Technical Notes Anal. Chem. 1996, 68, 226-229
A Photochemical Procedure for Determining Reaction Quantum Efficiencies in Systems with Multicomponent Inner Filter Absorbances Alistair J. Lees
Department of Chemistry, Binghamton University, State University of New York, Binghamton, New York 13902-6016
A kinetic procedure for measuring the photochemical quantum efficiencies of reactions in which several components have overlapping absorbances is fully described. This method has been found to be particularly suitable for photochemical determinations where inner filter effects are substantial, such as those typically observed in the ligand substitution and intermolecular C-H/Si-H bond activation mechanisms of metal complexes. The quantitative measurement of the Si-H bond activation photochemistry of (η5-C5H5)Rh(CO)2 in triethylsilane solution is demonstrated in detail, although the procedure has widespread application in photochemistry. Quantitative measurements of photochemical processes are of fundamental importance in many chemical events.1-3 In cases where only a single species absorbs light, it is a relatively simple matter to determine the amount of energy absorbed by the chromophore.1,2,4 For a multicomponent system, however, the situation becomes more complicated when several of the species present absorb light at the excitation wavelength. In such instances, quantitative data can be obtained only after inner filter effects are ascertained.5-8 As a practical way of dealing with several inner filter absorbances, quantitative determinations for photochemical reactions are often made over relatively low reaction conversions, or the reaction conditions themselves may be altered to simplify the treatment.1,2,4 The difficulty arises when a photoproduct species absorbs an increasing fraction of the light at the excitation wavelength. In either case, the lack of an experimental procedure (1) Calvert, J. G.; Pitts, J. N. Photochemistry; Wiley: New York, NY, 1966. (2) Parker, C. A. Photoluminescence of Solutions; Elsevier: Amsterdam, 1968. (3) Turro, N. J. Modern Molecular Photochemistry; University Science Books: Mill Valley, CA, 1991. (4) Rabek, J. F. Experimental Methods in Photochemistry and Photophysics; Wiley: New York, 1982. (5) Christmann, D. R. Ph.D. Thesis, Michigan State University, East Lansing, MI, 1980. (6) Adamsons, K.; Sell, J. E.; Holland, J. F.; Timnick, A. Am. Lab. 1984, 16 (11), 16-29. (7) Yappert, M. C. Ph.D. Thesis, Oregon State University, Corvallis, OR, 1985. (8) Ingle, J. D.; Crouch, S. R. Spectrochemical Analysis; Prentice Hall: Englewood Cliffs, NJ, 1988; pp 449-458. (9) Yappert, M. C.; Ingle, J. D. Appl. Spectrosc. 1989, 43, 759-767. (10) Christmann, D. R.; Crouch, S. R.; Timnick, A. Anal. Chem. 1981, 53, 276280. (11) Christmann, D. R.; Crouch, S. R.; Timnick, A. Anal. Chem. 1981, 53, 20402044.
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to deal with the multicomponent absorbances in the system compromises the photochemical measurement. Several successful approaches have been reported that account for inner filter effects in fluorescence measurements.5-8 Generally, conventional methods have been employed which seek to minimize these effects rather than account for them. However, advances in microelectronic detection have now made it possible to determine correction factors based on the measurement of both fluorescence and absorbance of the same solution.9 Corrections have also been carried out using cell-shift10,11 and cell-rotation techniques,6,12 where the fluorescence intensity is determined from different volume elements within the solution cell. In recent years, we have extensively investigated ligand photosubstitution and photochemically induced C-H and Si-H bond activation reactions of organometallic complexes. A number of these processes involve multicomponent absorbances