MMP Chapter 5

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MMP Chapter 5

• Photophysical Radiationless Transitions

Kathy-Sarah Focsaneanu November 28, 2002
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6.2 A Classical Interpretation of Radiationless
Electronic Transitions as Jumps between Surfaces

• radiationless jumps occur at critical nuclear
  geometries, rc
• probability of surface jump _at_ rc is

P e-(?E/?? s)
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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 rc ? Final

• mixing is needed to produce the jump
  otherwise, the point will continue along original
  surface
• frequency of resonance called electronic
  tautomerism, where
• ? h/?E 10-13/?E s ?ltltlt ??

resonance region
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• point passes through unperturbed
• if E of ?1 ?2 coupling is lt Evib, may consider
  E0

• typical for ? or ? bond breaking

• no Z.O. linkage
• no dynamic coupling near rc

• jump probability varies inversely with how
  strongly the crossing is avoided
• occur most readily when there is little geometry
  change

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6.4 Formulation of a Parameterized Model of
Radiationless Transitions

• processes must be isoenergetic
• radiationless transitions enduced by
• mixing of n and ? orbitals by out-of-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 rc

Selection Rules 1. 1n, ?? 3?, ? allowed 2. 1n,
? ?3n, ? not allowed 3. 1?, ? ?3n, ?
allowed 4. 1?, ? ?3?, ? not allowed
El-Sayeds Rules for S1?T n,? ? n, ?
Forbidden n, ?? ?, ? Allowed ?,? ? ?, ?
Forbidden
T1 ? S0 n,? ? n2 Allowed ?,? ? ?2 Forbidden
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6.5 The Relationship of Rates and Efficiencies
of Radiationless Transitions to Molecular
Structure
Vibrational promoters of radiationless
transistions -Loose boltstrong 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. ??S1?S2dr? is very
small
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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

• electronic motion and position change
• local excited vibration
• electronic-vibrational radiationless transition
• excess energy is transferred through the molecule
  to surrounding solvent molecules

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6.7 The Evaluation of Rate Constants for
Radiationless Processes from Quantitative
Emission Parameters

• measurement of lifetimes and quantum yields
  allows calculation of rate constants

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6.8 Internal Conversion (Sn? S1, S1? So)
? absorption (S0 ? Sn)
krad S0 ? Sn
?F
knonrad Sn ? S1
kST
Zero Order crossings are common above S1 ? IC
from Sn is easy! (Kashas rule)
Ermolevs 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 ?
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6.9 Intersystem Crossing from S1 to T1

• the S1 to T1 transition can occur via
• -direct S1 coupling to upper vibl levels of T1
• -coupling of S1 to Tn, followed by rapid Tn to
  T1 IC
• variation in size of kST from
• -amount of electronic coupling between S and T
• -size of energy gap between S and T
• -amount of spin-orbit coupling between S and T
• Temp dependence
• -krad does not vary with temp, but knonrad does
• kST obs kSTo Ae-E/RT
• -?F and ?S thus vary with temp, but not at T lt
  100 K (energy term is less significant)
• Triplet Sublevels
• -ISC occurs from an individual sublevel
• -processes from different sublevels have
  different rate constants

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6.10 Intersystem Crossing (T1 ? So)

• Size of kTS varies with E(T1)
• Excess energy dissipated through C-H vibrations
• Deuterium effects
• -more significant than in the singlet
• -large T1 to S0 gap smaller frequency for C-D
  stretch means that many more vibrational quanta
  are needed
• -inhibition of ISC (enhancement of
  phosporescence?)
• Temp effects kTS relatively independent of temp
• Triplet sublevels k(TS0), k(T0S0), k(T-S0) may
  be resolved at 4K

T1
phosphorescence
kTS
S0
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6.11 Perturbation of Spin-Forbidden
Radiationless Transitions

• Heavy Atom effect
• -kST, kTS, kP increased by adding a heavy atom,
  kF, kIC unchanged
• -again, phosphorescence is a trade-off between
  kTS and kP
• -i.e. who wins? ?P or ?TS?
• External Perturbation
• -outside influence on spin-orbit coupling and
  energy transfer
• -kST obs kST kST-XX (pure
  perturbation by X)