© Copyright 1996 by the American Chemical Society
VOLUME 100, NUMBER 9, FEBRUARY 29, 1996
LETTERS Free Energy Dependence of Intermolecular Triplet Energy Transfer: Observation of the Inverted Region Angeles Farra´ n and Kurt D. Deshayes* Department of Chemistry and Center for Photochemical Sciences, Bowling Green State UniVersity, Bowling Green, Ohio 43403 ReceiVed: October 26, 1995; In Final Form: December 1, 1995X
The bimolecular rate constants for triplet energy transfer between biacetyl (2,3-butanedione) encapsulated within a hemicarcerand and a series of triplet energy acceptors are reported. Because all of the rate constants for energy transfer involving 1‚biacetyl are well below the diffusion-limited value, they can be interpreted as reflecting differences in the rates of energy transfer. There is a significant spread in the rate constants of energy transfer for 1‚biacetyl with the slowest acceptor, molecular oxygen, 3 orders of magnitude slower than the fastest acceptor, pyrene. The large decrease in the values of the rate constants can be accounted for by a model in which the increase in intervening distance decreases the electronic coupling between the donoracceptor pair. The variation in energy transfer rate constants can be explained by a Marcus dependence on the thermodynamic driving force that places exothermic energy transfer into the inverted region.
A great deal of interest has developed concerning the role of the intervening media in electron and triplet energy-transfer reactions.1 As part of our program in this area, we recently described long-distance intermolecular triplet energy transfer from an acetophenone encapsulated within a closed surface host molecule (“hemicarcerand”) to energy acceptors residing outside the host boundaries.2 Triplet energy transfer was observed although the hemicarcerand walls prevented atom-to-atom contact between the donor-acceptor pair,3 demonstrating that long-distance intermolecular triplet energy transfer is possible. However, these experiments did not directly probe the influence of the intervening hemicarcerand structure or investigate the mechanism of long-distance intermolecular triplet energy transfer. In subsequent work involving triplet energy transfer between encapsulated biacetyl (2,3-butanedione) and a series of triplet energy acceptors, it was found that the hemicarcerand walls retard the rate of triplet energy transfer in all the cases investigated. Furthermore, the observed decrease in rate X
Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-3305$12.00/0
constant with increased driving force is consistent with a nonadiabatic system that moves into the inverted region at low exothermicity. The high quantum yield for solution-phase biacetyl phosphorescence provides means for facile determination of triplet energy-transfer rate constants using competition plots with a variety of triplet energy acceptors.4 This situation does apply to encapsulated biacetyl. The biacetyl-containing complex (1‚ biacetyl) (Figure 1), was constructed using the procedure of Cram et al. for the encapsulation of small molecules within the interior of 1.5 Analysis of 1H NMR peak integration areas shows one biacetyl is encapsulated within each complex, and the 4.3 ppm upfield shift of the resonance of the methyl group from 2.3 to -2.0 ppm indicates that the biacetyl guest is deeply buried within the aromatic interior of the hemicarcerand. Solutions of 1‚biacetyl show no signs of decomplexation after standing for weeks at room temperature and are even unchanged after being heated for 36 h at 130 °C. Model studies6 predict that © 1996 American Chemical Society
3306 J. Phys. Chem., Vol. 100, No. 9, 1996
Letters
Figure 2. Rates of triplet energy transfer vs. -∆G for 1‚biacetyl and theoretical curve for eq 2 with λs ) 0.2 eV and λv ) 0.2 eV.
Figure 1. Structure of 1‚ biacetyl.
