Anal. Chem. 1995, 67, 1361-1370
Multidimensional LeastlSquares Resolution of Raman Spectra from Intermediates in Sensitized Photochemical Reactions Julius C. Fister, 111, and Joel M. Harris* Depattment of Chemistty, University of Utah, Salt Lake City, Utah 841 12
Nonlinear least-squares analysis of transient resonance Raman spectra of a triplet-state photosensitizer (benzophenone) acquired as a function of quencher concentration and laser intensity allows the Raman spectra of the sensitizer excited state and intermediate photoproducts to be resolved from the data. Transient Raman spectra of benzophenone acquired as a function ofbiacetyl concentration allow a Raman spectrum containing contributions drom only the triplet states of benzophenone and biacetyl to be resolved from bands of solvent and groundstate species. The carbonyl stretching frequency of biacetyl decreases by -580 cm-' upon excitation to the triplet state; the rate constant to produce this state by energy transfer from benzophenone triplet state was determined to be k, = 2.4 f 0.8 x lo9 L mol-' s-l. A similar analysis of Raman scattering of benzophenone reactingwith triethylamine, acquiredversus laser intensity and triethylamine concentration, allows the spectra of benzophenone triplet state and its ketyl radical photoproduct to be resolved from each other and from contributions from solvent and ground-state benzophenone bands. Photosensitized reactions comprise an important category of synthetic chemistry.' The objective of photosensitization is the formation of a reactive intermediate that cannot readily be produced as a direct result of light absorption. Two common sensitization schemes involve long-lived electronic triplet states of an aromatic ketone sensitizer produced following absorption of ultraviolet radiation by the ground-state ketone. The photoexcited sensitizer triplet state may react with a target molecule via triplet-triplet energy transfer to produce a triplet state of the target and ground-state sensitizer, or it may abstract hydrogen from a suitable H-atom donor to produce an unreactive ketyl radical of the sensitizer and a reactive radical from the H-atom donor. Either of these reactive intermediates can propagate chemistry by reacting with other species in solution. Progress in the understanding of these and other reacting chemical systems requires that the behavior of small dynamic populations of intermediates be distinguished from each other and from the larger populations of precursor and solvent molecules. Structural information provided by Raman spectra about the photosensitized transients can yield valuable insight about parameters governing the efficiencies and rates of reaction. In addition, the distinctive spectral features inherent in vibrational spectroscopy often allow (1) Decker, C.; Fouassier, J. P. In Lasers in Polymer Science and Technology Applications; CRC Press: Boca Raton, FL, 1990; Vol. 3, Chapter 1. 0003-2700/95/0367-1361$9.00/0 8 1995 American Chemical Society
better resolution of component spectra data than electronic absorption or emission spectroscopies. Brus et al. utilized transient Raman spectroscopy to study the kinetics of hydrogen abstraction by triplet-state #-benzoquinone from alc0hols.2-~ They were able to establish that hydrogen abstraction occurs through the vibrationallyrelaxed lowest triplet state of pbenzoquinone on a time scale of several nanoseconds to produce the semiquinone radical. These studies relied upon two-laser, pump-probe experiments with background subtraction methods to distinguish bands of pbenzoquinone triplet state from those of the semiquinone radical produced following hydrogen abstraction. In complex systems, however, it may not be possible to obtain a Raman spectrum of the desired intermediate free from spectral overlap with reactants and photoproduct species. This can prevent unambiguous assignment of bands, which can limit the utility of the method. Multidimensional data analysis techniques which simultaneously utilize information from both the kinetic and spectral dimensions to allow resolution of overlapping component spectra can be brought to bear on this p r ~ b l e m . ~ - ~ In the present work, multidimensional least-squares approaches for the analysis of triplet-state photosensitization by transient Raman spectroscopy is described. Raman scattering is accumulated from a series of single laser pulses that both photoexcite the sample and then probe the subsequent reaction between the populations of triplet-state sensitizer and ground-state target quencher. Kinetic variables including laser intensity and quencher concentration govern the evolution of the excited-state sensitizer and photoproduct populations which, as a consequence, determines the amplitude of Raman scattering for each transient species. Multidimensional least-squares methods in conjunction with a kinetic model for the component responses allow the Raman spectra and kinetic parameters of the reactive intermediates to be resolved. THEORY Raman spectra of triplet-state sensitizers, their ground-state precursors, and photoproducts may be acquired as a function of laser intensity and/or quencher concentration and the resulting data expressed as a matrix, D. Within D, the wavenumber of the spectral measurement varies along the rows as index i, and kinetic (2) Beck, S. M.; BNS, L. E.]. Am. Chem. SOC.1982, 104, 1103-1104. (3) Beck, S. M.; Brus, L. E. ]. Am. Chem. SOC.1982, 104, 4789-4792. (4) Rossetti, R;Brus, L.E. J Am. Chem. SOC.1986, 108, 4718-4720. (5) Lawton, W. H.; Sylvestre, E. A Technometrics 1971, 13, 617-633. (6) Knorr, F. J.; Thorsheim, H. R;Harris, J. M. Anal. Chem. 1981, 53,821825. (7) Knorr, F. J.; Harris, J. M. Anal. Chem. 1981,53, 272-276. (8) Frans, S.D.; Harris, J. M. Anal. Chem. 1984,56,466-470.
