5850
J . Phys. Chem. 1991, 95, 5850-5858
Intramolecular Electron Transfer in the Inverted Region Pingyun Chen, Rich Duesing, Darla K. Craff, and Thomas J. Meyer* Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290 (Received: January 4, 1991)
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In the series [(4,4'-(X),-bpy)Re1(CO)3(py-PTZ)]+ (X = W H 3 ,CHI, H, C(0)NEtz,C02Et) and [(bpz)Re1(C0),(py-PTZ)]+ (bpz is 2,2'-bipyrazine), dr(Re) r*(4,4'-(X),-bpy) excitation is followed by rapid, intramolecular electron transfer to give the redox-separated states, [(4,4'-(X)2-bpy')Re1(CO)3(py-PTZ'+)] '. They return to the ground states by intramolecular, back electron transfer, [(4,4'-(X)2-bpy')Re'(CO)3(py-PTZ'+)]+ [(4,4'-(X),-bpy)Re(CO),(py-PTZ)]+. The back electron transfer reactions are highly exergonic, AGO -1.18 to -1.93 eV in 1,2-dichloroethane, and occur in the inverted region. As determined by transient absorbance measurements following laser flash photolysis, k b varies from 6.7 X lo6 s-l for X = OCH3 to 9.1 X lo7 s-l for the bpz complex. The energies of the related MLCT excited states, [(4,4'-(X),-bpy'-)ReI1(C0),(4-Etpy)]+* (4-Etpy is 4-ethylpyridine) fall in the range Eo = 1.77-2.31 eV in the same medium. In this series the variations in the rate constant for nonradiative decay with driving force, k,, = 2.6 X 105-2.8 X IO's-I, are in accord with the energy gap law. Nonradiative decay has been analyzed quantitatively based on the results of a Franck-Condon analysis of emission spectral profiles. For back electron transfer in the inverted region, kb decreases logarithmically with -AGO as that between In (knr predicted by the energy gap law. The slope of the correlation between In ( k b X 1s) and -AGO is X Is) and Eo. An analysis based on the energy gap law provides an explanation for the decrease. The implications of our findings for the design of long-lived, redox-separated states are presented.
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Introduction In the classical theories of electron transfer developed by Marcus and Hush, a bell-shaped dependence of the electron-transfer rate constant on the free energy change, AGO, is predicted to exist.'-3 When -AGO > A, where X is the sum of the intramolecular (Xi) and solvent (A,,) reorganizational energies, the "inverted region" is reached and electron-transfer rate constants are predicted to decrease as AGO becomes more favorable. For fast, bimolecular reactions, the appearance of inverted behavior can be hidden if the reactions occur at the diffusion-controlled limit.4~~Additional complications can arise because reaction channels become available in which one of the products is formed in an excited state. Nonetheless, examples of inverted behavior have been found in rigid organic glasses? in unsymmetrical, linked organics: in charge recombination in geminate ion in photochemical electron transfer in linked porphyrinquinones,9 and in long-range electron transfer in proteins.I0 (1) (a) Marcus, R. A. J . Chem. Phys. 19!6,24,966. (b) Marcus, R. A. Discuss. Faruday Soc. 1%0,29,21. (c) Marcus, R. A. J. Chem. Phys. 1965, 43, 679. (d) Marcus, R. A. Annu. Rev. Phys. Chem. 1964, 15, 155. (e) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acfa 1985,811,265. (0 Siders, P.; Marcus, R. A. J. Am. Chem. Soc. 1981,103, 748. (2) (a) Hush, N. S. J . Chem. Phys. 1958,28,962. (b) Hush, N. S . Trans. Faraday SOC.1961, 57, 557. (c) Hush, N. S. Elecfrochim. Acta 1968, 13, 1005.
(3) (a) Sutin, N. Acc. Chem. Res. 1982, I S , 275. (b) Sutin, N. J . Phofochem. 1979, 10, 19. (c) Sutin, N. Prog. Inorg. Chem. 1983,30, 441. (d) Newton, M. D.; Sutin, N. Annu. Reu. Phys. Chem. 1984, 35, 437. (4) (a) Rehm, D.; Weller, A. Is?. J . Chem. 1970.8, 259. (b) Bock, C. R.;
Connor, J. A.; Gutierrez, A. R.; Meyer, T. J.; Whitten, D. G.; Sullivan, B. P.; Nagle, J. K. Chem. Phys. Lett. 1979, 61, 522. (5) (a) Beitz, J. V.;Miller, J. R. J . Chem. Phys. 1979, 71, 4579. (b) Miller, J. R.; Beitz, J. V. Ibid. 1981, 74,6476. (c) Miller, J. R.; Beitz, J. V.; Huddleston, R. K. J . Am. Chem. SOC.1984, 106, 5057. (6) (a) Miller, J. R.; Calcaterra, L. T.; Closs, G. L. J . Am. Chem. SOC. 1984, 106: 3047. (b) Closs, 0. L.; Calcaterra, L.T.; Green, N. J.; Penfield, K. W.; Miller. J. V. J . Phys. Chem. 1986, 90, 3673. (c) Closs, G. L.; Miller, J. R. Science 1988, 240, 440. (7) (a) Ohno, T.; Yoshimura, A.; Mataga, N.J . Phys. Chem. 1986, 90. 3295. (b) Asahi, T.; Mataga, N. Ibid. 1989, 93, 6575. (8) (a) Gould, 1. R.; Ege, D.; Mattes, S. L.;Farid, S. J . Am. Chem. SOC. 1987,109, 3794. (b) Gould, 1. R.; Moser, J. E.;Armitage, B.; Faris, S. Ibid. 1989, 1 1 1 , 1917. (c) Gould, 1. R.; Moody, R.; Faris, S. Ibid. 1988, 110, 7242. (9) (a) Irvine, M. D.; Harrison, R. J.; Beddard, G.S.; Leighton, P.; Sanders, J. K. M. Chem. Phys. 1986, 104, 315. (b) Archer, M. P.; Gadzekpo, V. P. Y.; Bolton, J. R.; Schmidt, J. A.; Wetdon, A. C. J . Chem. Soc., Faraday Trans. 2 1984,82,2305. (c) Wasielewski, M. R.; Niewczyk, M. P.; Svec, W. A.; Pewitt, E. B. J . Am. Chem. SOC.1985, 107, 1080. (10) (a) McLendon, G.; Miller, J. R. J . Am. Chem. Soc. 1985,107,7781. (b) McLendon, G.Acc. Chem. Res. 1988, 21, 160.
