Triplet Extinction Coefficients, Triplet Quantum Yields, and (mainly) Laser Flash Photolysis This weekend

Competitive Kinetics out of Singlet State 1 M + h  1 M*, k ex 1 M*  products, k pc 1 M*  3 M* + heat, k isc 1 M*  1 M + heat, k ic 1 M*  1 M + h f, k f k S = k pc + k isc + k ic + k f  T = k isc /k S

Competitive Kinetics out of Triplet State 3 M*  products, k’ pc 3 M*  1 M + heat, k’ isc 3 M*  1 M + h p, k p k T = k’ pc + k’ isc + k p

Competitive Kinetics p isc T S0S0 Intramolecular decay channels Intermolecular decay channels T + Q  S 0 + Q’

Transient Absorption 3 M* + h’  3 M** k’ ex 3 M** 3 M*

Creation of Triplets 3 M 1 * + 1 M  1 M M* (1) Intramolecular radiationless transitions (2) Intermolecular energy transfer (3) Transfer from solvent triplets in radiolysis of benzene. 1 M + h  1 M*k ex 1 M*  3 M* + heat k isc

Beer’s Law Connection between light absorption and concentration OD =  T * [ 3 M*] l OD = log 10 (I 0 /I)  A  = log 10  0   I PMT II0I0 time  A  t laser 0 time 

Spatial Overlap of Laser and Monitoring Beam Laser Monitoring Light Beam Cell Laser Monitoring Light Beam Unexcited Excited Proper alignment: Sample is excited along the entire optical pathlength Improper alignment: Sample is not excited along the entire optical pathlength

Placement of Monitoring Beam Relative to Incident Laser Laser Monitoring Light Beam Cell [ 3 M*] from Beer’s Law Cell Wall Laser Entering Cell Wall Laser Exiting Extrapolated [ 3 M*] for long cells

Triplet-Triplet Absorption Spectra of Organic Molecules in Condensed Phases Ian Carmichael and Gordon L. Hug Journal of Physical and Chemical Reference Data 15, (1986)

Methods of Determining Triplet Extinction Coefficients Energy Transfer Method Energy Transfer Method Singlet Depletion Method Singlet Depletion Method Total Depletion Method Total Depletion Method Relative Actinometry Relative Actinometry Intensity Variation Method Intensity Variation Method Kinetic Method Kinetic Method Partial Saturation Method Partial Saturation Method

Energy Transfer (General) Two compounds placed in a cell. Two compounds placed in a cell. Compound R has a known triplet extinction coefficient. Compound R has a known triplet extinction coefficient. Compound T has a triplet extinction coefficient to be determined. Compound T has a triplet extinction coefficient to be determined. Ideally, the triplet with the higher energy can be populated. Ideally, the triplet with the higher energy can be populated. Thus triplet energy of one can be transferred to the other. Thus triplet energy of one can be transferred to the other.

Energy Transfer (General) If the lifetimes of both triplets are long in the absence of the other molecule, then If the lifetimes of both triplets are long in the absence of the other molecule, then One donor triplet should yield one acceptor triplet. One donor triplet should yield one acceptor triplet. In an ideal experiment In an ideal experiment  T * =  R * ( OD T / OD R ) Note it doesn’t matter whether T or R is the triplet energy donor.

3 R* + 1 T  1 R + 3 T* k et = 1 × 10 9 M -1 s -1 [ 3 R*] 0 = 1 M [ 1 T] 0 = 1 mM k obs = k et [ 1 T] 0 [ 3 R*] = [ 3 R*] 0 exp(k obs t) [ 3 T*] = [ 3 T*]  {1  exp(k obs t)} Initial Conditions [ 3 T*]  = [ 3 R*] 0

Also a  isc Method k obs = k et [ 1 T] 0 [ 3 R*] = [ 3 R*] 0 exp(k obs t) [ 3 T*] = [ 3 T*]  {1  exp(k obs t)} [ 3 T*]  = [ 3 R*] 0 If  T * and absorption of 3 R* is mainly hidden under its ground-state absorption,  isc (R) = [ 3 T*]  / # photons into R = (OD  l) / ( T * photons)