Analytical Chemistw, Vol. 67, No. 8, April 15, 1995 1361
variables (e.g., laser intensity or quencher concentration) increase across the columns with index j . The Raman intensity at any wavenumber for a given combination of laser intensity and quencher concentration,dij, will be the sum of contributions from the components in the sample:
...........
n
-.....
! I
I /
,IOR,P ,"
I k3
k=l
where aik contains the wavenumber variation (indexed t] of the Raman scattering of the kth component and ckj contains the relative amplitude of scattering from the kth component at the jth combination of laser intensity and quencher concentration. This relationship is more conveniently expressed as a matrix product D =AC
(2)
where A is a column matrix containing the unknown Raman spectra of the sample componentswhile the kth row of C contains the laser intensity and quencher concentration dependence of the amplitude of the kth component Raman spectrum. If a physical model can be found for the component response to intensity and composition variation in order to build C, the least-squares estimategJOof the matrix A containing the component spectra is given by
a = DCT(CCT)-'
(3)
In order to build a model for C, one must first consider the conditions for generating a Raman spectrum from a laser pulse, where Raman scattering is observed only for duration of the pulse, to,and the amplitude of the kth component Raman spectrum is given by
I
-'-.a
k,
[QI
Photoproducts
1
so
I
Figure I. Four-level photophysical model for triplet-sensitized photoproduct formation. Ground-state sensitizer Raman scattering occurs at a rate /uR,s,~. Triplet states, TI, are produced following laser excitation of the ground state at a rate /ai, internal conversion, k l , and intersystem crossing, k2, to the triplet manifold. Triplet-state Raman scattering then occurs at a rate /uR,T,,. Absorption within the triplet manifold at a rate, /UZ, is followed by relaxation, k ,to TI. The triplet state reacts with a quencher at a rate &[a],producing photoproducts that undergo Raman scattering at a rate / U R , P , ~ .
excitation and decay of benzophenone are illustrated in an energylevel diagram in Figure 1. Following excitation of the groundstate benzophenone with 342 nm radiation, internal conversion within the singlet manifold and intersystem crossing to the triplet manifold occur within 15 ps.l1JZ Internal conversion and vibrational relaxation populate the lowest excited triplet state, TI,within 50 ps of photoexcitation.12 The resulting sensitizer triplet state may then react with a target quencher to produce photoproducts. The ratelimiting processes of triplet-state generation by photoexcitation and decay by a quenching reaction may be characterized by the following kinetic model
(4) where It is the laser intensity (in quanta cm-2 st),u ~ kis, the ~ Raman scattering cross section of the kth component at wave number v,and [C& is the concentrationof Ck at time t. A model for the amplitude of the kth component Raman spectrum, therefore, begins with a description of the laser intensity and quencher concentration dependence on the transient population ck. Benzophenone was chosen as a triplet sensitizer to develop multidimensional approaches for the analysis of transient Raman data of photoinitiated reactions because its excited-state photophysics and role in triplet-state photochemistry are typical of many triplet-state photosensitizers.l,llJz Furthermore,this molecule was previously used to test a multidimensional approach to resolving the Raman spectrum of an excited triplet state from a series of Raman spectra acquired as a function of laser intensity, which serves as background for the present study.13J4 The kinetics of (9) Strang, G. Applied Linear Algebra; Aacademic Press: New York, 1976. (10) Draper, N. R;Smith, H.Applied Regression Analysis, 2nd ed.; Wiley: New York, 1981. (11) Greene, B. I.; Hochstrasser, R M.; Weisman, R B. /. Chem. Phys. 1979, 70,1247-1259. (12) Rentzepis, P.M. Science 1970,169, 239-247. (13) Fister, J. C.; Harris, J. M. Computer Enhanced Analytical Spectroscopy; Vol. 5, in press. (14) Fister, J. C.; Harris,J. M. Submitted for publication in Anal. Chem.
1362 Analytical Chemistry, Vol. 67, No. 8, April 75, 7995
where ut is the ground-state absorption cross section, bise is the quantum yield for intersystem crossing to form triplet states, It is the excitation laser intensity (in quanta cm-2 s-l), and k, is the second-order rate constant for the reaction between the quencher, Q, and the triplet-state sensitizer to produce photoproducts, P. The nature of the photoproducts depends on the particular quenching reaction. For example, the products of TI So energy transfer are a ground-state sensitizer molecule and a triplet-state quencher. In the absence of kinetic bottlenecks within the excited singlet-state manifold and assuming pseudo-first-order conditions for the reaction where [QI >> [TI],the sensitizer and photoproduct populations evolve according the following rate equations:
-
Several assumptions can be made to simplify the timedependent description of the transient populations. First, at the
laser intensities employed, the time between excitation events by the ground state is typically smaller than the laser pulse duration, l/(Zod, so that the ground-state population is not significantly depleted during the laser pulse and can be treated as constant. Second, although the lowest excited triplet state of the sensitizer may absorb the excitation laser radiation, the triplet-state population is not perturbed by uppumping if the decay rate of the upper excited triplet state exceeds the pumping rate, Io2