0022-3654/91/2095-5850$02.50/0
SCHEME I [(4,4'-(X)p-bpy'-)Re"(CO)3(py-PTZ)]+'
hv
11
llr
% [(4,4'-(X)2-bpy'-)Re'(CO)~(~~-PTf+)1+
We report here a quantitative study on the free energy dependence of intramolecular electron transfer in the inverted region. It was based on the series [(4,4'-(X)z-bpy)Re(C0)3(py-PTZ)]+ (X = OCH3, CH3, H, C(O)NEt,, C0,Et) or [(bpz)Re(CO),(py-PTZ)]+ (bpz = 2,2'-bipyra~ine).".~, In this series, dr(Re)
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~*(4,4'-(X),-bpy), metal-to-ligand charge transfer (MLCT) excitation is followed by intramolecular electron transfer, Scheme I. When combined, these photophysical events provide a pathway for the intramolecular sensitization of the ligand-based, redoxseparated states [(4,4'-(X)2-bpy'-)Re(CO)3(py-PTZ'+)]+. These states return to the ground state by back-electron-transfer reactions that are highly exergonic and w u r in the inverted region.11v12By making variations in the substituent X, it has been possible to vary the driving force by -0.8 eV, and this has provided an experimental basis for exploring the dependence of kb on AGO in the inverted region. In a parallel study, rate constants for nonradiative decay of the related MLCT excited states, [(4,4'-(X)z-bpy'-)Re11(C0)3(4Etpy)]+* (4-Etpy is 4-ethylpyridine), were measured. The goal
knJ
[(4,4'-(X)z-bpy'-)Re11(CO)3(4-Etpy)]+*
( I I ) (a) Chen, P.; Duesing, R.; Tapolsky, G.; Meyer, T. J. J . A x . Chem. Soc. 1989, 111,8305. (b) Duesing, R.; Meyer, T. J. Manuscript in prepa-
ration.
(12) (a) Chcn, P.; Westmoreland, T. D.; Danielson, E.; Schanze, K.; Anthon, D.; Neveux, P. E., Jr.; Meyer, T. J. Inorg. Chem. 1987, 26, 11 16. (b) Westmoreland, T. D.; Schanze, K. S.; Neveux, P. E. Jr.; Danielson, E.; Sullivan, B. P.; Chen, P.; Meyer, T. J. Ibid. 1985, 24, 2596.
0 1991 American Chemical Society
Intramolecular Electron Transfer of the combined study was to investigate electron transfer and nonradiative decay in related systems where the energy changes were comparable. We wanted to establish an experimental link between the two processes. Although they are fundamentally different, there are similarities between them. Electron transfer in the inverted region occurs between chemical sites that are weakly coupled electronically. In nonradiative decay there is also a change in electronicdistribution, but it accompanies a transition between different electronic states. Both processes share the mechanistic demands imposed by a large energy release. In this domain, the mechanism depends upon whether or not high or medium-frequency vibrations are present that respond to the change in electronic distribution between the initial and final states. If such modes are present, they act as energy acceptors, and nuclear tunneling and the overlap of vibrational wave functions between the initial and final states play If the participating modes a dominant role in the tran~ition.’~~’ are classical in nature, the mechanism involves thermal activation to the intersection regions between the potential energy curves for the initial and final states. If there are participating high- or medium-frequency modes, rate constants are predicted to depend upon their frequencies, the changes in their equilibrium displacements, and the energy gap between the initial and final states. These parameters can be obtained by Franck-Condon analysis of spectral profiles. Once they are available, it is possible to analyze nonradiative decay quantitatively. This approach has been applied to nonradiative decay of MLCT excited states.‘& In this paper we have extended the analysis to electron transfer in the inverted region and utilized it to compare the dynamics of nonradiative decay in [(4,4’(X)2-bpy’-)Re11(CO)3(I-Etpy)]+* and back electron transfer in [ (4,4’-(X)2-bpy*-)Re(CO)3(py-PTZ+)]+. Experimental Section Materials. Solvents for preparations were reagent grade. The exception was T H F and it was freshly distilled over potassium. The solvents CH3CN and CH2CICH2Cl (DCE) for electrochemical and spectroscopic measurements were high-purity solvents purchased from Burdick & Jackson. The supporting electrolyte was [N(n-C,H9),] (PF6). The ligand 4-ethylpyridine (4-Etpy) (Aldrich) was distilled prior to use. The compound Re(CO)5Cl was purchased from Pressure Chemical Co. and used without further purification. The compound 4,4’-dimethyl2,2’-bipyridine (4,4’-(CH3)2-bpy)was purchased from Aldrich. The compound 4,4’-bis(diethylcarbamoyl)-2,2’-bipyridine (4,4’-(C(0)NEt2),-bpy) was provided by Dr. P. E. Neveux Jr.’* The compounds I0-(4-picolyl)phenothiazine (py-PTZ),19 4,4’(CH30)2-bpy,204,4’-(NH2)2-bpy,20and 4,4‘-bis((ethy1oxy)carbonyl)-2,2’-bipyridine) (4,4’-(C02Et)2-bpy)21*22 were synthesized by literature procedures. The preparations and char(13) (a) Kestner, N. R.; Logan, J.; Jortner, J. J . Phys. Chem. 1974, 78, 2148. (b) Efrima, S.; Bixon, M. Chem. Phys. 1976,13,447. (c) Ulstrup, J.; Jortner, J. J. Chem. Phys. 1975, 63, 4358. (14) (a) Englman, R.; Jortner, J. Mol. Phys. 1970. 18, 145, (b) Bixon, M.; Jortner, J. J . Chem. Phys. 1968, 48, 715. (c) Freed, K. M.; Jortner, J. Ibid. 1970, 52, 6272. (.1 9, la) . . Mever. T. J. Acc. Chem. Res. 1978.11.94. Ib) Mever. T. J. Prop. Inorg. Chem. h 3 , 3 0 , 3 8 9 . (c) Meyer, T. J.: Taube, H: In domprehensi;e Coordination Chemistry; Sir Wilkinson, G., Ed.; Pergamon Press: Oxford, 1987; Vol. I , p 331. (16) (a) Kober, E. M.; Caspar, J. V.;Lumpkin, R. S.;Meyer, T. J. J. Phys. Chem. 1986, 90,3722.. (b) Caspar, J. V.; Meyer, T. J. Ibid. 1983,87, 952.
(c) Caspar. J. V.; Sullivan, 9. P.; Kober, E. M.; Meyer. T. J. Chem. Phys. Ltf.1982. 91, 91. (17) Ovchinnikov, A. A,; Ovchinnikova, M. Y. Adu. Quantum Chem. 1982, 16, 161. ( 1 8) Neveux. P. E. Ph.D. Dissertation. Universitv of North Carolina. Chapel H!II, NC, 1987. (19) Ciana, L. D.; Hamachi, I.; Meyer, T. J. J. Org. Chem. 1989,51, 1731. (20) Maerker, G.; Case, F. H. J . Am. Chem. Soc. 1958, 80, 2745. (21) Bos, K. D.; Kraijkamp, J. G.; Noltes, J. G. Synth. Commun. 1979, 9, 497. (22) Worl, L. A.; Duesing, R.; Chen, P.; Ciana, L. D.; Meyer, T. J. J . Chem. SOC.,Dalton Trans. 1991, 849.
