J. Phys. Chem. 1995,99, 51-54
51
Temperature Dependence of Nonradiative Decay Juan Pablo Claude and Thomas J. Meyer* Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290 Received: September 28, 1994@
The temperature dependences of nonradiative decay for the metal-to-ligand charge transfer excited states of [Re(bpy)(CO)3(bEtpy)](PF6)and [Os(bpy)2(CO)(py)](PF& (bpy = 2,2’-bipyridine; 4-Etpy = 4-ethylpyridine; py = pyridine) follow the behavior predicted by the energy gap law. The variations with temperature can be calculated to within a factor of 2-3 by using parameters derived from a Frank-Condon analysis of emission spectral profiles.
Introduction The metal-to-ligand charge transfer (MLCT) excited states of polypyridyl complexes of Ru(II), Os(II), and Re(I), e.g., [Ru(bpy)3lZf (bpy is 2,2’-bipyridine), have played a central role in the study of photoinduced electron and energy transfer.’ Much has been learned about these excited state^.^^^ Resonance Raman measurements and Franck-Condon analysis of emission spectral profiles have been used to identify acceptor vibration^.^-^ Mode averaging and parameters derived by spectral analysis have been used to demonstrate quantitative application of the energy gap law to nonradiative decay. We show here that the energy gap law analysis can be extended to predict the temperature dependence of nonradiative decay and that the prediction can be verified by emission and lifetime measurements.
Theory
The quantity aEdaT is the entropic change accompanying excited state decay, neglecting changes in electronic entropy. It arises mainly from frequency changes in the solvent librations, A$,? (3)
Experimental Section
Nonradiative decay from MLCT states occurs with energy release into medium frequency v(polypyridy1) modes and, to a lesser degree, low-frequency modes and the s0lvent.43~ By averaging the medium frequency modes and combining lowfrequency modes and solvent in a single classical mode, k, is predicted to vary with the energy gap, EO,as in eq l b with ~ U M and EOin cm-1.5,6 In k, = In@,)
+ ln[F(calc)]
(la)
YE0
16 In 2
+
(lb)
,& includes the vibrationally induced electronic coupling matrix element (Vk) and F(ca1c) is the vibrational overlap factor. The remaining parameters are the electron-vibrational coupling constant SM,the vibrational spacing ~ U M and , the bandwidth AVO,^,^. These parameters (EO,SM,APo,l/z, ~ W M also ) define the emission spectral profile and can be extracted from the spectra by a Franck-Condon analysis and fitting procedure described el~ewhere.~ @
The “energy gap law” result in eq 1 is valid if EO>> S M ~ W M and ~ W > M> ~ B T If . ~BO and y have negligible temperature dependencies,8k, is predicted to vary with T as
Abstract published in Advance ACS Abstracts, November 15, 1994.
0022-3654/95/2099-0051$09.00/0
Materials. Spectrograde methanol was purchased from Burdick and Jackson Laboratories and p-dioxane from Aldrich; both were used as received. Ethanol was distilled from Mg turnings activated by 12. Laser dyes BBQ and bis-MSB were purchased from Exciton. The 1 x M solutions in p-dioxane were pumped with the 337.1 nm nitrogen laser fundamental. The complexes [Re(bpy)(CO)3(4-Etpy)](PF6) (4Etpy = 4-ethylpyridine) and [Os(bpy)z(CO)(py)l(PF6)2 (py = pyridine) were prepared according to literature p r o c e d ~ r e s . ~ J ~ Samples were prepared as optically dilute solutions (OD x 0.1 at the excitation wavelength) in 4: 1 (v:v) ethanol-methanol. Solutions were filtered, freeze-pump-thaw degassed a minimum of four cycles, and vacuum sealed. Measurements. Steady-state emission spectra were collected on a SPEX Fluorolog 212 photon-counting fluorimeter interfaced to a SPEX DMlB computer. The spectra were corrected for instrument response by the procedure supplied by the manufacturer. Emission decays were measured following laser flash excitation by using a PRA nitrogen laser model LNlOOO and a PRA dye laser model