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J. Phys. Chem. 1981, 85,3205-3206
An in the solvent contribution to the reorganization energy.
f and f o p is given by
X is the total reorganization energy.
P82f
hFo = AFov"
6h/6f = P,2/2 = -6AFo/6f
-2
AFo is the free energy of exciplex formation in the solvent. AFovac is the free energy of exciplex formation in vacuo. ke is the dipole moment of the exciplex.
(21)
Therefore 6hF*
or 2
n is the refractive index of the solvent. t, is the dielectric constant of the solvent. p is the radius of the cavity in the solvent. 6hFo/6f = -f/Zll82
(18)
The activation energy for an electron-transfer process is given by1781b = (X/4)(1 ~ F o / X )=~ h / 4 mo/2 + mo2/4h (19)
+
h=X~+Xi=Xi+/L~(f--foP)/2
(20)
yk is the intrinsic contribution to the reorganization energy.
8
Since the difference between free energy of solvation and the energy of solvation is low for a dipole, it can be expected that M and AH* follow the same trend on changing the solvent polarity. Acknowledgment. The authors are indebted to the University Research Fund, the Administration of Scientific Programmation, and NFWO for financial support to this laboratory. The latter agency is also thanked for a predoctoral fellowship to Mark Van der Auweraer. We thank EPA for a travel grant which facilitated collaboration with Dr. Gilbert.
COMMENTS To the Questlon of Doublet-State Photochemistry in
Sir: An important unresolved problem in chromium(II1) photochemistry is whether the quenchable photochemistry occurs directly from the doublet state or via reverse intersystem crossing and reaction by the quartet state. Fukuda et al.' recently presented data on the ratio of slow to prompt product formation, R , for Cr(en)?+ consequent to nanosecond pulse excitation. Based on the observed dependence of R on analysis wavelength these authors claimed unequivocally that their data proved that a major fraction or all of the slow reaction occurred by direct reaction of the doublet state. Their analysis required that the intersystem crossing yield, fie,, was 0.3, that back-intersystem crossing was negligible, that the quantum yield of prompt photochemistry was 0.11, and that doublet photochemistry occurred with an efficiency ( ~ D R )of 0.88 (Le., &low = f i , j D R ) . (The symbolism has been altered slightly in this paper, to emphasize the distinction between overall quantum yields and fractional efficiencies for the elementary processes.2) It is immediately evident that the value of the intersystem crossing yield required for this model is significantly low compared to a literature value3of 0.7 based on (1)R.Fukuda, R.T. Walters, H. Macke, and A. W. Adamson, J. Phys. Chern., 83,2097 (1979). (2)G. B. Porter, V. Balzani, and L. Moggi, Adu. Photochem., 9,147 (1974). (3)F. Bolletta, M.Maestri, and V. Balzani, J. Phys. Chem., 80,2499 (1976). 0022-365418112085-3205$01.2510
a comparison of sensitized and directly excited emission. In support of the higher literature value are the observations that the intersystem crossing yield in [Cr(en),13+is relatively temperature invariant and has unit value for [Cr(en)J[Cr(CN)6]at low temperature.* Also it has been found that fk, for other chromium(II1) complexes is not particularly sensitive to solvent and temperaturee6 The available evidence therefore casta suspicion on the Fukuda value. Their model requires also that back-intersystem crossing is negligible. Although no measurements are available for Cr[enIs3+it is significant that the complex t-[Cr(en),F2]+ shows delayed fluorescence in aqueous room temperature solution,6 showing that reverse intersystem crossing does occur in a Cr(II1) complex with similar ligand TI donor strengths. In view of the suspicions raised by these other observations, this communication seeks to critically examine the published model and alternatives and reevaluate the data7 on which the published model was based. It is shown in the complete version of this comment (available as supplementary material) that the published conclusions are (4)F. Castelli and L. S. Forster, J. Phys. Chem., 81,403(1977). (5) Y.S.Kang, F. Castelli, and L. S. Forster, J.Phys. Chem., 83,2368 (1979). (6)A. D.Kirk and G. B. Porter, J. Phys. Chem., 84,887(1980). (7)The data reevaluation was made possible by the generosity of A. W. Adamson in allowing the author access to the original data and notebooks during an extended visit to his laboratory in early 1980. The author also was extended the opportunity to use the laser monitoring system and was able to obtain data for [Cr(en),]*+ in agreement with Fukuda et al. over the range 570-610 nm. During that period the optical alignment waa such that the very small absorbance changes observed at 620 nm could not be measured.
0 1981 American Chemical Society
3206
J. Phys. Chem. 1981, 8 5 , 3206
TABLE I: Calculated and Experimental Values of R 580 Ya 48 model 1 2.52 model 2 2.55 model 3 2.50 A,
nm
exptlC a
2.0
f
590 48 2.52 2.55 2.50 0.5 2.5:
Reference 1.
t::
600 35 2.61 2.81 2.70 2.5:
610 20 2.87 3.81 3.38
620 10 3.73 13.5 7.24
io2 2.9 1" 11 :;Ob
Based on data of ref 1.
