598
J. Phys. Chem. 1991, 95, 598-601
and 29,all calculated with wrong sign by Fpc. The CF parameter inverts one of the signs (no. 22) and changes appreciably the intensities of the four remaining bands toward better agreement with experiment. This effect is not straightforward to analyze but nevertheless demonstrates the significance of the C-O charge flow parameter also for modes only weakly coupled to C-O stretches. Further deficiencies in the CF-VCD and APT-VCD models become apparent when one considers that the rotatory strengths, but not the dipole strengths, are predicted consistently low throughout the spectrum, including the C-O stretching modes. It therefore appears that the magnitudes of the magnetic dipole transition moments are still underestimated, probably causing the most serious of the remaining deficiencies in these models. It may be possible to apply further corrections to the C F approach by taking into account more detailed charge flow descriptions, e.g., charge flow not only following bonds, or other possible VCD mechanisms.
Conclusion The absorption and VCD spectra of 6,8-dioxabicyclo[3.2.1]octane have been measured between 800 and 1500 cm-l. An SCF ab initio MO calculation with the 3-21G basis set provided the molecular geometry and subsequently the harmonic force field and atomic polar tensors. After scaling the force field with appropriate factors, vibrational frequencies and absorption intensities were obtained, allowing the complete assignment of the spectrum in the reported region. The absorption intensities calculated with the FPC model were unsatisfactory particularly in the (2-0 stretching region, suggesting that charge density redistributions play an essential role in these modes. It was demonstrated that the most important of these electronic redistributions, which occur along the C-O bonds, can be modeled by introducing a single charge flow parameter, d€co/dRco = -0.35 e/A, which in the present instance was transferred from 2-methyloxetane, and suggesting further that
properly determined charge flow parameters may be generally transferable. The VCD spectrum obtained with the AFT model reproduced most of the observed signs and also the relative intensities. This is the first case of which we are aware where APT-VCD calculations in the region below 1500 cm-' yield favorable results. We suggest that the molecular size is an important factor for the success of APT for this compound as well as for other comparable molecules. F'FC predicts many VCD signs correctly, but not the intensities. The origin of this deficiency can be traced again to missing electronic contributions to the dipole moment derivatives. The magnitudes of the latter are calculated too low, particularly for C-O stretching modes. Addition of charge flux in the C-O bonds by means of the above charge flow term enhances the VCD intensities of many bands such that the qualitative agreement with the APT and experimental spectra is improved. In summary, this work demonstrates that in the case of 6 3 dioxabicyclo[3.2.l]octane the VCD spectrum can be interpreted in some detail with simple APT and C F intensity calculations by qualitatively comparing calculated and experimental spectra. However, both models still considerably underestimate the rotatory strengths, whereas the dipole strengths are reproduced more accurately. This deficiency is probably due to neglected contributions to the magnetic dipole transition moments and may originate from missing charge flow terms or from other VCD mechanisms not considered here. Systematic investigations to develop C F parameters for other internal coordinates as well as cross terms are currently in progress in our laboratory. Acknowledgment. This project was funded by an operating grant from the Natural Sciences and Engineering Research Council of Canada. The award of a University of Calgary Graduate Faculty Council Scholarship (to T.E.) is gratefully acknowledged. We also thank the Academic Computing Services and the Supercomputer Services of the University of Calgary for their continued support.
Singlet Oxygen Infrared Luminescence: Unambiguous Confirmation of a Solvent-Dependent Radiative Rate Constant A. A. Corman,*-' A. A. Krasnovsky,*~* and M. A. J. Rodgem*" Chemistry Department, University of Manchester, Manchester MI 3 9PL, U.K.; Biology Faculty, Moscow State University. Moscow, U.S.S.R.;and Center for Photochemical Sciences, Bowling Green State University, Bowling Green, Ohio 43403 (Received: April 4, 1990)
A combination of time-resolved and steady-state infrared emission techniques, together with thermal lensing and 1,3-di-
phenylisobenzofuran bleaching experiments, in both benzene and cyclohexane, has confirmed that the magnitude of the singlet oxygen, 0 2 0 ), radiative rate constant, k,, is indeed solvent dependent. It is therefore imperative that determinations of 02(lA8) yields?J y comparison of infrared luminescence intensities, in either steady-stateor time-resolved modes, be confined to comparisons of photochemical systems located in a single medium.