LN102 with excitation at 370 nm for Re1 and at 420 nm for Osn. The decays were monitored at the emission maximum by using a PRA monochromator model B204-3 and a Hamamatsu R-928 phototube operating within the range -600 to -750 V. The output was recorded on a LeCroy 7200A digital oscilloscope, and the digitized traces were fit to single exponential decays by using a LevenbergMarquardt routine. Temperature was varied in both experiments by using a Janis 6NDT cryostat and a Lake Shore 84C temperature controller. Emission quantum yields were measured relative to [Ru(bpy)3](PF& in acetonitrile.loa Low-temperature 0 1995 American Chemical Society
52 J. Phys. Chem., Vol. 99, No. 1, 1995
Claude and Meyer
TABLE 1: Emission Spectral Fitting Parameters in 4:l
(v:v) EtOH-MeOW
17 783 17820 17822 17853 17889 17925 17945 17954 17967 18002 17 106 17 125 17 141 17 162 17 172 17 190 17204
[Re(bpy)(CO),(4-Etpy)](PFs) 170 OM = 1400 cm-I) 180 190 200 210 220 230 240 250 260 [Os(bpy)z(CO)(py)](PF& 160 OM = 1240 cm-l) 170 180 190 200 210 220
1.63 1.65 1.63 1.64 1.66 1.67 1.67 1.66 1.65 1.66 1.34 1.35 1.35 1.36 1.35 1.35 1.35
2 252 2269 2323 2384 2354 2381 2410 2462 2491 2503 1577 1607 1646 1674 1733 1762 1819
a The maximum standard deviations are 12 (EO),0.012(SM),and 23 (ABo,I/z).Within this error, the last digits in the values of EOand ABo,I,z are not significant but were kept for purposes of plotting the data and
calculating slopes. quantum yields were estimated by 4LT
=42%3(3
where &T and ZLT are the quantum yield and the integrated emission intensity at low temperature. This approximation is based on the observation that the changes in index of refraction and optical density due to solution contraction with temperature are largely compensatory in 4: 1 (v:v) ethanol-methanol.lOb Nonradiative decay rate constants (k,) were calculated from lifetimes (z) and quantum yields (4) by 1-4 k, = z
-1 3
14
12 140
,
I
160
180
In general, nonradiative lifetimes of MLCT exicted states have complex temperature dependences. For example, low-temperature (< 77 K) measurements by Crosby et al. on [M(bpy)3J2+ (M = Ru, Os) have shown that there are three closely spaced, low-lying MLCT states." At higher temperature, where Boltzmann population of all three is appreciable, they behave kinetically as a single state. As room temperature is approached,
1
240
260
280
Figure 1. Plots of In k , vs T, 9 is 0.97 for Re' and 0.99 for Osn. additional complications appear from thermal population and decay through additional, low-lying MLCT or dd states.lZb The result in eq 2 is generally applicable only to nonradiative decay from a single state (or "averaged" state). For [Re(bpy)(C0)3(4-Etpy)l(PF6) and [O~(~PY)~(CO)(P~)J(PF~)Z, there are extended temperature ranges where there is no evidence for complications arising from contributions to k, by thermal population and decay through additional states, Figure 1. In our analysis of these data we assume that nonradiative decay in these ranges is dominated by a single state or averaged state. For both complexes the variation of k, with T becomes more complex at higher temperatures, presumably due to population and decay through upper excited states. Emission spectra and spectral fits for [Re(bpy)(CO)3(4-Etpy)J(PF6) and [Os(bpy)~(CO)(py)](PF6)~ in 4:l (v:v) ethanolmethanol are compared in Figure 2 , and fitting parameters at various temperatures are listed in Table 1. For [Re(bpy)(C0)3(4-Etpy)](PF6) at 250 K, the standard deviations for the individual parameters from the fits were 11 (EO),0.011 (SM), and 18 (APoJ~),with the correlation matrix
r=
Results and Discussion
I
220
Temperature (K)
Emission Spectral Fitting. The spectra were fit by a 1-mode Franck-Condon analysis from the equation5,'