The Journal of Physical Chemistry, Vol. 95, No. IS, 1991 5851 acterizations of the chloro complexes [(4,4’-(X),-bpy)Re(CO)3Cl] and the 4-Etpy complexes [(4,4’-(X)2-bpy)Re(C0)3(4-Etpy)l+ will appear e l ~ e w h e r e . ~The ~ . ~preparation ~ of [ ( b ~ y ) R e ( C 0 ) ~ (py-PTZ)](PF6) has been reported.’” [(4,4’-(X),-b~y)Re(CO)~(p~PTz)l(PF6) (X = OCHD CH3) and [(bpz)Re(CO),(py-PTz)](PF6).These salts were prepared by a procedure similar to that given in the literature.’% The compound [(4,4’-(CH30)2-bpy)Re(CO)3C1] (260 mg) and 130 mg of AgTFMS in 40 mL of T H F were heated at reflux for 30 min. The ligand py-PTZ (220 mg) was added to the reaction mixture, and it was heated at reflux for 2 h. After removal of AgCl by filtration, the solvent was removed on a rotary evaporator to give a reddish brown oil. The oil was redissolved in 40 mL of 3:l (v:v) MeOH/H20, and 1.2 g of NH4PF6 dissolved in -10 mL of water was added with stirring. The yellow precipitate that formed was filtered and washed with a copious amount of H20 and three times by 20-mL portions of diethyl ether to yield 276 mg of the product. For X = OCH3, v ( C 0 ) 2033, 1925 cm-I. Elemental Anal. Calcd: C, 43.0%; H, 2.84%; N, 6.08%. Found: C, 43.53%; H, 2.89%; N, 5.95%. For X = CH3, v(C0) 2034, 1934, 1925 cm-l. For [(bpz)Re(Co),(py-PTZ)](PF,),v(C0) 2043, 1947 cm-I. Elemental Anal. Calcd: C, 40.47%; H, 2.34% N, 9.77%. Found: C, 41.89%; H, 2.44%; N, 9.59%. [(4,4’-(C(0)NEt2)2-bpy)Re(C0)3(py-FTZ)]( PF6). This salt was prepared by a similar procedure. The product was further purified by dissoiving in CH2C12and reprecitating from diethyl ether. IR spectrum v(C0) 2037, 1930 cm-l. Elemental Anal. Calcd: C, 46.46%; H, 3.8050; N, 7.93%. Found: C, 43.22%; H, 3.86%; N, 7.47%. [(4,4’-(Co2Et)2-bpy)Re(C0)3(py-FTZ)](PF6). This salt was prepared by a similar procedure. The product was purified on a silica gel column by using 2: 1 CH2C12/acetoneas eluant. The first nonemissive band was collected. v(C0) 2038, 1937 cm-’. Elemental Anal. Calcd: C, 44.18%; H, 3.01%; N, 5.57%. Found: C, 44.15%; H, 3.18%; N, 5.56%. Measurements. UV-visible absorption spectra were obtained by using an HP 8451A diode array spectrophotometer. Emission spectra were recorded on a Spex Fluorolog 21 2 photon-counting fluorimeter. The spectra were corrected for the instrument response by the procedure supplied by the manufacturer. IR spectra in CH3CN or 1,Zdichloroethane were recorded on a Nicolet 20D FTIR spectrometer. Electrochemical measurements were conducted on a PAR Model 264A polagraphic analyzer/stripping voltammeter in a one-compartment cell. Solutions were deaerated by bubbling with Ar or N2 for at least 5 min. Emission lifetimes were measured by using a PRA LN 1000/LN 102 nitrogen laser/dye laser combination for sample excitation. Emission was monitored at a right angle to the excitation by using a PRA B204-3 monochromator and a cooled, 10-stage, Hamamatsu R928 PMT coupled to either a LeCroy 9400 digital oscilloscope or a LeCroy 6880 transient digitizer interfaced to an IBM PC. The absorbance of the solutions in 1-cm cuvettes was -0.1 at the excitation wavelength. Solutions were deaerated by bubbling with Ar for at least 10 min. The decay data were fit to eq 2 in which Io and I ( t ) were the emission
I(r) = Io exp(-kt)
(2)
intensities at the monitoring wavelength at times 0 and t , and k was the decay rate constant. Emission quantum yields, &,, were measured in optically dilute solutions relative to [(bpy)Re(CO)3(4-Etpy)](PF6)for which = 0.18 in CH2C12at 295 K.16b*24 They were calculated by using eq 3. In eq 3, A is the absorbance at the excitation wavelength, (3) I is the integrated area of the emission band, and n is the refractive (23) Hino, J. K.; Ciana. L. D.; Dressick, W. J.; Sullivan, B. P. Manuscript in preparation. (24) Demas, J. N.; Crosby, G. A. J . Phys. Chem. 1971, 75, 991.
5852 The Journal of Physical Chemisrry, Vol. 95, No. 15, 1991
Chen et al.
TABLE I: Spectral and Electrochemical Data in 1,Z-Dichloroetbmeat 23 A 2 O C
L, nm complexa (e, M-’ cm-I)* [ ( ( N H ~ ) Z ~ P Y ) R ~ ( C ~ ) , ( ~ - E ~ P Y ) I + 348 (7.7x 103) [((CH~)Z~PY)R~(CO),(~-E~PY)I’ 356 (4.5 x 103) 364 (4.1 X lo3) [(~PY)R~(C~),(~-E~PY)I+ [((COzEt)zbpy ) R ~ ( C O ) ~ ( ~ - E ~ P Y ) I + 398 (4.9x 103) [((CH,O)Z~PY)R~(C~),(PY-FTZ)I+350 (5.4 x 103y [((CH,)Z~PY)R~(CO),(PY-PTZ)I+ 360 365 (4.4x 103y [(bpy)Re(Co),(py-PTZ)It 374 (4.8x 103) [((C(O)NE~Z)Z~PY)R~(CO),(PY-PTZ)I+ 394 (6.0 x 103) [ ( ( C O Z E ~ ) Z)~RPeY( C o ) d p ~ - P T z ) l + 406 (4.2X IO3) [(~P~)R~(CO)~(PY-PTZ)I+
u(CO), cm-I 2027, 1916 2034, 1928 2036, 1930 2038, 1936 2033, 1925 2034, 1925 2036, 1932 2037, 1930 2038, 1937 2043, 1947
Re(II/I) 1 .59‘ 1 .78‘ 1.74‘ 1 .89‘J g g g g g g
E 1 p V (VSSSCE)‘ FTZ+lO
bpy-1° -1.62”’ -1.16‘ -1.17‘ -0.77‘ -1.30 -1.29 -1.14 -0.98 -0.73 -0.55
0.85 0.80 0.85 0.82 0.86 0.85
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(X)2bpy is 4,4’-(X)2-bpy; bpy is 2,2’-bipyridine; bpz is 2,2’-bipyrazine. bAbsorption maxima (*2 nm) for d r r*(bpy) MLCT transitions. Numbers in brackets are the molar extinction coefficients at the wavelength cited. c.EIIzvalues (A0.02V) were obtained in 0.1 M [N(n-C4H9)?](PF6)-CH2CICH2CI by taking an average of anodic and cathodic peak potentials in cyclic voltammograms by using PI bead working, PI wire auxiliary, and saturated sodium chloride calomel (SSCE) reference electrodes at a scan rate of 100 mV/s. dEstimated because it overlaps with bpyand PTZ-based T T* transitions; c was calculated from the absorbance at the wavelength cited. @Obtainedin 0.1 M [N(n-C,H9),](PF6)-CH3CN. ’Irreversible, the potential cited is the peak potential. #Obscured by the chemically irreversible, second oxidation wave at PTZ.
