Kathy-Sarah Focsaneanu
November 28, 2002

6.2 A Classical Interpretation of Radiationless
Electronic Transitions as Jumps between Surfaces
• radiationless “jumps” occur at critical nuclear geometries, r c
• probability of surface jump @ r c is
P ~ e -
(∆E/  s)

6.3 Wave Mechanical Interpretation of Radiationless
Transitions between States
• adiabatic (Born-Oppenheimer) approximation: simplifies to motion of nuclei only
• treat nuclei classically; electrons as waves

2
 
1
 
2
 
1
Initial
 mixing near r c

Final
• mixing is needed to produce the “jump”; otherwise, the point will continue along original surface
• frequency of “resonance” called electronic tautomerism, where

= ħ /∆E ~ 10 -13 /∆E s  <<< ∆ 
“resonance region”

•point passes through unperturbed
•if E of 
1

2 coupling is <
E vib
, may consider E’~0
• jump probability varies inversely with how strongly the crossing is avoided
• occur most readily when there is little geometry change
• no Z.O. linkage: no dynamic coupling near r c
• typical for
 or
 bond breaking

6.4 Formulation of a Parameterized Model of
Radiationless Transitions
• processes must be isoenergetic
• radiationless transitions enduced by:
•mixing of n and  orbitals by outof-plane vibrations (see Fig 6.6)
•spin-orbit coupling, where a force is required to change the spin; this force must act while the point is near r c
Selection Rules
1. 1 n,

*

3

,

* allowed
2.
4.
1
1 n,

*

3 n,

* not allowed
3. 1

,

*

3 n,

* allowed

,

*

3

,

* not allowed
ElSayed’s Rules for S
1
 T n,

*  n,

* Forbidden n,

*  
,

* Allowed

,

*  
,

* Forbidden
T
1
 S
0 n,

*  n 2 Allowed

,

*  
2 Forbidden

6.5 The Relationship of Rates and Efficiencies of
Radiationless Transitions to Molecular Structure
Vibrational “promoters” of radiationless transistions:
-Loose bolt:strong vibration in another part of the molecule
-Free Rotor: twisting of a bond; efficiency
 constraint within molecule and within the environment
Matching Surfaces:
-no intersection means no opportunity to mix
-probability is poor, e.g.

S
1

S
2 dr
 is very small

6.6 Factors that Influence the Rate of
Vibrational Relaxation
•transfer of excess energy to the environment (solvent) is fast because the solvent behaves as a heat bath
1.
electronic motion and position change
2.
local excited vibration
3.
electronic-vibrational radiationless transition
4.
excess energy is transferred through the molecule to surrounding solvent molecules

6.7 The Evaluation of Rate Constants for Radiationless
Processes from Quantitative Emission Parameters
 process
= k process k process
+ k competing processes
•measurement of lifetimes and quantum yields allows calculation of rate constants

S n
S
1
S
0 k SS
IC k
IC
6.8 Internal Conversion (S n

S
1
, S
1

S o
) k
ST
T k TT
IC n
 absorption (S
0

S n
) k rad
S
0

S n

F k nonrad
S n

S
1
T
1
Zero Order crossings are common above S
1

IC from S n is easy! (Kasha’s rule)
Ermolev’s Rule:

F
+

IC
+

ST
= 1 or 1 – ( 
F
+

ST
) ~

Deuterium Effect:
-switching C-D for C-H
 wavenumber
-as a result,


 thus IC
 and

F
&

S


6.9 Intersystem Crossing from S
1 to T
1
•the S
1 to T
1 transition can occur via:
-direct S
1 coupling to upper vib’l levels of T
1
-coupling of S
1
•variation in size of k
ST to T from n
, followed by rapid T n to T
1
-amount of electronic coupling between S and T
IC
-size of energy gap between S and T
-amount of spin-orbit coupling between S and T
•Temp dependence
-
-k rad

F does not vary with temp, but k nonrad k
ST obs = k
ST o + Ae -E/RT and

S does thus vary with temp, but not at T < 100 K (energy term is less significant)
•Triplet Sublevels
-ISC occurs from an individual sublevel
-processes from different sublevels have different rate constants

S
0
6.10 Intersystem Crossing (T
1

S o
) k
TS
T
1
•Size of k
TS varies with E(T
1
)
•Excess energy dissipated through C-H vibrations
•Deuterium effects:
-more significant than in the singlet
-large T
1 to S
0 gap: smaller frequency for
C-D stretch means that many more vibrational quanta are needed
-inhibition of ISC (enhancement of phosporescence?)
•Temp effects: k
TS relatively independent of temp
•Triplet sublevels: k(T
+
S
0
), k(T
0
S
0
), k(T
-
S
0
) may be resolved at 4K

6.11 Perturbation of Spin-Forbidden Radiationless
Transitions
•Heavy Atom effect:
-k
ST
, k
TS
, k
P increased by adding a heavy atom, k
F
, k
IC unchanged
-again, phosphorescence is a trade-off between k
TS and k
P
-i.e. who wins?

P
•External Perturbation: or

TS
?
-outside influence on spin-orbit coupling and energy transfer
-k
ST obs = k
ST
+ k
ST-X
[X] (pure + perturbation by X)