Anal. Chem. 1995,67, 701-709
Multidimensional LeastlSquares Resolution of ExcitedlState Raman Spectra Julius C. Fister, 111, and Joel M. Harris* Deparfment of Chemistv, Universify of Utah, Salt Lake City, Utah 841 12
A multidimensional least-squares analysis of transient Raman data acquired during a single laser pulse is used to resolve the spectra of excited-state species from the spectra of ground-stateand solvent species. The kinetics of optical excitation produce a higher order dependence on laser intensity for Raman spectra of the excited states. In the absence of saturation of the ground- or excitedstate populations, the excited-state spectrum increases quadraticallywith laser intensity. In cases where excited states cause signtscant absoxption of the excitation source, the scattering from a solvent band may be used as an in situ intensity reference to correct the measured laser energies for the analysis. Saturation of excited-state populations causes deviations from the simple quadratic dependence of Raman intensities on laser energy. Leastsquares regression analysis with a model describing the saturationkinetics allows the spectrum of the excited state to be resolved. The method is introduced in this work and applied to the detection of the Raman spectrum of benzophenone excited triplet states. A kinetic model describing the loss of triplet states through dissociation of upper triplet states of benzophenone produced during the laser pulse explains the results observed with 3 16 nm excitation.
species can prevent unambiguous assignment of bands which can limit the utility of the method. Transient Raman spectra of excited electronic states in photochemical reactions have traditionally been acquired by pump-probe methods followed by spectral subtraction. This approach requires two laser pulses to isolate the spectrum of the desired transient species from spectra of ground-state precursors and other transients produced during or following the pump pulse. A recent approach described by Noda and Takahashi7jsutilized two-dimensional correlation spectroscopy to identify Raman bands of the benzil radical anion in time-resolved Raman data acquired as a function of delay time between pump and probe pulses. This method does not allow component spectra to be isolated, however, nor does it employ a physical model for component responses to extract meaningful kinetic information about the reaction intermediates. The information (in bits) of a two-dimensional measurement increases as the product of the number of uncorrelated channels in each dimension? Correlations between measurement channels limit the variability of response and significantly reduce the informing power of the observation. One can take advantage of correlations between channels, however, in a dimension of lower information such as chemical kinetics, by modeling this dimension and using the results to resolve spectral data along a second dimension having higher informing power.1°-12 If a physical model describing the correlated behavior along the second dimension Recent advances in multichannel detectors for spectroscopy, can be found, rich analytical information may be extracted from especially charge-coupled devices,la2have produced outstanding the spectral dimension by a regression or least-squares analysis. gains in detection and efficiency in Raman spectro~copy.~-~ Fitting the entire spectral dimension simultaneously,along which Charge-coupled devices exhibit a wide linear dynamic range and component contributions to the data vary, enables component allow rapid acquisition of spectra with a high signal-to-noiseratio. kinetic responses to be resolved in cases where one-dimensional These attributes may be brought to bear on the analysis of curve f i t t i n g fails.11 complex chemical reactions by the simultaneous acquisition of In the present work, a multidimensionalleast-squaresapproach kinetic and spectral information. Progress in understanding is adapted to the analysis of transient Raman data acquired from reacting chemical systems requires that the behavior of small single laser pulses that both generate and probe the excited-state dynamic populations of intermediates be distinguished from each populations. During each laser pulse, excited-state populations other and from the larger populations of precursor and solvent evolve at rates determined by both the excitation conditions and molecules. Structural information provided by Raman spectra for the kinetic parameters intrinsic to each species. For example, these transient species can yield valuable insight about the increasing the laser intensity simultaneously increases both the parameters that govern the efficiency and rate of reaction. pumping rate of excited states and the rate of Raman scattering However, spectral overlap between the intermediates and reactant from all species in solution. The pumping kinetics produce a d8erent Raman intensity dependence on laser power for spectra (1) Bilhorn, R. B.; Epperson, P. M.; Sweedler, J. V.; Denton, M. B. Appl. Spectrosc. 1987,41, 1114-1125. of excited states than for spectra of ground-state precursors and (2) Sweedler, J. V.; Bilhom, R B.; Epperson, P. M.; Sims, G. R; Denton, M. B. Anal. Chem. 1989,60,282A-291A. (3) Murray, S. B.; Dierker, S. B. J. Opt. SOC.Am. A 1986,3, 2151-2159. (4) Dierker, S. B.; Murray, S. B.; Legrange, J. D.; Schlotter, N. E. Chem. Phys. Left. 1987,137, 453-457. (5) Harris, T. D.; Lamont, M. G.; Seibles, L. Mater. Res. Soc. Symp. Proc. 1987, 104, 479-481. (6)Harris, T.D.; Lamont, M. G.; Seibles, L. Anal. Chem. 1989,61, 994-998.