Introduction It is now quite clear that the classical channels for reaction of electronically excited triplet states with oxygen4 (eqs 1-3) inad'S* + O#C;) '[S*.*O2]*-m S + 02(IAg) (1) %*
+ 02(%;)==? 3[S...02]* %* + 02(3z;)
(1) University of Manchester. (2) Moscow State University. (3) Bowling Green State University.
-s +
02(32,)
s[s...02]*
(2)
(3)
equately describe the real situation for many molecules. In circ~mstanceswhere 0 2 ( I A g ) is Produced exclusively via oxygen quenching of the triplet state, the quantum yield for its formation (eq 4) is often very significantly less than that anticipated on the
~A=WA
(4)
basis of the triplet yield, h. This is often true when the observed rate constant for oxygen quenching is about one-ninth that for (4) Kawaoka, K.; Khan, A. U.; Kearns, D. R. J . Chem. Phys. 1%7,16, 1842. Kearns, D. R. Chem. Rev. 1971,71,395. Gijzcman, 0.L. J.; Kaufman, F.; Porter, G. J . Chem. SOC.,Faraday Trans. 2 1973, 69, 708, 721.
0022-3654/91/2095-0598$02.50/00 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 599
Singlet Oxygen Infrared Luminescence diffusion, Le., the value anticipated for exclusive reaction via the singlet encounter complex of channel 1. This inefficiency is reflected in SA,the fraction of oxygen quenchings of the triplet state that leads to 02(14).5 There would appear to be no general explanation of this phenomenon, and rationalizations in individual cases have involved charge-transfer character within the encounter comple~,6*~ leakage of the singlet encounter complex to ground states,5 and formation of !,4-biradical intermediates.8-'0 That SAand therefore 4,, can vary greatly places a premium on the accurate determination of such values. In recent years the advent of sensitive infrared detectors has allowed observation, in both steady-state" and time-resolvedI2 modes, of emission corresponding to the forbidden 0,O transition of eq 5. Although this 02(lAg)
-
02(32;)+ hv (1269 nm)
(5)
has greatly enhanced the potential accuracy of O,(IA,) yield measurements, two particular problems are associated with work of this kind. Firstly, the infrared emission technique only allows determination of relative 02(1$)yields, and therefore comparative standards, with accurately known absolute 4Avalues, are required. Second!y, the radiative rate constant of the O,(l$) molecule can, in principle, vary with medium, and therefore (vide infra) each solvent requires its own comparative standard of known in that solvent. Two of usI3 have recently described the establishment of standards for several solvents based on time-resolved experiments in which naphthalene (N) triplet was produced with unit efficiency in each medium via the sequence summarized in eq 6 where AK 'AK*
-
'AK*(&=l.O)
N 4
'N*(&=l.O)
-02
oz(lAg)
(6)
is an aromatic ketone of high triplet energy and a 4 T of unity. Subsequent comparison of Oz(l$) emission yields, extrapolated to time zero, under standard conditions, clearly demonstrated that the radiative rate constant, k,, exhibited relarive values which varied significantly from 1.O (water-d2) to 13.0 (benzene). Where overlap occurred, independent work by one of us," Scurlock and Ogilby,15 and Losev et a1.I6 provided both qualitative and quantitative agreement with these findings. Indeed, Scurlock and 0gilbyl5 were able to demonstrate a correlation between the solvent polarizability and k, which varied over a 25-fold range. In light of this unanimity, it is perhaps surprising that, in a very recent paper, Schmidt et al.I7 have claimed that k, is independent of solvent, the six solvents examined overlapping appreciably with those used in earlier experiments.I3-l6 Ogilby has already commented in print on this claim.I8 The issue here is not simply a question of whose data are correct. (5) Gorman, A. A.; Lovering, G.; Rodgers, M. A. J. J . Am. Chem. Soc. 1978,100,4527. (6) Garner, A.; Wilkinson, F. Singlet Oxygen; Ranby, B., Rabek, J. F.; Us.; W h y : New York, 1978; p 48. (7) Redmond, R. W.; Braslavsky,S.E. Chem. Phys. Lerr. 1988,148, 523. (8) Gonnan, A. A.; Rodgers, M. A. J.; J. Am. Chem. Soc. 1986,108,5074. (9) Bruce, J. M.; Gonnan, A. A.; Hamblett, 1.; Ken, C. W.; Lambert, C.; McNeeney, S.P. Phorochem. Phorobiol. 