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# MMP+ Chapter 5 Photophysical Radiationless Transitions Kathy-Sarah Focsaneanu November 28, 2002.

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MMP+ Chapter 5 Photophysical Radiationless Transitions 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 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 r c Selection Rules 1. 1 n,  *  3 ,  * allowed 2. 1 n,  *  3 n,  * not allowed 3. 1 ,  *  3 n,  * allowed 4. 1 ,  *  3 ,  * not allowed El-Sayed’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

6.8 Internal Conversion (S n  S 1, S 1  S o ) SnSn S1S1 S0S0 TnTn T1T1 k SS IC k IC k TT IC fluorescence phosphorescence  absorption (S 0  S n ) k rad S 0  S n FF k nonrad S n  S 1 Zero Order crossings are common above S 1  IC from S n is easy! (Kasha’s rule) k ST  F +  IC +  ST = 1 or 1 – (  F +  ST ) ~  Ermolev’s Rule: 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 to T n, followed by rapid T n to T 1 IC variation in size of k ST 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 -k rad does not vary with temp, but k nonrad does k ST obs = k ST o + Ae -E/RT -  F and  S 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

6.10 Intersystem Crossing (T 1  S o ) S0S0 T1T1 k TS phosphorescence 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 or  TS ? External Perturbation: -outside influence on spin-orbit coupling and energy transfer -k ST obs = k ST + k ST-X [X] (pure + perturbation by X)

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