0003-2700/95/0367-0701$9.00/0 0 1995 American Chemical Society
(7) Noda, I. Appl. Spectrosc. 1993,47, 1329-1336. (8) Ebihara, K; Takahashi, H.; Noda, I. Appl. Spectrosc. 1993,47, 1343-1344. (9) Kaiser, H. Anal. Chem. 1970,42(2), 24A-41A. (10) Frans, S. D.; Harris, J. M.Anal. Chem. 1984,56, 466-470. (11) Knorr, F. J.; Harris, J. M. Anal. Chem. 1981,53, 272-276. (12) Knorr, F. J.; Thorsheim, H. R.; Hams, J. M. Anal. Chem. 1981,53, 821825.
Analytical Chemistty, Vol. 67,No. 4,februmy 75, 7995 701
.............................. I
.. Dissociation Photoproducts
so Figure 1. Energy level diagram for a typical triplet-state photosensitizer, such as benzophenone.
solvent molecules. Multidimensional regression analysis in conjunction with models describingthese photophysics allows the Raman spectra of excited states to be extracted from a series of Raman spectra acquired as a function of laser intensity.
THEORY The rate of spontaneous Raman scattering from the kth component in a solution is given by
where lois the laser intensity in photons cm-2 s-l, UR,QL," is the Raman scattering cross section of the kth component at wavenumber Y , and [CJt is the concentration of the kth component at time t. Since Raman scattering is observed only for the duration of the exciting laser pulse, the integral of eq 1 over the pulse duration determinesthe relative contribution of the kth component Raman spectrum to the observed data. Therefore, to develop a description for the intensity dependence of transient Raman spectra on the excitation laser intensity, the evolution of each component concentration, IC&, must be modeled over the laser pulse duration. Model for Triplet-StateRaman Intensities. Benzophenone was chosen as a test solute to develop multidimensional analysis approaches to transient Raman data because its excited-state photophysics are typical of triplet-state photosensitizers and its triplet Raman spectrum has previously been obtained by background subtraction t e ~ h n i q u e s . ~The ~ J ~excited-statephotophysics of benzophenone (and many other triplet sensitizers) can be described within the framework of a simple four-level model, as shown in Figure 1. Prior to the excitation pulse, the sample contains only solvent and ground-state solute molecules. Since the solvent concentration does not change during the laser pulse, only the ground- and excited-state populations of the solute need to be modeled. Following excitation at a rate Z@l to either the l(n,?r*), SI, or the '(n,n*), SZ, excited singlet state, internal (13) Tahara, T.; Hamaguchi, H.; Tasumi, M. Chem. Phys. Lett. 1988,152,135139. (14)Tahara, T.; Hamaguchi, H.; Tasumi, M. j.Phys. Chem. 1987, 91, 58755880.
702 Analytical Chemistry, Vol. 67, No. 4, February 15, 1995
conversion withiin the singlet manifold followed by intersystem crossing to the triplet state occurs in less than 15 ps with unit quantum efficiency yield.15J6 Internal conversion in the triplet manifold to the lowest lying 3(n,n*) triplet state, TI, is complete withii 50 ps of ground-stateexcitation."j Once triplet states have been produced, uppumping of these states by TI T,absorption occurs at a rate Z ~ Z Internal . conversion and vibrational relaxation, k3, repopulate the lowest excited triplet state within 10 ps;17J8 photochemistry (k4) from the upper triplet state is possible (see discussion below). Raman scattering from the triplet state, TI, occurs at a rate ZOUQT,~. In the absence of high concentrationsof quenching species, direct decay pathways out of TI are slow on the time scale of the laser pulse. Similarly, triplet-triplet annihilation does not contribute signiicantly to decay of the excited-statepopulation on a nanosecond time scale over the range of laser intensities and ground-state concentrationsin this experiment.lg As a result, the lifetime of TI is limited by molecular oxygen to approximately 50 ns, which is an order of magnitude longer than the duration of the laser pulse. One additional assumption simpliiies expressions for the rate of triplet-state production. Internal conversion and intersystem crossing to the triplet state occur much more rapidly than the ground-state excitation rate, Zeal