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index for the sample (s) and the reference (r) solutions. Since the solutions were dilute, n, and n, were taken to be equal to those of the pure solvents. Transient absorption measuremerits were performed by using the third harmonic of a Quanta Ray DCR-2A Nd:YAG laser. The excitation beam was coincident with the monitoring beam of an Applied Photophysics laser kinetic spectrometer, which included a 250-W pulsed Xe arc probe source, a f/3.4 grating monochromator, and a five-stage PMT. The output was coupled to a Tektronics 7912 transient digitizer or a LeCroy 9400 digital oscilloscope interfaced to an IBM PC. Electronic control and synchronization of laser, probe, and the digital oscilloscope was achieved by electronics of our own design.2s Solutions were freeze-pump-thaw deoxygenated for at least four cycles. The absorbance at the excitation wavelength was typically -0.7. The absorbancetime decay data were fit to eq 4, where A. and A(r) were the absorbances at times 0 and 1. A(r) = A. exp(-kr)
I\
A
B
(4)
Emission Spectral Fitting. The procedure for the FranckCondon analysis of emission spectral profiles has been described in detail elsewhere.16a.26Only a brief outline of a single-mode analysis is presented here. Calculated emission profiles were generated by using eq 5 and compared with the measured spectra. In eq 5 , I(P) is the emitted
--,--,
350
300
400
4 50
-
IO
Wavelength (nm) Figure 1. UV-visible absorption spcctra in 1,2-dichloroethane for (A) [(~,~’-(CH,)Z-~PY)R~(CO)~(~-E~PY)~+ (--I, [(bpy)Rc(CO)l(eEtpy)I+ (-3,and [(4,4’-(C02Et)2-bpy)Re(CO)~(4-Et~~)lt (B) [(bpy)Re(CO)Apy-PTZ)l+ (--I, [(4,4’-(C02Et)~-bpy)Re(CO)~(py-PTZ)1+ (-), and [(bpz)Re(CO),(py-PTZ)]+ (.-). All of the samples were PFC salts. (e-);
intensity in quanta at energy B in cm-I relative to that of the 0 transition. The quantity u is the vibrational quantum number for the acceptor mode in the ground state, and haMis the vibrational spacing. For the bpy-based, MLCT excited state, this mode is an average of seven contributing u(bpy) modes that occur from 1 100 to 1650 cm-’ and a higher frequency, u(CO), mode at -2030 cm-1.1h*2z26 The quantity SMis the electron-vibrational coupling constant. It is proportional to the square of the change in equilibrium displacement for the averaged mode between the excited and ground states. The quantity A30,1/2is the full width at half-maximum of the vibronic components. It includes contributions from low-frequency modes and the solvent. The quantity Eo is the u* = 0 u = 0 energy difference between the excited and ground states in the single-mode approximation. In the fitting
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(25) Danielson, E. In preparation. (26) (a) Carpar, J. V.;Watmoreland, T.D.;Allen, G. H.; Bradley, P.G.; Meyer, T. J.; Woodruff, W. H.J . Am. Chcm. Soc. 1984, 106, 3492. (b) Lumpkin. R. S.Ph.D. Dissertation, University of North Carolina, Chapel Hill, NC, 1989.
procedure, trwM was fixed at 1450 cm-I, and the remaining three parameters were varied to obtain the best match between the calculated and experimental spectral profiles. Results UV-Visible Absorption Spectra. Representative absorption spectra for the series [(4,4’-(X),-bpy)Re(Co),(4-Etpy)]+ are shown in Figure 1A. The bands at low energy are d r r*(4,4’-(X),-bpy) transitions. The bands at X < 330 nm are polypyridyl-based, ?r ?r* transition^.'^*"^'^"^ Absorption maxima
-
-
(27) (a) Wrighton, M.; Morse, D. L. J . Am. Chcm. Soc. 1974, 96, 998. (b) Geoffroy, G. L.; Wrighton, M. Organometallic Photochemistry; Academic: New York, 1979. (c) Juris, A,; Campagna, S.;Bidd, 1.; Lehn, J.; Ziessel, R. Inorg. Chem. 1988, 27,4007. (28) Barqawi, K. R.; Llobet, A.; Meyer, T. J. J . Am. Chcm. Soc. 1988, 110.7751.
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5853
Intramolecular Electron Transfer TABLE II: Emision Energks, Lifetimes, rad Quantun Yields for [(a4’-(X),-bpy)Re(Co),(eEtpy)l+ in 1,tDkbloroetbrae It 23 2OC A-, nm k,,C s-I X (E,,eV)’ 7 , ~ ~ s , Q d (XIO”)
*
CH3’ OCH, H C6H5
CI CO2Et C02Me
#:
540 (2.30) 565 (2.19) 570 (2.17j 577 (2.15) 608 (2.04) 625 (1.98) 630 (1.97) 717 (1.73) 645 (1.92)
2.300 0.380 0.510
0.870 0.1 15 0.275 0.250 0.035 0.091
0.40 0.086 0.13 0.26 0.030 0.069 0.058 0.0023 0.025
0.262 2.41
1.71 0.868 8.43 3.39 3.77 28.5 10.7
‘4,4’,5,5’-(CH3),-2,2’-bipyridine. *Emission band maxima in nm (*2) or in eV. ‘Lifetimes (*1%) obtained by analyzing emission decay curves at the emission maxima following laser excitation at 377 nm. dEmission quantum yields (110%). eCalculated from the relationship k,, = ( 1 - Q,)/ The i. values are *2% except for the first (*5%), third (*3%), and fourth (*3%) entries. f[(bpz)Re(CO),(4,4’-bpy)l+.