1989, 49, 439. (10) Gorman, A. A.; Rodgers, M. A. J. J . Am. Chem. Soc. 1989, 1 1 1 , 5557. (11) Krasnovsky. A. A. Phorochem. Phorobiol. 1979, 29, 29. Khan, A. U.;Kasha, M. Proc. Natl. Acad. Sci. U.S.A. 1979, 76,6047. Khan, A. U. Chem. Phys. Lett. 1980,72, 1 1 2. Kanofsky, J. R. J . Phorochem. 1984, 25, 327. (12) Bytcva, 1. M.; Gurinovich, G. P. J . Lumfn. 1979, 21, 17. Salokhiddinov, K. 1.; Byteva, 1. M.; Dzhagarov, B. M. Opt. Specrrosc. 1979,47,881. Hurst, J. R.; McDonald. J. D.; Schuster, G. B. J . Am. Chem. Soc. 1982, 104, 2065. Parker, J. G.; Stanbro, W. D. J . Am. Chem. SOC.1982, 104, 2067. Ogilby, P. R.; Fate, C. S. J . Am. Chem. Soc. 1982.104,2069. Rodgers, M. A. J.; Snowden, P. T. J. Am. Chem. Soc. 1982. 104, 5541. (13) Gorman, A. A.; Hamblett, 1.; Lambert, C.; Prcscott, A. L.; Rodgers, M. A. J.; Spence, H. M. J . Am. Chem. Soc. 1987, 109, 3091. (14) Krasnovsky, A. A.; Egorov, S.Y.; Nasarova, 0. V.; Yartsev, E. 1.; Ponomarcv, G. V. Stud. Biophys. 1988, 124, 123. ( I S ) Scurlock, R. D.; Ogilby, P. R. J . Phys. Chem. 1987, 91, 4599. (16) Loscv, A. P.; Bytwa, 1. M.; Gurinovich, 0.P. Chem. Phys. Leu. 1988, 143, 127. (17) Schmidt, R.; Seitel, K.; Brauer, H.-D. J . Phys. Chem. 1989, 93,4507. (18) Ogilby, P. R. J . Phys. Chem. 1989, 93, 4691.
TABLE I: Singlet Oxygen Qunntum Yields, 4 ~and , Lifetimes, T A (PS)
solvent benzene cyclohexane
&Ab
TAC
0.06 0.92 f 0.1
32 23
&A"
0.55 f 0.08 1.O f 0.15
0.58
a From DPBF bleaching. From thermal lensing. solved infrared luminescence.
e From
time-re-
The determination of O2(I$) yields, using infrared emission in both time-resolved and steady-state modes, is becoming increasingly prevalent, for instance as work on potential sensitizers for the phototherapeutic treatment of tumors expands. It is clearly of critical importance for researchers to know whether or not it is sensible to compare molecules of interest in one medium with comparative standards in another. The claims of Schmidt et al. imply that this is the case. It is clear that the only requirement for resolution of the above controversy is the unambiguous demonstration that, for just two appropriately chosen solvents, the radiative rate constants are significantly different. In principle, just two measurements per medium would be necessary, to give and the 02(1$)emission intensity. In practice, one would wish to provide confirmation of the accuracy of the data by recourse to additional independent techniques. We report here on the use of just such an approach for the solvents benzene and cyclohexane.
Experimental Section Time-resolved experiments, both infrared luminescence and thermal lensing, were performed with the third harmonic (355 nm) of a Quantel YG 471C or a J.K. Lasers System 2000 Qswitched Nd:YAG laser. Time-resolved infrared emission spectroscopy was essentially as described."J9 Thermal lensing experiments were performed with an arrangement based on a published systemm using a 1-MW Melles Griot He-Ne C W laser (632.8 nm) as the analyzing probe and a Centronix BPX 65 photodiode as the detector. Steady-state luminescence experiments were basically as described.,I In no cases were signals perturbed by emission other than that of 02(lA,). Analysis by either full emission curve integration or measured signal intensity gave essentially identical relative values. Benzene (Fluka) and cyclohexane (Aldrich) were anhydrous grades, used as received. Benzophenone and 4'-methoxyacetophenone (Aldrich) were recrystallized from ethanol. Naphthalene (Aldrich, Gold Label) was used as received.