This work.
dependent solely on the R value at 620 nm, the most experimentally inaccessible and uncertain value. Furthermore, the reevaluation of the data, using a technique that allows for the occurrence of systematic as well as random errors, supports a quartet reactivity model in this system. The relevant conclusions are summarized in Table I which shows that the rather different R value for 620 nm of this work is seen to be consistent with models 2 and 3 invoking back-intersystem crossing, whereas the value required for model 1lies just outside the estimated range of R. It is unfortunate that the uncertainties are so large, but at the present state of these experiments it is not likely that better 620-nm data could be obtained. Also there are other uncertainties to be considered, among these uncertainties in y (ratio tpr~ud/treectanJ8and the probability that some excited doublet-state absorption persists at 620 nma9 With the information available there seems little basis on which to choose between the two quartet reactivity models or some intermediate reality. Model 3 requires a back-intersystem crossing yield of unity, thus identifying the doublet/quartet level spacing with the apparent activation energy12of 10 kcal mol-l for the emission lifetime decrease. For model 2, fbi, < 1so that the emission lifetime would depend on two rate constants, implying a nonlinear Arrhenius plot. That this need not be in contrast to experiment, however, is readily shown by a proper kinetic analysis. Finally, the doublet reactivity model' unambiguously predicts a greater than twofold increase in photochemical quantum yield on irradiation into the doublet absorption band, which, particularly in [Cr(en)#+, is quite accessible and distinct from the quartet band. Such a yield increase has not been observed in the relevant experimental in(8) Other workers have measured somewhat different y values than quoted in ref 1: R. G. Linck, personal communication. (9) Excited doublet-stateabsorption spectra for Cr(II1)complexes are broad,lOJ1and it is unlikely that 6 decreases from 4 at 560 nm to zero at 620 nm as claimed.' (IO) T.Ohno and S. Kato, Bull. Chem. SOC.Jpn., 43,8 (1970). (11) A. D.Kirk, P. E. Hoggard, G. B. Porter, M. G. Rockley, and M . W. Windsor, Chem. Phys. Lett., 37, 199 (1976). (12)R.T.Walters and A. W. Adamson, Acta Chem. Seand., Sect. A, 33, 53 (1979). (13) E. E.Wegner and A. W. Adamson, J. Am. Chem. Soc., 88,394 (1966). (14) S. N.Chen and G. B. Porter, Abstracts of Xth Informal Conference on Photochemistry, Oklahoma State University, Stillwater, OK, 1972.
0022-3654/81/2085-3206$01.25/0
ve~tigations.'~J~ This is therefore also a major obstacle to belief in the doublet reactivity model and further supports the quartet reactivity analysis presented here. Acknowledgment. The author thanks Dr. A. W. Adamson for the use of the laser equipment, for access to the earlier data, for financial support, and for stimulating discussion and debate of this question. He also thanks Marina Larsen and Alistair Lees for instruction and advice on the use of the laser system. Supplementary Material Available: At the request of the Editor, this manuscript was abbreviated, necessitating removal of the kinetic analysis and the details of the data reevaluation. The full manuscript is available as supplementary material (15 pages). Ordering information is available on any current masthead page. Department of Chemistry University of Victoria Victoria, British Columbia, Canada V8 W 2Y2
A. 0. Kirk
Received: March 25, 1980; In Flnal Form: Aprll6, 1981
Reply to the Comment by Kirk. The Case of Two Reactive and Intercommunicating Exclted States
Sir: The exact kinetics of a pulsed laser experiment producing two potentially reactive and potentially intercommunicative states are examined in detail, with special reference to aqueous Cr(en)l+. The various possible regimes of rate constant values in all cases but one lead to physically questionable absolute values. The acceptable regime is that in which the first doublet thexi state is directly chemically reactive. A dissent to the reading of earlier results on the monitoring of the rate of appearance of the primary photoproduct is discussed. Supplementary Material Available: At the Editor's request, only an abbreviated version of this reply to the comment by Kirk is published in the printed edition of the Journal. The complete text is available as supplementary material (21 pages). Ordering information is available on any current masthead page. Department of Chemistry University of Southern California Los Angeles, California 90007
Arthur W. Adamson*
Baffelle Pacific Northwest Laboratory Richland, Washington 99352
Robert C. Fukuda
Chemistry and Chemical Engineering University of Saskatchewan Saskatoon, Saskatchewan Canada S7N OW0
R. Torn Walters
Received: June 18, 1980; In Final Form: Aprll29, 1980
0 1981 American Chemlcal Society