TABLE 1 acceptor naphthalene piperylene pyrene anthracene cycloheptatriene oxygen 1Σ oxygen 1∆
kET (M-1 s-1) -∆G, -∆G, energya (kcal/mol) kcal/mol eV biacetylb 1‚biacetylc 61.0 57.4 48.6 42.5 38.0 37.5 22.5
-4.6 -1.0 7.8 13.9 18.6 18.9 33.3
-0.19 -0.04 0.34 0.60 0.80 0.81 1.44
2 × 106 9 × 109 6 × 109 8 × 109 3 × 109
1.1 × 106 9.2 × 106 2.2 × 107 4.0 × 106 3.4 × 104
8 × 109 1 × 104
a The values for the excited state energies were taken from ref 8. Values taken from ref 4 except for the rates of piperylene and cycloheptatriene which were determined experimentally. c Measurements at room temperatue in benzene. The estimated errors are (10% with the exception of oxygen, where the error is (50%. b
biacetyl would rotate freely within the interior of 1; however, the symmetric structure of the biacetyl guest masks any asymmetry in the structure of 1‚biacetyl so that direct determination of the biacetyl mobility by 1H NMR was not possible, unlike the case with the 1‚acetophenone complex.2 Surprisingly, irradiation of 1‚biacetyl dissolved in aerated benzene at 430 nm yields the triplet excited state of the biacetyl encapsulated within 1‚biacetyl which emits at 534 nm with a lifetime of 880 µs and a quantum yield of 0.093. Structural models predict triplet energy transfer between the biacetyl triplet and the energy acceptor would take place within an encounter complex in which the donor-acceptor pair is separated by approximately 7 Å.6 The donor-acceptor distance is defined by the size of 1‚biacetyl and therefore should remain constant for all the acceptors investigated. A series of triplet energy transfer experiments were carried out with several acceptors that have been shown to undergo energy transfer reactions with the biacetyl triplet.4 Rate constants for triplet energy-transfer were determined from competition plots measuring changes in triplet lifetime as a function of acceptor concentration.7 Rate constants for 1‚biacetyl, biacetyl, acceptor energies and reaction driving force are given in Table 1. The driving force for energy transfer was calculated as the difference in energy between the biacetyl triplet (56.4 kcal/mol) and the triplet state of the acceptor,8 except for molecular oxygen where the driving force was calculated for both the upper 1Σ and lower 1∆ singlet states.9 In highly exothermic energytransfer reactions it has been shown that an upper electronic
state of the acceptor can be involved, and there is sufficient driving force for energy transfer to either 1Σ or 1∆.10 The rate constants for exothermic triplet energy transfer from uncomplexed biacetyl are near or at the diffusion-controlled limit. The rate of energy transfer is much slower for 1‚biacetyl in all cases. There is a also significant spread in bimolecular rate constants, with the rate constant of the slowest quencher, molecular oxygen, 3 orders of magnitude slower than the fastest quencher, pyrene. Since all of the rate constants for energy transfer involving 1‚biacetyl are well below the diffusion-limited value, they can be interpreted as reflecting differences in the rates of energy transfer occurring within the donor-acceptor encounter complex. The decrease in triplet energy-transfer rate constants with 1‚ biacetyl suggests that the increased intervening distance imposed by the hemicarcerand skeleton coincides with a decrease in the electronic coupling between the donor-acceptor pair. If this model is correct than energy transfer through hemicarcerand 1 is a weakly coupled nonadiabatic process for which the Golden Rule, eq 1, should be obeyed:
k ) (2π/p)|ν|2FCWDS
(1)
where ν is the electronic coupling matrix element, FCWDS are the Franck-Condon weighted density of states, and all the other variables have the standard meaning. The above equation has been used to correlate distance11 and driving force dependence10,12,13 for intramolecular and intermolecular triplet energy transfer. The Golden Rule can be divided into a preexponential factor, A, and a term that describes the driving force dependence of the energy transfer rate, eq 2:
k ) A exp[-(λs + ∆G + λv)2/4λskBT]
(2)
where λs is the solvent reorganization energy, λv is the vibrational reorganization energy, ∆G is the thermodynamic driving force, and the other variables have the standard meaning. If the Golden Rule is obeyed, the rate constants for triplet energy transfer from 1‚biacetyl should decrease with increased thermodynamic driving force as expressed in eq 2. A plot of log kET vs -∆G and a normalized theoretical curve generated using eq 2 with a standard value of 0.20 eV for both λs and λv are in good qualitative agreement (Figure 2).12 The systematic decrease in rate constant with increasing exothermicity is analogous to what has been reported by Meyer,10 Sigman,12 and Schanze13 for nonadiabatic triplet energy transfer and strongly suggests that energy transfer through hemicarcerand 1 can be described by the Golden Rule formalism.14