-
and molar extinction coefficients for the d r ~*(4,4’-(X)~-bpy) transitions in 1,2-dichloroethane are listed in Table I. IR Spectra. i n the IR spectra of the complexes, two v(C0) stretching bands appear, Table I. The band at lower energy is an overlap of two bands that are nearly equal in energy. These bands increase in energy as the substituents X are varied from electron donating to electron withdrawing. This is because the d r orbitals that participate in d?m*(CO) back-bonding are also involved in back-bonding with n*(4,4’-(X)2-bpy).22*31i32 As d7rr (4,4’-( X) 2- bpy) back-bonding increases, d r - r * (CO) backbonding decreases, which leads to the increase in the energy of v(C0). Electrochemistry. E1j2values in 0.1 M [N(n-C,H,),](PF,)1,2-dichIoroethane obtained by cyclic voltammetry are listed in Table I. For [(4,4’-(X)2-bpy)Re(CO)3(4-Etpy)]+, a chemically reversible wave was observed for the couple [4,4’-(X),-bpyl0/- in the range -1 -62 V (vs SSCE) for X = NH2 to -0.77 V for X = C02Et. Potentials for the Re”/’ couples were in the range 1.59 V for X = NH2 to 1.89 V for X = C02Et. The pattern of waves that appeared in cyclic voltammograms of [(4,4’-(X)2-bpy)Re(CO),(py-PTZ)]+ was the same except for the appearance of the characteristic oxidation waves for PTZ. The second of these waves was irreversible and obscured the waves for the Re”/’ couples.I2 Emission and Emission Lifetimes. Emission maxima (Ee,,.,), quantum yields (&,,), and lifetimes ( 7 ) for the MLCT-based emissions from [(4,4’-(X)2-bpy)Re(CO)3(4-Etpy)]+ in 1,2-dichloroethane at 295 K are listed in Table II.23*29 The emission decays were first order. Nonradiative decay rate constants, k,,, were calculated by using the relationship k, = l / ~ ( -l I&,). They are also listed in Table 11. The emission spectra were broad and featureless because interactions with the surrounding solvent molecules broaden the individual vibronic components resulting in Gaussian-appearing envelops.22 The parameters derived from emission profiles by spectral fitting are listed in Table 111. An energy gap law plot of In (k,, X Is) vs Eo is shown in Figure 2A. The factor 1s was included so that k,, X Is is dimensionless. The line in the figure is the least-squares fit to the equation In (k,, X 1s) = 27.5 (f3) - 5.9 (fl.4)Eo (Eo in electronvolts). Very weak but detectable emissions could be observed from samples of [(4,4’-(X)2-bpy)Re(CO)3(py-PTZ)]+ that had been purified by column chromatography. The emission energies and lifetimes were comparable to those of the 4-Etpy analogues. They (29) Tapolsky, G.; Duesing, R.;Meyer, T. J. J . Phys. Chem. 1989, 93, 3885. (30) (a) Bryant, G. M.; Fergusson. J. E.; Powell, H. K. J. Aust. J. Chem. 1971, 21, 259. (b) Bryant, G. M.;Fergusron, J. E. Ibid. 1971, 21, 275. (31) Cotton, F. A.; Wilkinmn. G. Advanced Inorgank Chemistry, 4th ed.; John Wiley and Sons: New York, 1980; Chapter 25, p 1049. (32) Chen, P.; Curry, M.;Meyer, T. J. Inorg. Chem. 1989, 28, 2271.
TABLE 111: Elnission Spectnl ntthg PIt8Pleten for [(4,4’-(X)*-bpy*)R@(C0)3(4Etpy)r* h 1,2-Dkblontbrae It 298 K‘
X
Eo, cm-I (eV)
S”
y‘
A P ~ , ~cm-’ ,~,
CHI OCH, H C6H5 CI C02Me bpzb NO2
18650 (2.31) 18000 (2.23) 17850 (2.21) 17450 (2.16) 16900 (2.10) 16200 (2.01) 16050 (1.99) 14300 (1.77)
1.4 1.1 1.1 0.97 1.2 0.98 1.10 0.95
1.2 1.4
2,700 3,100 3,000 2,900 2,600 2,500 2,600 2,300
1.4 1.5
1.3 1.4 1.3 1.3
In F(calc)d -17.17 -17.98 -17.90 -18.41 -16.08 -16.99 -15.61 -14.44
“Based on a four-parameter fit by using eq 5 with huh( = 1450 cm-I. The estimated uncertainties are EO (*5%), SM(*IO%), A P o , ~ , ~ (is%),and In [F(calc)] (*3%). The uncertainties in the individual parameters are relatively large, but the parameters are highly correlated., This leads to the relatively small uncertainties in In [F(calc)]. A combination of parameters that give an acceptable fit fall within the range cited above. ‘This complex is [(bpz)Re(C0),(4,4’-bpy)]+. ‘y = In (EO/(SMhuM)) I , q 1Oc. dDefined in q 13b.
-
1
18 1 n
w
17
d
X L
r’ W
c
I
16 15 14 13: 1.7
lo
.
.
I
1.8
I
1.9
.
I
2.0
.
I
2.1
.
I
2.2
.
I
2.3
I
171
.
I 2.4
/I
B
X L
A’ W C
I
-19
-18
-17
-16
-15
-14
In [ F( ca IC)] Figure 2. (A) Plot of In (k, X Is) vs Eo in 1,2-dichloroethane for [(4,4’-(X)2-bpy’)Re’’(CO)3(4-Etpy)]+*. The substituents are indicated on the plot. The least-squares line drawn through the data points is to the equation In (k,, X Is) = 27.5 (*3) - 5.9 (h1.4)Eo (Eo in electronvolts). (B) Plot of In (kn, X 1s) vs In [F(calc)]. The term In [F(calc)] was calculated by using eq 13 and the parameters in Table 111. A slope of 1 was imposed in constructing the linear correlation. The intercept was 33.0 0.5.
arose from small amounts of emissive impurities in the samples.’= Transient Absorbance. Transient absorption difference spectra were acquired following laser flash excitation of [(4,4’-(X)2bpy)Re(CO),(py-PTZ)]+ at 355 nm. Absorbance increases occured during the laser pulse ( - 5 ns) at 370-390 nm, r T*(4,4’-(X)2-bpy‘),’229.33 and 510 nm, r T + ( P T Z + )These .~~~
-
-
(33) (a) Creutz, C.; Chou, M.;Netzel, T. L.;Okumura, M.;Sutin, N. J . Am. Chem. Soc. 1979, 102, 1309. (b) Milder, S.J.; Gold, J. S.;Kliger, D. S . J . Phys. Chem. 1986,90,548. (c) Lachish, U.; Infelta, P. P.; GrBtzel, M. Chem. Phys. Lett. 1979,62.317. (d) Braterman, P. S.;Harriman, A.; Heath, G. A.; Ycllowlees, L. J. J . Chem. Soc., Dalton Trans. 1983, 1801.