Kinetic Corrections (1) Need to account for unimolecular decay of the triplet donor: 3 D*  1 Dk D 3 D* + 1 A  1 D + 3 A*k et P tr = k et [ 1 A] / (k et [ 1 A] + k D ) The probability of transfer (P tr ) is no longer one, but  A * =  D * ( OD A / OD D ) / P tr

3 D* + 1 A  1 D + 3 A* k obs = k D + k et [ 1 A] 0 [ 3 D*] = [ 3 D*] 0 exp(k obs t) [ 3 A*] = [ 3 A*]  {1  exp(k obs t)} [ 3 A*]  = [ 3 R*] 0 P tr k D = 0.5 × 10 6 s -1 k et = 1 × 10 9 M -1 s -1 [ 1 A] 0 = 1 mM Unimolecular 3 D* decay Otherwise same initial conditions as before

Kinetic Corrections (2) May need to account for the unimolecular decay 3 A*  1 Ak A if the rise time of 3 A* is masked by its decay. Then the growth-and decay scheme can be solved as [ 3 A*] =W {exp(-k A t) - exp(-k et [ 1 A]t-k D t)} W =[ 3 D*] 0 k et [ 1 A] / (k D + k et [ 1 A] - k A ) the maximum of this concentration profile is at t max t max = ln{k A /(k et [ 1 A] + k D )} / (k A - k et [ 1 A] - k D ) OD A = OD A (t max ) exp(k A t max )

Kinetics involving decay of both triplets k D = 0.5 × 10 6 s -1 k et = 1 × 10 9 M -1 s -1 [ 1 A] 0 = 1 mM Unimolecular 3 D* decay k A = 0.5 × 10 6 s -1 Unimolecular 3 A* decay 3 D* + 1 A  1 D + 3 A* 3 D*  1 D 3 A*  1 A Energy Transfer

Uncertainty in Probability of Transfer If there is a dark reaction for bimolecular deactivation of 3 D* + 1 A  1 D + 1 A,k DA then the true probability of transfer is P tr = k et [ 1 A] / (k DA [ 1 A] + k et [ 1 A] + k D )

Energy Transfer Advantages and Disadvantages The big advantage is over the next method which depends on whether the triplet-triplet absorption overlaps the ground state absorption. The big advantage is over the next method which depends on whether the triplet-triplet absorption overlaps the ground state absorption. The big disadvantage is the uncertainty in the probability of transfer. The big disadvantage is the uncertainty in the probability of transfer.

Singlet Depletion By Kasha’s Rule, after the excited singlets have decayed, only the lowest triplet state and the ground state should be present. By Kasha’s Rule, after the excited singlets have decayed, only the lowest triplet state and the ground state should be present. Any ground state molecules that are missing should be in the lowest triplet state. Any ground state molecules that are missing should be in the lowest triplet state. In other words, the missing concentration of ground states should be the same as the triplet concentration. In other words, the missing concentration of ground states should be the same as the triplet concentration. At a wavelength where they both absorb At a wavelength where they both absorb OD = ( T *   S ) [ 3 M*] l

Singlet Depletion Assuming that there is a wavelength region ( 1 ) where the ground state absorbs and the triplet doesn’t OD S ( 1 ) =   S [ 3 M*] l  A  = log 10  0       II0I0 time  A    t laser 0 time  “bleaching” Step 1

Singlet Depletion Step 2 Go to a wavelength region ( 2 ) where the ground state doesn’t absorb OD T ( 2 ) =  T * [ 3 M*] l  A    = log 10  0       II0I0 time  A    t laser 0 time 

Singlet Depletion Advantages and Disadvantages The main problem is the assumption in Step 1: that the chosen wavelength 1 is in a region where the triplet does not absorb. The main problem is the assumption in Step 1: that the chosen wavelength 1 is in a region where the triplet does not absorb. There are methods for attempting to compensate for this, but they involve further assumptions. There are methods for attempting to compensate for this, but they involve further assumptions. The main advantage of singlet depletion is that it is free from kinetic considerations. The main advantage of singlet depletion is that it is free from kinetic considerations.