Letters Although not enough information is available at the present time to identify the singlet state of oxygen involved, the driving force for energy transfer to the 1Σ state of oxygen and cycloheptatriene triplet are similar, and the observed rate constants appear to correspond. Our model proposes that the slow rate of energy transfer to oxygen is the consequence of the dominant role of Frank-Condon factors in determining the rate of triplet energy transfer15 and is not an anomaly due to the unique structure 1‚biacetyl.16 It is interesting to note that diatomic oxygen is regarded as a highly efficient triplet energy quencher; however, our results suggest that when oxygen is prevented from coming into atom-atom contact with the energy donor, the rate of oxygen quenching drops off drastically. The calculation of the Frank-Condon factors and electronic coupling elements, the variation of the electronic nature of the hemicarcerand cage, the examination of different donoracceptor pairs, and complementary studies on single-electron transfer are currently underway in this laboratory. Acknowledgment is made to the donors to the Petroleum Research Fund, administered by the American Chemical Society, for support of this work and NSF Grant CHE-930219 for support of the NMR facilities at BGSU. We would also like to acknowledge Piotr Piotrowiak for his invaluable assistance in the interpretation of our data and Peter J. Wagner for helpful discussion. Supporting Information Available: Phosphorescence spectra of 1‚biacetyl and competition plots for quenching of 1‚ biacetyl phosphorescence (7 pages). See any current masthead page for ordering information. References and Notes (1) (a) Stemp, E. D. A.; Arkin, M. R.; Barton, J. K. J. Am. Chem. Soc. 1995, 117, 2375. (b) Meade, T. J.; Kayyem, J. F. Angew. Chem., Int. Ed. Engl. 1995, 34, 352. (c) Sessler, J. L.; Wang, B.; Harriman, A. J. Am. Chem. Soc. 1995, 117, 704. (d) Nocera, D. G.; Kirby, J. P.; Roberts, J. A. J. Am. Chem. Soc. 1995, 117, 8051. (e) Gray, J. P.; Winkler, J. R.; Richards, J. H.; Germanas, J. P.; Chang, I.; Langen, R. Science 1995, 268, 1733. (f) de
J. Phys. Chem., Vol. 100, No. 9, 1996 3307 Rege, P. J. F.; Williams, S. A.; Therien, M. J. Science 1995, 269, 1409. (g) Brun, A. M.; Harriman, A. J. Am. Chem. Soc. 1992, 114, 3656. (2) Farra´n, A.; Deshayes, K.; Matthews, C.; Balanescu, I. J. Am. Chem. Soc. 1995, 117, 9614. (3) (a) Cram, D. J.; Tanner, M. E.; Thomas, R. Angew. Chem., Int. Ed. Engl. 1991, 30, 1024. (b) Robbins, T. A. ; Cram, D. J. J. Am. Chem. Soc. 1993, 115, 12199. (4) (a) Sandros, K. Acta Chem. Scand. 1964, 18, 2355. (b) Turro, N. J.; Engel, R. Mol. Photochem. 1969, 1, 359. (c) Turro, N. J.; Engel, R. J. Am. Chem. Soc. 1969, 91, 2113. (5) Cram, D. J.; Blanda, M. T.; Paek, K.; Knobler, C. B. J. Am. Chem. Soc. 1992, 114, 7765. (6) The commercial SPARTAN 3.0, modeling package from Wavefunction, Inc., 18401 Van Karman Ave. Suite 370, Irvine, CA 92715, running the SYBIL force field was used in the modeling experiments. (7) The equation 1/τ ) 1/τ0 + kq[Q] was used to calculate the rate constants, where τ is the observed lifetime, τ0 is the lifetime in the absence of quencher, kq is the bimolecular rate constant, and [Q] is the concentration of quencher. The value for the rate constant for oxygen was acquired by comparing the lifetime of the 1‚biacetyl triplet in degassed, aerated, and oxygen-saturated benzene solutions. (8) Murov, S. L.; Carmichael, I.; Hug, G. L. In Handbook of Photochemistry, 2nd ed.; Marcel Dekker Inc.: New York, 1993. (9) Turro, N. J. Modern Molecular Photochemistry; University School Books: Mill Valley, CA, 1991; p 586. (10) Murtaza, Z.; Graff, D. K.; Zipp, A. P.; Worl, L. A.; Jones, W. E.; Bates, W. D.; Meyer, T. J. J. Phys. Chem. 1994, 98, 10504. (11) (a) Closs, G. L.; Johnson, M. D.; Miller, J. R.; Piotrowiak, P. J. Am. Chem. Soc. 1989, 111, 3751. (b) Closs, G. L.; Piotrowiak, P.; MacInnis, J. M.; Fleming, G. R. J. Am. Chem. Soc. 1988, 110, 2652. (12) Sigman, M. A.; Closs, G. L. J. Phys. Chem. 1991, 95, 5012. (13) MacQueen, D. B.; Eyler, J. R.; Schanze, K. S. J. Am. Chem. Soc. 1992, 114, 1897. (14) Intermolecular singlet energy transfer has also been previously observed in the inverted region: Engel, P. S.; Fogel, L. D.; Steel, C. J. Am. Chem. Soc. 1974, 96, 327. (15) Patterson, L. K.; Porter, G.; Topp, M. R. Chem. Phys. Lett. 1970, 7, 612. (16) (a) Turro, N. J.; Cox, S. G.; Li, X. Photochem. Photobiol. 1983, 37, 149. (b) Balzani, V.; Pina, F. A.; Parola, J.; Ferreira, E.; Maestri, M.; Armaroli, N.; Ballardini, R. J. Phys. Chem. 1995, 99, 12701. The authors investigated the effect of encapsulation within hemicarcerand 1 on the molecular oxygen quenching of the biacetyl triplet and obtained results virtually identical with those reported here. However, no results with other triplet energy acceptors were reported, nor were free energy effects mentioned.
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