5854 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 TABLE I V R8te Constlab for Back Electron Trader in [(4,4’-(X),-bpy’-)Re(CO)~(py-PTZ’+)r in 1,2-M~hloroetb” 8t
v
AE1/2: 2.15 2.09
kb
x
S-’
0.67 0.77
1.99
&Y
1.80
1.1 1.8
1.59 1.40
4.0 9.1
kb
x lo-’:
S-’
0.98 1 .o 1.7 3.0 6.7 e
OAEll2 = E!/2(PTZ+/o)- E1/z(4,4’-(X)z-bpy-/0)was calculated by using the data in Table I, h0.04 V. ‘Rate constants for back electron transfer were calculated from single-exponential fits to transient absorbance decays monitored at 510 or 370-390 nm, *5% except for the third (*IO%), fourth (*25%), and the last (f30%) entries. ‘In 0.1 M [N(n-C4H9),](PF6)-1 ,2-dichloroethane solution. Errors are the same as in the previous column. [(bpz)Re(CO),(py-PTZ)]+. .The rate constant for back electron transfer was too rapid to measure.
s; rl
--
-
-
[(4,4’-(X)2-bpy’-)Re11(C0)3(py-PTZ)]+*
18
[ (4,4’- (X),-bpy’-) Re’( CO),( py-PTZ’+)]+ (6)
X
st
W
9
from electron donating to electron withdrawing, the relative energies of the ?r* orbitals decreased by 0.75 eV as shown by the electrochemical mea~urements.~~,~~,~~~~’-~~ These variations are sufficient, for example, to cause shifts in dr(Re) **(4,4’(X)2-bpy)absorption maxima from 348 nm for X = NH2 to 398 nm for X = C0,Et and in emission maxima from 540 to 630 nm. The spectral and redox properties of the [(4,4’-(X)2-bpy)Re(CO),(py-PTZ)]+ were nearly a superposition of those of [(4,4’-(X),-bpy)Re(C0),(4-Etpy)]+ and PTZ. By inference, electronic interactions between PTZ and [(4,4’-(X)2-bpy)Re(CO),-] are insignificant. This is an expected result given the -CH2- group that links them. A modicum of electronic coupling does exist as evidenced by the fact that rapid, PTZ Re” electron transfer occurs following excitation of the Re (4,4’-(X)2-bpy) chromophore. Intramolecular Electron-Transfer Quenching. The transient absorbance measurements provide direct evidence for the appearance of [(4,4’-(X),-bpy0-)Re(CO),(py-PTZ’+)]+ following laser flash excitation at 355 nm. From this observation, it can be inferred that Re’ (4,4’-(X)2-bpy)excitation is followed by rapid intramolecular electron transfer, eq 6. The excitation/ %
-
23 i 2 OC X OCH3 CHI H C(0)NEtz
Chen et al.
17
16
‘
15 1.2
I
I
I
I
1.4
1.6
1.8
2.0
A h 2 9
2.2
2.4
v
Figure 3. Plot of in ( k b X Is) vs AEV2 for back electron transfer in [(4,4’-(X)2-b~~’-~Reii(CO)3(~Y-PTZ’ 11’ or [(bpy’-)Re(CO)3(py,,.+)I+ in 1,2-dichloroethanein the absence (0)or presence (m) of 0.1 M [N(n-C,H9),](PF6). The least-squares lines are of the equations In (kb x 1s) = 22.9 (k0.3) 3.4 ( f 0 . 2 ) u l / 2 or In (kb x 1s) = 23.4 (*0.3) - 3.4 (*0.2)AE1/z(AE1,2in eV).
-
changes were consistent with the formation of [(4,4’-(X)2bpy’-)Re1(C0)3(py-PTZ’+)]+during the pulse. They were followed by a return to the ground state by back electron transfer. The kinetics of back electron transfer, as monitored at 370-390 or 510 nm, were first order. Rate constants are listed in Table IV. Plots Of In (kb x 1s) VS AEl/2(=Ei/2(PTZ+Io)- E1/?(4,4’(X),-bpyO/-)) are shown in Figure 3 for data acquired in 1,2dichloroethane in the absence or presence of 0.1 M [N(nC4H9W(PF6). The lines are the least-squares fits to the equations In ( k b X 1s) = 22.9 (k0.3) - 3.4 (f0.2)M1 ( M I in electronvolts) in 1,2-dichloroethaneor In (kbX Is$ = 23.6 ( f 0 . 3 ) 3.4 (f0.2)hEl/2 in 0.1 M [N(n-C4H9)4](PF6)-l,2-dichloroethane. Discussion Having acccss to the series [(4,4’-(X)rbpy)Re(CO)3(py-PTZ)]+ and [(4,4’-(X),bpy)Re(C0),(4Etpy)]+ has allowed us to explore the effects of free energy change on two related processes, electron transfer in the inverted region and nonradiative decay. The variations in AGO or Eo were achieved through an electronic effect by varying the substituents X. As the character of X was varied (34)(a) Biehl, E. R.;Chiou, H.;Keepen, J.; Kennard, S.;Reeves, P. C. J . Hcterocycl. Chcm. 1975. 12, 397. (b) Alhitis, S. A.; Beck, G.; GrBtzel, M. J . Am. Chcm. Soc. 1975.97,5723. (c) Shine, H.J.; Mach, E. E. J . Org. Chem. 1965, 30, 2130. (d) M e a , C.; Silberg, 1. Ado. Hetcrocycl. Chcm. 1968, 9,321.
electron-transfersequence leads to the intramolecular sensitization of a lower energy, redox-separated ~ t a t e . ’ ~ . ’ ~ In all cases, the growth in absorbance at 370-390 nm for (4,4’-(X)2-bpy‘-) or at 510 nm for PTz’+occurred within the laser pulse ( - 5 ns) and could not be time resolved with our system. From this observation, a lower limit of 2 X IO8 s-’ can be placed on kp. Rapid quenching is consistent with the absence of intrinsic emissioii from these complexes. In a previous study, k (CH3CN, 298 K) = 4.8 X IO9 s-I was found for [(bpy’-)Re’qCO),(pyPTZ’+)]+* by analyzing the rise-time kinetics of PTZ’+ in a picosecorid transient absorption experiment.I” Back Electron Transfer in [(4,4’-(X),-bpy’-)Re1(CO),(pyPTz’+)1+*. Following excitation and quenching, the ground state reappears by intramolecular, ligand-to-ligand, back electron transfer, eq 7. The rate constants for these reactions are listed in Table IV.
-
[(4,4’-(X),-bpy*-)Re1(CO),(py-PTZ’+)]+ [(414’-(X),-bPY)Re’(co),(PY-~Z)l+ (7) Their free energy changes can be calculated from the differences in redox potentials for the PTZ+/O and (4,4’-(X)2bpy)0/-couples, hE,,, = EIl2(PTZ+/O)- El/2(4,4’-(X)2-bpy-/0),by using eq 8. In
eq 8, the work term, w,, is an approximate correction for the coulombic energy of interaction between (4,4’-(X)2-bpy’-) and PTZ’+assumed to be spherical ions. The quantities 0, and p are the static dielectric constant and ionic strength of the medium, e is the unit electroniccharge, d is the separation distance between the ions, and 6 = (8aNAe2/1000DakeT)’~2.3i4~1Sb The estimated distance of closest approach between (4,4’-(X)rbpy‘) and PTZ’+ in [4,4’-(X)2-bpy’-)Re’(CO)3(py-PTZ’+)]+ is 6 ( i l ) A. At this distance, w, = 0.23 eV at p = 0 or w, = 0.22 eV at p = 0.1. On the basis of the value of in Table IV and eq 8, the range in AGO values is -1.18 to -1.93 eV. These values of AGO are sufficiently exergonic that back electron transfer occurs well into the inverted region for all cases. The sum of the intramolecular (A,) and solvent (A,,) reorganizational energies (A = 4 A,,) can be estimated from self-exchange rate constant data by using eq 9.3Js In eq 9, KA is the equilibrium
+
(35) (a) Crosby, G. A.; Highland, K. A,; Trutsdell, K. A. Coord. Chem. Rev. 1985,6441. (b) Truesdell, K. A,; Crosby, G. A. J . Am. Chem. Soc. 1985,107,1787. (c) Perkins, T.A.; Poumau, D. B.; Netzel, T. L.; Schanze, K.S . J . fhys. Chem. 1989,93,451I . (d) Vogler, A,; Kunkely, H.Comments Inorg. Chem. 1990, 9,201.