Results The decay of O2(I$) in solution is determined exclusively by the nonradiative rate constant, kd = i A - I , which is several orders of magnitude larger than k,. Therefore, the only physical parameter dependent on k, is the intensity IA of the O2(I4)emission (cf. eq 5 ) . This parameter is directly related to and k, in time-resolved experiments, eq 7 (IAmeasured a t time zero), and $J~, k,, and iA in steady-state experiments, eq 8. In these equations I A = A4Akr (7) IA= A'4Akr7A (8) A and A' are instrumentation-dependent constants. Given, therefore, a determination of I, under optically identical conditions, for two solvents, a comparison of k, values requires only a knowledge of for time-resolved experiments and of 4Aand f A for steady-state experiments. The work to be described is therefore concerned with the parameters iA, and ZA and optimization of their dependability. In all cases the photochemical system employed was that in which either benzophenone (BP h = 1.0) c#J~,
(19) Gorman, A. A.; Hamblett, 1.; Rodgers, M. A. J. J . Am. Chcm. Soc. 1984, 106, 4679. (20) Rossbroich, G.; Garcia, N . A.; Braslavsky, S.E. J . Phorochem. 1985, 31, 37. (21) Firey, P. A.; Ford, W. E.; Sounik, J. R.; Kenney, M. E.; Rodgers, M. A. J. J . Am. Chem. Soc. 1988, 110, 7626.
600 The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 or 4‘-methoxyacetophenone (4’-MAP; I#JT = 1.0) was selectivity excited in the presence of N ( 10-1mol-I) in aerated benzene or cyclohexane, according to eq 6. Thus, in all of those experiments to be described, 3N* is produced with a quantum yield of unity and then scavenged by oxygen (-2 X mol L-I) with unit efficiency.13*22 Determination of 4A. ( a ) Bleaching of 1 ,jl-Diphenylisobenzofuran. In our earlier work related to this problem,13 we determined the absolute value of I#JA (=SA)for the 4’-MAP/N system in both benzene and cyclohexane by means of the DPBF bleaching The values obtained, including a generous error of f15%,I3 are reproduced in Table I. Since we have considerable experience with this m e t h ~ d ,we ~ . see ~ ~no reason to doubt the validity of these values, particularly since comparative 02(1Ag) infrared luminescence measurements using 4’-MAP to sensitize N, biphenyl, and fluorene triplets provided strong circumstantial evidence for a I#JA value of unity in cy~lohexane.’~ Nevertheless, in light of the claims of Schmidt et al.,17 we have seen fit to cross-check these values by use of the entirely independent technique of thermal lensing (vide infra). (6) Thermal Lensing Experiments. The phenomenon of thermal lensing, Le., deflection of a focused analyzing light beam due to transient changes in the refractive index of the solvent, is observable when the energy absorbed by laser excitation of a molecule is lost to the solvent as heat. The use of this technique to determine O2(IA,) yields on an absolute basis is now welld o c ~ m e n t e d . ~Laser ~ * ~ excitation ~ (355 nm) of our aerated 4’MAP/N system is followed by the sequence of events summarized in eq 6 which is complete within 350 This will give rise to a “fast-heat” signal which will be followed by a “slow-heat” signal corresponding to the natural decay of 02(lAg) over tens of microseconds. The photochemical system used here has two particular advantages as far as the thermal lensing technique is concerned. Firstly, the triplet yield is unity, and therefore errors associated with the determination of a fluorescence quantum yield and the average energy associated with an emitted photon are avoided. Secondly, the values of T A in benzene and cyclohexane are large enough to allow the detection system (risetime 1 ps) to separate the “fast” and “slow” heat components but short enough to largely separate the grow in of the “slow heat” from the final heat dissipation process, a relatively small correction being required. In the absence of fluorescence, the relationship between the “slow heat” derived from 02(’Ag), AV, and the total heat derived from laser excitation, V, both measured in millivolts of deflection, is given by eq 9, where 22.5 and 80.6 are the energies in kcal mol-I