Z(P) is the emitted light intensity at energy P in cm-' relative to the emitted intensity at the maximum. The parameters EO, SM,and APo0,1/2were optimized with a least squares minimization by using a simplex routine15 with h u fixed ~ for each complex as indicated in Table 1. The variance-covariance matrix, correlation matrix, and standard deviations for the individual parameters were computed by means of a quadratic extrapolation at the minimum.16
200
[
EO 1.000 0.989 -0.944
sM
*'O,l/Z
0.989
-0.944
I
1.000 -0.963 -0.963 1.000
The correlation matrix shows that the parameters are highly correlated and not unique. The combination of high correlation and small standard deviation is surprising. It is possible that the x2 function has a steep, well-defined minimum, and within this minimum there is a high intrinsic correlation due to the model.16 In this case, the correlations should not induce a significant spread in the parameter set. This is confirmed by the excellent linearity observed in the plots of EO vs T (Figure 3) and ( A P o J ~ )vs ~ T (Figure 4). Plots of SMvs T show some scatter, which suggests that the correlations are transferring the majority of the error to the parameter of smallest magnitude. From the spectral fitting data, (AV,O,J/~)~ varies linearly with T for both complexes consistent with4* = (AP&)2
+ 16 In 2 kBxoT
(4)
At low temperature, includes inhomogeneous broadening and the reorganizational energy from low-frequency modes, XL (= SAUL), h u > ~ ~BT." Values of xo evaluated from the slopes, xo = 1767 & 84 cm-' (Re') and xo = 1762 f.93 cm-' (Os'), are comparable to 1100 & 120 cm-l found for
Temperature Dependence of Nonradiative Decay
1t
J. Phys. Chem., Vol. 99, No. I, I995 53
40000
6.5e+6
35000
6.0~6
30000
5.94
25000
5.0e+6
r
-6
20000
4.%+6
"-. 15000
i 4.0e+6
3
10000
3.%+6
5000
3.0e+6
0
2.%+6
450
500
550
600
700
650
750
800
850
Wavelength (nm)
2.0~6
140
350000 300000
-E 250000
I
I
I
I
I
220
240
260
280
Figure 4. Plots of (AVo,ln)*vs T,? is 0.98 for Re' and 0.99for Osu. As shown in Figure 1, the linear dependence between In k, and T predicted b eq 2 is observed. Of greater significance for the energy gap aw analysis is the fact that within a factor of 2-3, it is possible to use the values of AEdAT, xo, ~ W M and y from the spectral fitting procedure and eq 2 to calculate the slopes of the correlations. The experimental and (calculated) values are ( A In kJAT) = 2.1 x K-' (8.3 x K-l) for Re1 and ( A In k,JAT) = 3.7 x K-' (2.6 x K-l) for Os". The values of C1 and C2 in eq 2 are C1 = -1.79 x K-' for Re1 and C1 = -1.74 x K-l, CZ = 2.63 x K-l, Cz = 4.32 x K-' for Osn. As mentioned above, successful application of this analysis is limited to cases where there are no competing nonradiative processes. Attempted application to [Ru(bpy)#+* and related complexes of Ru(I1) have proven to be unsuccessful because competing, thermally activated nonradiative processes involving decay from low-lying MLCT or dd states interfere in the lowtemperature measurements. l2
f
~200000
150000 100000
-
50000 0
450
500
550
600
650
700
750
800
Wavelength (nm)
Figure 2. Comparison of experimental and calculated emission spectra in 4:l (v:v) ethanol-methanol for A, [Re(bpy)(CO)3(4-Etpy)])PF6)at 170 K (EO= 17 783 cm-', SM = 1.63,AVOJ~ = 2252 cm-I, h w =~ 1400 cm-') and 260 K (EO= 18 002 cm-l, SM = 1.66,A V O , I=~ 2503 cm-I, ~ U =M1400 cm-'), and B,[oS(bpy)z(co)(py)](PF6)~ at 160 K (EO= 17 106 cm-I, SM = 1.34,AVOJD= 1577 cm-I, h w = ~ 1240 cm-') and 220 K (EO= 17 204 cm-', SM = 1.35,AVo,ln = 1819 cm-', h w =~ 1240 cm-'). 16200
, 200
Tempontun ( K )
i
1
-
1
160
180
17000 140
1
,
,
I
160
160
200
220
I
240
260
280
Tempomtun ( K )
Figure 3. Plots of EO vs T, 9 is 0.98for Re' and 1.00for OS". [Re(bpy)(C0)3Cl] in the same solvent in an earlier study?a EO varies linearly with T for both complexes and from the slopes of the plots of EO vs T and eq 3, A$, = 6.9 eu (Re') and 4.6 eu (Osn). The contribution to the entropic change for excited state decay from the solvent, e.g., eq 5, is positive as expected given the loss of the excited state dipole and decreased solvent polarization.