Total Depletion Method Assumes that increasing the intensity of the pulse complete conversion of a small ground state conversion to the triplet state is possible if the intersystem crossing is not negligibly small. Assumes that increasing the intensity of the pulse complete conversion of a small ground state conversion to the triplet state is possible if the intersystem crossing is not negligibly small. Then the concentration of triplet is equal to the initial ground state concentration. Then the concentration of triplet is equal to the initial ground state concentration. [ 3 M*] = [ 1 M]

Total Depletion Kinetic Derivation d[ 1 M]/dt = -2303 S I p (t) T [ 1 M] d[ 3 M*]/dt = +2303 S I p (t) T [ 1 M] k ex = 2303  S I p (t) where the excitation rate constant is note its intensity dependence [ 3 M*] = [ 1 M] 0 (1 - exp{-2303 S I p  T t})

Total Depletion When a three-state model is used, namely including the excited singlet state, then it was found that 95% conversion could occur only if When a three-state model is used, namely including the excited singlet state, then it was found that 95% conversion could occur only if  S   T  p /2 where  p is the laser pulse width This is difficult to satisfy for most lasers This is difficult to satisfy for most lasers

Total Depletion Advantages and Disadvantages Principal advantage is that it offers a simple direct estimate of the triplet concentration Principal advantage is that it offers a simple direct estimate of the triplet concentration However, even though the approach to total depletion is inferred from a saturation in the OD, the curve can saturate for other reasons However, even though the approach to total depletion is inferred from a saturation in the OD, the curve can saturate for other reasons Multiphotonic processes, e.g. biphotonic ionization can come into play at high laser intensities Multiphotonic processes, e.g. biphotonic ionization can come into play at high laser intensities Excited state absorption can also invalidate the simple kinetic equations Excited state absorption can also invalidate the simple kinetic equations

Relative Actinometry This is a two cell experiment. This is a two cell experiment. In one cell there is a compound of unknown  T *( 1 ), but with a known intersystem crossing yield  T (T) In one cell there is a compound of unknown  T *( 1 ), but with a known intersystem crossing yield  T (T) In the other cell there is a compound of known  R *( 2 ), and also with a known intersystem crossing yield of  T (R) In the other cell there is a compound of known  R *( 2 ), and also with a known intersystem crossing yield of  T (R)

Relative Actinometry If the optical densities at the respective wavelengths are the same, then the number of photons absorbed by each cell is exactly the same and If the optical densities at the respective wavelengths are the same, then the number of photons absorbed by each cell is exactly the same and This is a consequence of Beer’s Law This is a consequence of Beer’s Law The monitor beam must also be fixed relative to the cell and the laser The monitor beam must also be fixed relative to the cell and the laser  T *( 1 ) = { OD T  T (R) / OD R  T (T) } R *( 2 )

Relative Actinometry Advantages and Disadvantages Disadvantage is that both triplet quantum yields must be known Disadvantage is that both triplet quantum yields must be known However, it is more often used to measure intersystem crossing quantum yields once both triplet extinction coefficients are known However, it is more often used to measure intersystem crossing quantum yields once both triplet extinction coefficients are known

Relative Actinometry and  isc  T () =  T (R) OD T ( 1 )  R *( 2 ) OD R ( 2 )  T *( 1 ) Rearranging formula from one of the preceding slides This is one of the most popular ways to measure triplet yields Need two extinction coefficients and the reference triplet yield

Partial Saturation Method OD = a(1  exp{bI p }) a = ( T *   S )[ 1 M] 0 l b = 2303 S t T t is length of pulse

Partial Saturation Method Advantages and Disadvantages This has the same conceptual foundation as the Total Depletion Method This has the same conceptual foundation as the Total Depletion Method However, the fitting parameters a and b can be obtained without total saturation being reached However, the fitting parameters a and b can be obtained without total saturation being reached It has this advantage over the Total Depletion Method It has this advantage over the Total Depletion Method The disadvantage is that high laser intensities must be used to reach the region where the plots of OD vs I p becomes nonlinear. The disadvantage is that high laser intensities must be used to reach the region where the plots of OD vs I p becomes nonlinear.