at the excitation wavelength which vary during the course of these photochemical reactions.13-18 Consequently, to quantify these processes, we have developed a mathematical treatment that takes into account the complicated inner filter effects in these photochemical transformations. Herein, we report the full details of this procedure, including a representative example involving a Si-H activation reaction of a transition-metal complex. This quantitative method appears to have widespread application in photochemistry. PHOTOCHEMICAL PROCEDURE Quantitative measurement of a photochemical process involves the determination of its quantum efficiency for chemical reaction (φcr), according to
(RbCR) -dCR ) φcrI0 (1 - 10-Atot) dt Atot
(1)
Here, CR is the concentration of the reactant species at various photolysis times t, I0 is the incident light intensity (in einsteins (12) Adamsons, K.; Timnick, A.; Holland, J. F.; Sell, J. E. Anal. Chem. 1982, 54, 2186-2190. (13) Charalambous, E.; Gade, L. H.; Johnson, B. F. G.; Kotch, T.; Lees, A. J.; Lewis, J.; McPartlin, M. Angew. Chem., Int. Ed. Engl. 1990, 29, 11371139. (14) Gade, L. H.; Johnson, B. F. G.; Lewis, J.; McPartlin, M.; Kotch, T.; Lees, A. J. J. Am. Chem. Soc. 1991, 113, 8698-8704. (15) Drolet, D. P.; Lees, A. J. J. Am. Chem. Soc. 1990, 112, 5878-5879. (16) Drolet, D. P.; Lees, A. J. J. Am. Chem. Soc. 1992, 114, 4186-4194. (17) Ainscough, E. W.; Brodie, A. M.; Ingham, S. L.; Kotch, T. G.; Lees, A. J.; Lewis, J.; Waters, J. M. J. Chem. Soc., Dalton Trans. 1994, 1-6. (18) Purwoko, A. A.; Lees, A. J. Inorg. Chem. 1995, 34, 424-425. 0003-2700/96/0368-0226$12.00/0
© 1995 American Chemical Society
Figure 1. UV-visible absorption spectral changes accompanying the 458-nm irradiation of 2.5 × 10-3 M (η5-C5H5)Rh(CO)2 in deoxygenated decalin solution containing 0.1 M Et3SiH at 25 °C. Initial spectrum recorded prior to irradiation; subsequent spectra recorded after 30-min time intervals of irradiation.
Atot ) b[RCR + PCP]
(2)
CP ) CR° - CR
(3)
Atot ) b[(R - P)CR + PCR°]
(4)
and
thus
For a reaction where an additional species (L) is present (such as excess ligand in photosubstitutional processes), then Figure 2. FT-IR absorption spectral changes accompanying the 458-nm irradiation of 2.5 × 10-3 M (η5-C5H5)Rh(CO)2 in deoxygenated decalin solution containing 0.1 M Et3SiH at 25 °C. Initial spectrum recorded prior to irradiation; subsequent spectra recorded after 30min time intervals of irradiation.
per unit time‚solution volume), b is the cell path length, and Atot and R are the total absorbance of the solution and molar absorptivity of the reactant species at the irradiation wavelength, respectively. Hence, eq 1 appropriately represents the quantum efficiency in terms of the change in concentration of the reactant species divided by the fraction of the absorbed light that is due to the reactant in the presence of other absorbing species. For a simple reaction where reactant (R) and product (P) are the only light-absorbing species and CR° is the concentration of R at t ) 0, then
Atot ) b[RCR + PCP] + AL
(5)
Atot ) b[(R - P)CR + PCR°] + AL
(6)
or
For a reaction where the solvent (S) also absorbs at the irradiation wavelength, then
Atot ) b[RCR + PCP] + AL + AS
(7)
Atot ) b[(R - P)CR + PCR°] + AL + AS
(8)
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or
Table 1. Values of the Integral Function of Light Absorption at the Excitation Wavelength during the Photochemistry of the (η5-C5H5)Rh(CO)2 Complexa t, min
∫tt0i[(1 - 10-Atot)/Atot] dt, min
0 30 60 90 120 150
0 60 122 185 249 313
t, min
∫tt0i[(1 - 10-Atot)/Atot] dt, min
180 210 240 270 300
379 444 510 576 642
a Data determined from Figure 3; the integral function values are considered accurate to (3%.
Figure 3. Plot of the function [(1 - 10-Atot)/Atot] versus time. Data taken from Figure 1 at the excitation wavelength.