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5855
Intramolecular Electron Transfer
X 34k~T In ( u e $ ~ / k e , ) (9) constant for formation of the association complex between reactants, u, is the frequency factor for electron transfer, and k,, is the self-exchange rate constant. From the experimental value of k,, = 2.2 X lo9 s-I for the IO-methyl henothiazine+I0 selfexchange reaction in CH3CN,36X(PTZ+I) 5000 cm-' (0.62 eV), if it is assumed that K,u, = 10I2s-l. For bpyo/- self-exchange in [(bpy)2Ru(bpy'-)]+ in CH3CN at 298 K,X(bpyO/-) 1000 cm-I (0.12 eV).37938 From these values X [X(bpyo/-) X(PTZ+/O)J/2 = 0.37 eV, which justifies the claim that -AGO > A. Nonradiative Decay. The energy gap law has been applied successfully to nonradiative decay of MLCT excited states of polypyridyl complexes of Ru(II), Os(II), and Re(I).i6*2a26u28 In these analyses the following assumptions were made: (1) The role as energy acceptor is dominated by a series of seven mediumfrequency u(bpy) ring stretching modes that occur in the range 1000-1600 cm-I. These modes can be treated as a single, average, harmonic oscillator of quantum spacing hwM.268'39 (2) Nonradiative decay occurs in the weak coupling limit where Eo >> S M ~ ~ X MM . ' ~ The quantity SMis the electron-vibrational coupling constant and Eo is the energy gap. (3) There is a negligible contribution to nonradiative decay by levels above u * =~ 0 in the excited state since hwM >> ksT. (4) A lesser role as energy acceptor is played by low-frequency modes or solvent librational modes since SMhwM >> S L ~ WorL xo. The quantities SLand hwL are the electron-vibrational coupling constant and quantum spacing for an averaged low-frequency mode, and xo is the solvent reorganizational energy. It is the internal energy equivalent of &. (5) There is no change in vibrational frequency in hwM,hwL, or the solvent librational modes between the excited and ground states. (6)Within the series of related complexes, the electronic origins of the excited and ground states remain the same. If these approximations are valid, the nonradiative decay rate constant (knr)is given by eq 10.l6. The electronic states are mixed
-
.i4J6140
7
SM =
-+
In (knr X Is) = In Bo -
-
into the low-frequency modes and the solvent is included in the term containing As0,1/2. The contributions of the individual modes to the average quantities SMand wM are given in eq 1 1 The summation
1
(Av0,1/2)2= [ S L ( h ~ L )coth 2 2hWL k ~ T+ 2kBTxo (8 In 2) (1W by coupling to vibrations that break down the orthogonality of the adiabatic Born-Oppenheimer states. These vibrations are the promoting modes. The quantity Bo is the vibrationally induced, electronic coupling term, Ckis the vibronic coupling matrix element, and wk is the angular frequency or average frequency of promoting mode or modes, k. The term 7 E o / h w Mincorporates the energy release into hwM in the transition between electronic states. It arises from the overlap in vibrational wavefunctions between the excited and ground states. In the weak coupling limit, the extent of vibrational overlap decreases as the energy gap increases. Energy release (36) Kowert, B. A.; Marcoux, L.; Bard, A. J. J. Am. Chem. Soc. 1972.91, 551R
(37) Morris, D. E.; Hanck, K. W.; DeArmond, M. K. J. Am. Chem. SOC. 1983, 105, 3032. (38) Heath. 0.A.; Yellowless, L. J.; Braterman, P. S. Chem. fhvs. Lett. 198.2. 92, 646. (39) (a) Bradley. P. 0.;Kress, N.; Hornberger. B. A.; Dallinger, R. F.; Woodruff. W. H. J . Am. Chem. Soc. 1901.103.7441. Ib) Y a k . T.: Orman. L. K.;Anderson, D. R.; Yu. S.-C.; Xu, Y . ; Hopkins, J.'B. J . Phys. Chem: 1990, 91, 7128. (c) Mabrouk, P. A.; Wrighton, M. S. Inorg. Chem. 1986, 25, 526.
Esj 7
1 WM =
(114
J= 1
CSjaj/CSj j=i 1-1
(1lb)
is taken over the seven contributing u(bpy) modes. The electron-vibrational coupling constants for the individual modes are related to the changes in equilibrium displacement between states, AQqJ, as shown in eq 12. For the polypyridyl complexes, average
Sj !'dM~j/h)(AQcq~)~ (12) C-C, C-N bond distance increases of 0.01-0.02 A occur in the MLCT excited states.i61,22*26*28 The quantities Eo, SM,h w ~ and , Av0,1/2 for [(4,4'-(X)2bpy')Re11(CO)3(4-Etpy)]+* were obtained by the Franckxondon analysis of emission profiles, Table 111. From these data: (1) The magnitude of SMincreases as the energy gap increases. This effect has been found for other MLCT excited states where it has been attributed to the greater extent of charge transfer in the excited . ~The .~~ state as the energy gap between states i n ~ r e a s e s . ~ ~(2) quantum spacing hwMis higher for complexes of Re(1) than for polypyridyl complexes of Os(I1) or Ru(I1) (1450 vs 1350 cm-I) because of participation of a higher frequency v(C0) mode at 2020-2040 cm-'.22 Based on the magnitudes of the relevant parameters--SM 1.1, hwM 1450 cm-', and EO = 13000-20000 cm-lnonradiative decay in the Re complexes occurs in the weak coupling limit and eq 10 should be appli~able.'~ In Figure 2A is shown a plot of In (knr X 1s) vs Eo for nonradiative decay in [(4,4'(X)2-bpy'-)Re11(CO)3(4-Etpy)]+*. The slope of the linear correlation is (t3 In (k, X ls)/t3Eo) = 5.9 eV-I. This value is in the same range but on the low side of values that have been obtained for other polypyridyl complexes of Ru(II), Os(II), or Re(I).I6The linear relationships that are found in these correlations exist because SMincreases linearly with E and variations in SLhwL and xo with Eo are relatively sma11.i88v22,26 The relationship between k, and the parameters obtained by emission spectral fitting can be evaluated more quantitatively by utilizing eq 10 in the form of eq 13. A plot of In (knr X 1s) vs In (knr X 1s) = In (Bo X Is) + In [F(calc)] (13a) In [F(calc)] = hwMEO yEo y + 1 2(A30,i/2)2 1' (1000 Cm-112) - s M (13b) In [F(calc)] is shown in Figure 2B. In the construction of the linear correlation a slope of 1 was imposed on the fit. From the intercept at In [F(calc)] = 0, In Po = 33 f 0.5, Bo = 2 X I O l 4 s-l, The relationship between Bo and V,, the electronic interaction integral, is shown in eq 14. By assuming that the promoting mode Bo = C,2w,(ls)(*/2)I/2/1000 cm-I = ( Vk2/h )( 1s) (27r) I 12/ ( 1000 cm-I ) ( 14)
-
-
-i (
G (G) +
-
-
is a metal-ligand skeletal mode of h@k = 300 cm-I, Vk 650 cm-I. The same analysis gave vk 600 cm-I for nonradiative decay in [(4,4'-(X)2-bpy*)Rei1(CO)3Cl]* 22 and v k 1300 cm-I for a series of excited states based on O S ( I I ) . ' ~ Electron Transfer. Back electron transfer in [ (4,4'-(X)?bpy'-)Re'(CO)3(py-PTZ+)]+ occurs with energy gaps that are comparable to those for nonradiative decay in [(4,4'-(x)2bpy'-)Re11(CO)3(4-Etpy)]+*,Tables 111 and IV. The same donor
-
(40) (a) Heller, E. J. Ace. Chem. Res. 1981,14, 368. (b) Tutt, L.; Tannor, D.; Schindler, J.; Heller, E. J.; Zink, J. 1. J . fhys. Chem. 1983, 87, 3017. (41) Kamper, E.; Neilands, 0. Russ. Chem. Reo. 1986, 55, 334.
