a place where the energies of singlet
and triplet are identical. Occurs at curve crossing.
• The electron spin must either remain unchanged or change by one unit of angular
momentum, (say, +1/2  ® -1/2 ).
• A spin change is exactly compensated by an equal and opposite change of angular
momentum which occurs from some other (coupled) interaction with another source
of angular momentum.
• In a spin-flip, induced by the spin-orbit interaction, the conservation of angular
momentum is guaranteed from the magnetic orbital quantum number ml.
py
Dml=0;Dms=1
px Dml=1;Dms=0
Energy and angular momentum conservation
px Dml=1;Dms=1
allowed
Energy is fine, but
orbitals don’t overlap,
remain perpendicular
Breakdown of Born-Oppenheimer Approximation
Vibronic mixing enables surface mixing
Vibronic mixing enables overlap of
n and p orbitals
Vibration and SO helps ISC
py
px
Dml=1;Dms=1
Spin flip
Conservation of spin and orbital angular momentum favors ISC
The Effect of Spin-Orbit Coupling on Intersystem
Crossing from S1 (pp*) to T1 in carbonyls
π
π*
n
π
n
n
π
π*
n
π
π*
n
π
π*
n
π
π*
The Effect of Spin-Orbit Coupling on Intersystem
Crossing from S1 (np*) to T1
π
π*
n
π
n
El-Sayed’s Rule
Intersystem crossing is likely to be very slow unless it
involves a change of orbital configuration.
Chem. Rev., 1966, 66, 199-241
S1 T2
T1
DEST
kST=1011s-1
DEST = 5Kcal/mol
O
kST=108s-1
DEST = 5Kcal/mol
S1
T2
T1
DEST
O
O
≅
Thus, for ketones with T1 (n, p*), the only mechanism to undergo a Singlet-Triplet ISC is
going through a T2 (p, p*) followed by internal conversion to T1 (n, p*)
S1
T1
n,p*
T2
p,p*
n,p*
Thus, the ISC crossing rate depends whether or not it is allowed and on the energy gaps
involved.
S1
T1
n,p* T2
p,p*
n,p*
El-Sayed’s Rule
Intersystem crossing is likely to be slow unless it involves a change of orbital configuration.
Summary
kisc
krt kqtkqskrs
- hν
T1
S1
S0
- hν '
kST
kP K2[Q]kF k1
Room Temperature Phosphorescence
Strategy to record phosphorescence at room temperature
through supramolecular approach
Make more triplets through
the heavy atom effect
Stage 1
Make triplets emit faster in
competition with quenching
processes
Stage 2
Crown ethers, micelles and zeolites
contain cations
Phenanthrene@Cyclodextrin: effect of CH2Br2 as co-guest
Cyclodextrins as hosts
Induced Intersystem Crossing Depends on the SOC:
Cations as the heavy atom pertuber
Atom Ionic Spin-Orbit
Radius of Coupling ζ cm-1
the Cation (Å)
Li 0.86 (+) 0.23
Na 1.12 11.5
K 1.44 38
Rb 1.58 160
Cs 1.84 370
Tl 1.40 3410
Pb 1.33 (2+) 5089
External heavy atom effect: Crown ether approach
Tl: Z = 81Na: Z = 11
Naphthalene@SDS micelle: effect of heavy atom
counterions
Micelles as hosts
Heavy atom produces more triplets and the triplets produced
phosphoresce at a faster rate
kisc
krt kqtkqskrs
- hν
T1
S1
S0
- hν '
Cation Effect
Heavy Cations Enhance the S1 to T1 Crossing
T
h
e
p
i
c
t
u
r
e
c
a
n
'
t
b
e
d
i
s
p
l
a
y
e
d
z
x
y
Emission Spectra of Naphthalene Included in MY Zeolites
Room temperature phosphorescence
Phosphorescence from Diphenyl Polyenes
Phosphorescence from Azo Compounds in TlY at 77 K np*–
np* crossing
N
N
KubelkaMunK
Wavelength/ nm
RelativeIntensity
Absorption
Phosphorescence
Excitation
So to S1
So to T1
So to S2
S1
T1
S0
nπ* nπ*
S2
ππ*
ππ*T2