Consequently, the variable Atot in eq 1 represents the total absorbance (A ) AR + AP + AL + AS) at the excitation wavelength, and the component (RbCR/Atot) is the fraction of the absorbed light that is absorbed by the reactant species within the solution mixture at any point throughout the reaction. Thus, application of eq 1 accounts for the changing inner filter effects during the reaction caused by the varying light absorbances of the reactant and photoproduct and, if necessary, any additional species. Rearrangement and integration of eq 1 yields the following:
d ln CR ) -φcrI0Rb[(1 - 10-Atot)/Atot] dt
(9)
and
∫ [(1 - 10
ln(CR/CR°) ) R
ti
t0
)/Atot] dt
(10)
-Atot
where
(11)
R ) -φcrI0Rb
APPLICATION The photochemically induced Si-H bond activation reaction of (η5-C5H5)Rh(CO)2 in triethylsilane (Et3SiH) (eq 12) provides a representative example for treatment of the above procedure.16 hν, 458 nm
8 (η5-C5H5)Rh(CO)(SiEt3)H + (η5-C5H5)Rh(CO)2 9 Et SiH 3
CO (12) UV-visible and FT-IR spectra recorded during the course of this photochemical transformation are shown in Figures 1 and 2. These spectral data are initially treated by plotting the variable [(1 - 10-Atot)/Atot] against the total irradiation time, where Atot is the optical density at 458 nm; this graph is depicted in Figure 3. The function ∫tt0i[(1 - 10-Atot)/Atot] dt is subsequently obtained by determining the cumulative areas from this plot at the various times t. For ease of calculation, each segment of the function can be approximated to be that of a trapezoid, and these results are summarized in Table 1. It should be noted that in this silane activation reaction AL and AS are negligible. In the analogous photosubstitution reactions with PR3 ligands, the term AL is significant.16 228 Analytical Chemistry, Vol. 68, No. 1, January 1, 1996
Figure 4. Kinetic representations of the FT-IR absorbances at 2046, 1982, and 2009 cm-1, respectively. Data taken from Figure 2 and Table 1.
Thereafter, plots of ln[(At - A∞)/(A0 - A∞)] versus ∫tt0i[(1 dt can be made, where A0, At, and A∞ are absorbance values at any particular wavelength throughout the photolysis reaction. It should be recognized that the ln[(At - A∞)/(A0 -
10-Atot)/Atot]
A∞)] values represent ln(CR/CR°) in eq 10. These absorbance values can be taken from the UV-visible data, usually at an absorption maximum in the initial spectrum, or they can be obtained from different spectroscopic data. In the case of (η5C5H5)Rh(CO)2, the FT-IR data of the carbonyl stretching region display more substantial absorbance changes (see Figure 2), and it is preferable to use them. Figure 4 illustrates these kinetic plots for the ν(CO) bands at 2046, 2009, and 1982 cm-1. The two decreasing infrared bands at 2046 and 1982 cm-1, representing the starting complex, both reveal straight line plots when A∞ ) 0 and yield slopes R ) (1.78 ( 0.09) × 10-3 and (1.91 ( 0.10) × 10-3, respectively. The increasing infrared band at 2009 cm-1 is due to photoproduct and displays a straight line plot when A∞ ) 0.76; this value is estimated from the spectral progression (see Figure 2). Plots based on estimates of A∞ that are either too high or too low exhibit deviation from linearity which are especially pronounced in the later stages of photolysis (at higher values of the integral function). Moreover, the value R ) (1.79 ( 0.09) × 10-3 from this graph is coincident with the above determinations. These kinetic observations, in conjunction with a knowledge of the infrared spectrum of the product, illustrate that the reaction proceeds cleanly without
interference from secondary photochemical or thermal processes and confirms the stoichiometry of this photochemical reaction as written in eq 12. Having found a mean value of R ) (1.83 ( 0.09) × 10-3 from the above kinetic plots, it is then a straightforward matter to calculate φcr from eq 11, with the incident light intensity determined from the laser power or by actinometry.1,2,4 CONCLUDING REMARKS The above procedure can be applied to many different photochemical situations where multicomponent absorbances at the excitation wavelength change during the course of a chemical reaction. ACKNOWLEDGMENT We thank the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, U.S. Department of Energy for support of this research (Grant DE-FG02-89ER14039). Received for review August 1, 1995. Accepted October 10, 1995.X AC9507653 X
Abstract published in Advance ACS Abstracts, November 15, 1995.
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