-
A V / U = 22.54A/80.6 (9) available within 02(lAg) and 355-nm photons. A plot of AV/V should therefore be linear with a slope corresponding to I#Ja/3.58. In Figure 1 is shown a typical experimental trace, which clearly shows the “fast” and “slow” components of the emitted heat, for a thermal lensing experiment in benzene. The “slow” component is asymptotic to a sloping baseline defined by the final dissipation of deposited heat, a factor taken into account in determining AU and V. An excellent linear relationship between these two parameters was observed (Figure l ) as the laser energy was varied. Quite analogous behavior was observed for cyclohexane as solvent, the resulting @A values being given in Table I. These should be accurate to flW0,2~and clearly, agreement with the values from the DPBF bleaching experiments is excellent. (22) Gorman, A. A.; Hamblett, 1.; Rodgers, M. A. J. Photochem. Photobiol. 1987, 45, 215. (23) Merkel, P. 9.; Kearns, D. R. J. Am. Chem. Soc. 1972, 94, 7244. Adam. D. R.; Wilkinson, F. J. Chem. Soc., Furaduy Truns. 2 1972,68,586. Young, R. H.; Brewer, D.; Keller, R. A. J . Am. Chem. SOC.1973, 95, 375. (24) Gorman, A. A.; Rodgers, M. A. J. Chem. Phys. Lett. 1978, 55, 52. Lindig, 8. A.; Rodgers, M. A. J . J . Phys. Chem. 1979,83, 1683. Gorman, A. A.; Gould, 1. R.; Hamblett. 1. J . Am. Chem. SOC.1982, 104, 7098. Gorman, A. A.; Gould, 1. R.; Hamblett, 1.; Standen, M. C. J. Am. Chem. Soc. 1984, 106, 6956. (25) Fuke, K.;Ueda, M.;
Itoh, M. J . Am. Chem. SOC.1983, 105, 1091. Redmond, R. W.;Braslavsky, S. E. Chem. Phys. Lett. IW, 148, 523.
Gorman et al. AU/ mV
40
Figure 1. Plot of the “slow” heat emission (Arr) as a function of the total heat emission (v) as a consequence of pulsed laser excitation at 355 nm of 4’-methoxyacetophenone(OD = 0.4) in aerated benzene containing naphthalene (0.1 mol L-I). Inset: Typical heat emission profile as a function of time.
TABLE II: Determination of Relative Values for the Singlet Oxygen Radiative Rate Constant, k ,
(PI)
time resolved IA&A-‘(Ak,)”‘ \ad
solvent [A‘ benzene 290 cyclohexane 178 k,(benzene)/ k,(cyclohexane)
513 185
1.26
0.54
2.8
‘Units of mV mJ-’. bSee eq 7. Table I. dunits of mV. eSee eq 8.
steady state Ia&plr~-l(A ’k,)‘.‘
7.0
X
2.4 X 2.9
taken as an average of values in
Determinarion of T p . Although quite accurate 02(1$)lifetimes have come from indirect time-resolved the technique of choice involves time-resolved luminescence measurements (cf. ref 26 and references therein). As part of IAdeterminations (vide infra), we have used this technique to determine T p values for the 4’-MAP/N systems. The data (Table I) were in excellent agreement with optimum values.26 Those from the first-order treatment of the “slow heat” formation in the thermal lensing experiments (Figure 1) were generally 10% shorter. Determination of I p . As one part of the rationalization by Schmidt et al.” of the discrepancies between their results and those of others,I3-l6it was postulated that the use of high-powered lasers could have led to errors as a result of biphotonic processes. It should be emphasized that a major aspect of our work” involved a detailed experimental assessment of the possibility of such problems and their subsequent avoidance. In this section we remove any possible doubts on this score by reporting a comparison of results determined from infrared luminescence measurements in both time-resolved and steady-state modes. ( a ) Time-Resolved Experiments. Optically matched, aerated 4‘-MAP/N solutions (ODws = 0.4) were subjected to pulsed laser excitation at 355 nm as previously described.I3 The resultant O,(’$) infrared emissions decayed exponentially with expected lifetimes (Table I). Plots of the emission intensity (millivolts of deflection) extrapolated to time zero as a function of laser energy in millijoules per pulse were linear (Figure 2). The slopes of these
-
(26) Gorman, A. A.; Rodgers, M. A. J. Hundbook of Organic Photochemistry; Scaiano, J. C., Ed.; CRC Press: Boca Raton, FL. 1989; p 229.
The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 601
Singlet Oxygen Infrared Luminescence
'A/ mV 1
.