Conclusions Our results suggest that, even though the effect is small, k, is, in general, a function of T and that the effect can be accounted for by using the energy gap law. A similar conclusion has been reached for electron transfer in the inverted region.13 The distinction between nonradiative decay and electron transfer arises from the quantum mechanical approach taken to treat the two processes. In nonradiative decay, an electronic redistribution occurs between states (usually Born-Oppenheimer (BO) states) that are eigenstates of the same molecular Hamiltonian. This Hamiltonian includes Coulombic interactions between electrons (e*/rU), and the transition is promoted by vibronic coupling (a/aQk) included as a perturbation that breaks down the orthogonality of the BO states. Electron transfer occurs between donor and acceptor which are eigenstates of different Hamiltonians. The states are coupled by a perturbation V that includes both Coulombic interactions and vibronic coupling. Both terms in eq 2 contribute to the temperature dependence, the first from the entropic change and the second from the solvent reorganizational energy. Based on this analysis, k, could increase, decrease, or even be independent of T depending on the sign and magnitude of the entropic change since the solvent reorganizational energy is always positive. Acknowledgment. We thank the Department of Energy for supporting this research through Grant No. DE-FG05-86ER13633. References and Notes (1) (a) Kalyanasundaram, K. Photochemistry of Polypyridine and Potphyrin Complexes; Academic Press: London, 1992. (b) Balzani, V.; Scandola, F. Supramolecular Photochemistry; Ellis Horwood: Chichester,
,
54 J. Phys. Chem., Vol. 99, No. 1, 1995 U.K., 1991. (c) Meyer, T. J. Acc. Chem. Res. 1989, 22, 163. (d) Meyer, T. J. Pure Appl. Chem. 1986, 58, 1193. (e) Meyer, T. J. Progress in Inorganic Chemistry, Vol. 30; John Wiley and Sons: New York, 1983. (f) Kalyanasundaram, K. Coord. Chem. Rev. 1982,46, 159. (g) Geoffroy, G. L.; Wrighton, M. S. Organometallic Photochemistry;Academic Press: New York, 1979. (2) (a) Reitz, G. A.; Demas, J. N.; Degraff, B. A. J . Am. Chem. SOC. 1988,110,5051. (b) Midler, J. S.; Gold, J. S.; Kliger, D. S. J . Phys. Chem. 1986, 90, 548. (c) Reitz, G. A.; Dressick, W. J.; Demas, J. N.; Degraff, B. A. J . Am. Chem. SOC. 1986, 108, 5344. (d) Kober, E. M.; Meyer, T. J. Inorg. Chem. 1985, 24, 106. (e) Kober, E. M.; Meyer, T. J. Inorg. Chem. 1984,23,3877. (f) Drickamer, H. G.; Salman, 0. A. J . Phys. Chem. 1982, 77, 3337. (g) Bradley, P. G.; Kress, N.; Homberger, B. A.; Dallinger, R. F.; Woodruff, W. H. J . Am. Chem. SOC.1981, 103, 7411. (3) Caspar, J. V.; Meyer, T. J. J . Phys. Chem. 1983, 87, 952. (4) (a) Worl, L. A.; Duesing, R.; Chen, P.; Della Ciana, L.; Meyer, T. 3. J . Chem. SOC.,Dalton Trans. 