5
C
B V
I
I
I
I
0 Qo5 0.15 mJ F I m 2. Plot of O # 4 ) emission intensity at time zero, I,, as a function of laser energy, millijoules per pulse, as a consequence of laser excitation at 355 nm of 4'-methoxyacetophenone (OD = 0.4): (a) in aerated benzene and (b) in aerated cyclohexane, each containing naphthalene (0.1 mol L-l). Inset: Emission profile of Oz(lA,) infrared luminescence in benzene after absorption of a 0.125-mJ laser pulse; IO mV/division, IO ps/division; k' = 3.1 X IO4 s-'.
plots in millivolts per millijoule are recorded in Table I1 as IA values for the time-resolved experiments. Identical results were obtained with BP as sensitizer. (b) Steady-State Experiments. Optically matched, aerated BP/N solutions (OD3&= 1.0) were irradiated a t 366 nm with a 100-W mercury arc through a mercury line filter.27 The instrumentation for detection of the resulting 02('Ag) infrared luminescence has been described.2' Absolutely clean emission signals, peaking at 1270 nm, were obtained. Typical traces for benzene and cyclohexane are shown in Figure 3. Comparison of integrated intensities and peak heights at 1270 nm yielded the same relative results. Individual runs were reproducible to i5%. The I A values recorded in Table I1 are from signal intensities at 1270 nm, measured in millivolts, for an average of five determinations.
Discussion It is immediately obvious, from a superficial consideration of the results, that k, for benzene is significantly larger than the corresponding value for cyclohexane. This is simply because 4A is clearly significantly smaller (Table I), and yet the resulting emission intensity is significantly larger (Figures 2 and 3). The data in Table I1 put this difference on a quantitative basis. Importantly, the k, ratios are essentially identical for both timeresolved and steady-state determinations and very close to that obtained by us previ~usly.'~ Conclusions We have determined, by means of the thermal lensing technique, the absolute singlet oxygen quantum yield, 4A,for a well-defined (27) In these experiments BP was used because 4'-MAP exhibits extremely weak absorption at 366 nm.
Figure 3. Steady-state 02(14) infrared luminescence as a consequence of excitation at 366 nm of benzophenone (OD = 1.0): (a) in aerated benzene and (b) in aerated cyclohexane, each containing naphthalene (0.1mol L-I).
photochemical system in both benzene and cyclohexane. The results provide confirmation of previous determinations based on DPBF bleaching and supported by infrared emission data. The infrared luminescence resulting from these systems has been detected in both the time-resolved and steady-state modes, and both sets of data provide unambiguous evidence that the radiative rate constant in benzene is significantly larger by a factor of -3 than that in cyclohexane. This result vindicates the conclusions of o u r ~ e l v e s , Scurlock ~ ~ J ~ and Ogilby,l5 and Losev et a1.16 that the radiative rate constant is solvent dependent.28 Since the submission of this manuscript, an important contribution from Schmidt and A f ~ h a r reaches i ~ ~ those same conclusions. Clearly, therefore, the use of comparative standards to determine 02(IAg)quantum yields by infrared luminescence methods demands the employment of those standards in the medium of interest. Lack of availability of an appropriate standard in that medium can be overcome if the pertinent solvent calibration (vide supra) has been made. However, this can only introduce an additional source of error.
Acknowledgment. Experiments were carried out at the Center for Photochemical Sciences, Bowling Green State University, and the Christie Hospital and Holt Radium Institute, Manchester. We thank Dr. R. B. Redmond for the establishment of the thermal lensing facility and Drs. M. Bohorquez and I. Hamblett for thermal lensing and time-resolved luminescence measurements. Support for this project came from N I H Grant G M 24235 and the Center for Photochemical Sciences. (28) A particularly simple methodology for determination of relative values of k, therefore arises out of this work. It involves just two measurements per solvent, a thermal lensing experiment and a time-resolved lumintscence experiment, performed on identical solutions with the. same excitation source. The procedures of Schmidt et al.," which led to the claim that k, is independent of medium, were based on the determination of four parameters per solvent, two of which required extrapolation to an intercept. We feel that severe propagation of errors is the cause of thcse authors being unable to detect any solvent dependence of k,. (29) Schmidt, R.; Afshari, E. J . Phys. Chem. 1990, 94,4377.