1991, 849. (b) Mabrouk, P. A.; Wrighton, M. S. Inorg. Chem. 1986, 25, 3004. (c) McClanahan, S. F.; Dallinger, R. F.; Holler, F. J.; Kincaid, J. R. J . Am. Chem. SOC.1985, 107, 4860. (d) Caspar, J. V.; Westmoreland, T. D.; Allen, G. H.; Bradley, P. J.; Meyer, T. J.; Woodruff, W. H. J . Am. Chem. SOC.1984, 106, 3492. ( 5 ) Kober. E. M.: CasDar. J. V.: Lumokin. R. S.: Mever, T. J. J . Phvs. Chem.’ 1986, 90, 3722. (6) (a) Freed, K. F. Ton Cur. Chem. 1972.31.65. (b) Englman, R.; Jortner, J. Mol. Phys. 1970: 18, 145. (c) Freed, K. F.; Jortner, fJ . Chem. Phys. 1970, 52, 6272. (d) Bixon, M.; Jortner, J. J . Chem. Phys. 1968, 48, 715. (7) (a) Caspar, J. V.; Meyer, T. J. Inorg. Chem. 1983, 22, 2444. (b) Caspar, J. V.; Meyer, T. J. J . Am. Chem. SOC.1983,105,5583. (c) Caspar,
Claude and Meyer J. V. Ph.D. Dissertation, University of North Carolina, Chapel Hill,NC, 1982. (d) Lumpkin, R. S. Ph.D. Dissertation, University of North Carolina, Chapel Hill, NC, 1987. (8) In earlier studies on MLCT excited states, it was found that y was relatively independent of T since SM scales linearly with Eo?-’ (9) HUDD.J. T.: Nevhart. G. A.: Mever. T. J.: Kober. E. M. J . Phvs. Chem.’ 199i,-96, 10820.’ (10) (a) CasDar, J. V.: Mever, T. J. J . Am. Chem. Soc. 1989, 111,7448. (b)Lumpkn, R.S.; Meyer, ‘f’.J. J . Phys. Chem. 1986, 90, 5307. (1 1) Ballhausen, C. I. Molecular Electronic Structures of Transition Metal Complexes; McGraw-Hill: New York, 1979. (12) (a) Claude, J. P.; Meyer, T. J. Unpublished results. (b) Lumpkin, R. S.; Kober, E. M.; Worl, L. A,; Murtaza, 2.;Meyer, T. J. J . Phys. Chem. 1990, 94, 239. (13) Chen, P.; Mecklenburg, S. L.; Meyer, T. J. J . Phys. Chem. 1993, 97, 13126. (14) Sullivan, B. P.; Caspar, J. V.; Johnson, S. R.; Meyer, T. J. Organometallics 1984, 3, 1241. (15) Claude, J. P.; Meyer, T. J. Manuscript in preparation. (16) We have confirmed that the x2 hyper-surface has a single minimum in the region of physicially meaningful values for EO,SM,and AVO1/2.’~ (17) (a) Hagar, G. D.; Crosby, G. A. J . Am. Chem. SOC.1975,97,7031. (b) Hagar, G. D.; Watts, R. J.; Crosby, G. A. J . Am. Chem. SOC.1975,97, 7037. (c) Hipps, K. W.; Crosby, G. A. J. Am. Chem. SOC. 1975,97,7042. (d) Crosby, G. A,; Elfring, W. H., Jr. J. Phys. Chem. 1976, 80, 2206. (e) Pankuch, B. J.; Lacky, D. E.; Crosby, G. A. J . Phys. Chem. 1980,84,2061. (f) Lacky, D. E.; Pankuch, B. J.; Crosby, G. A. J . Phys. Chem. 1980, 84, 2068.