5856 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
Chen et al.
sites are involved and -AGO > A. By making the same approximations that were used in the derivation of eq 10, the rate constant for back electron transfer is given by eq 15.'3J4J".42
yAGo
In [F(calc)] = --
i
l
+
t
In eq 15, Ifabis the electron-transfer matrix element that couples the donor and acceptor sites. The relationship between AGO and Eo is given in eq 16. The energy gap term, E,, is approximately AGO Eo (SLhwL xo) (16) a free energy change. The corresponding change in entropy arises largely from changes in frequency between the initial and final states in the solvent librational modes.43 The parameters SMand hwM that appear in eq 15 have the same form as in eq 10, but they have a different meaning. In the electron-transfer reaction, there are two reacting sites and they are weakly coupled electronically. The role of energy acceptor can be played by vibrational modes at both [4,4'-(X)2-bpye] and PTZ', as well as by the solvent librational modes that respond to the change in electronic distribution that accompanies electron t r a n ~ f e r . ' ~ By * ~application ~*~ of the averaging procedure in eq 11, SM and ~ w are M defined in eq 17.'4*i6*40 The summations
+
+
j and k are over the seven v(bpy) modes and those u(PTZ) ring
stretching modes (or other high- or medium-frequency modes) that contribute as energy acceptors. On the basis of the relationships between the energy quantities that appear in eqs 8 and 16, In (kb X 1s) is predicted to vary with AEI12for back electron transfer as shown in eq 18. In these Y
reactions the electron acceptor, PTZ+, is the same and the variations in the donor, (4,4'-(X)'-bpy*-), occur on the periphery. If it is assumed that the distance separating the redox sites during electron transfer is maintained through the series, both w, and xo would remain nearly constant. Further, if changes in SLhuL are negligible, it is predicted by eq 18 that In (kb X Is) 0: YAEIj2/hwM*
This prediction is borne out experimentally. In Figure 3 are shown plots of In ( k b X 1s) in 1,2-dichloroethane or 0.1 M [N(n-C4H9)4](PF6)-1,2-dichloroethane vs AEi,2. The dependence on ionic strength will be discussed elsewhere. Important for the p"It purpose is that the slope of either correlation is (a In (kb X ~ s ) / ~ ( A E=~ 3.4 / ~ )eV-'. The magnitude of the slope is that found for nonradiative decay. The decrease can be understood based on the energy gap (42) Brunschwig, B. S.;Sutin, N. Comments Inorg. Chem. 1997, 6, 209. (43) (a) Marcus, R. A.; Sutin, N. Comment Inorg. Chem. 1986,5, 119. (b) Bruwhwig, B. S.;Ehrenson,S.;Sutin, N. J. Phys. Chem. 1987,91,4714. (c) Hupp, J.; Kober, E. M.; Neyhart, G. A.; Meyer, T. J. Manuscript in
preparation. (44) Lipari, N. 0.;Rice, M.J.; Duke, C. B.; Bozio, R.; Girlando, A.; Pecile, C.Inr. J. Quantum Chem. Quantum Chem. Symp. 1977, 11. 583.
Figure 4. Structures of [(4,4'-(CH3)z-bpy)Re1(CO)3(py-PTZ)]+ and [(PTZ-(CHz)-bpy)Re1(C0)3(4-Etpy)]+ illustrating the separation distances and relative orientations between the bipyridyl and PTZ groups.
law analysis. For nonradiative decay, the slope of the plot of In (kn,X 1s) vs Eo is equal to y / h w . By use of an average value of y = 1.3 and hwM= 1450 cm-', the calculated slope (7.2 eV-I) is in reasonable agreement with the experimental value of 5.9 eV-'. Two terms appear in the slope, hwM and y (=ln (Eo/SMhwM) - 1). For the electron-transfer reactions, it seems reasonable to assume that ring stretching modes for PTZ+,34d*45 which occur in the same region as the ring stretching modes for (4,4'-(X)2bpy'-), are the major contributor^.^^.^^ Therefore, the difference in slope between the two cases must lie in an increase in SMby 1.6 for back electron transfer compared to nonradiative decay. There are two factors that tend to increase SMfor electron transfer. The first is the participation of PTZ+ modes as energy acceptors. Given the averaging procedure in eq 17, an increase in the number of participating modes will necessarily increase SM. Thii is an expected result since the rate of energy dissipation should increase as the number of participating, acceptor modes increases. The second is that a complete electron transfer occurs in the back-electron-transfer reaction. The electron donor and acceptor sites are weakly coupled electronically. In nonradiative decay there is a change in electronic distribution, but this amounts to only a partial electron transfer as shown by resonance Raman measurements.26 The net effect is a decrease in the extent of charge transfer and a decrease in Sw. On the basis of earlier correlat i o n ~ , ~this ~ ~could . ~ ~lead , ~to~an increase in SMof -20% for the u(bpy) modes for back electron transfer. Electronic Coupling. The quality of the linear correlation in Figure 3 is striking, especially when compared to other correlations that have been found in the inverted region.'-1° Factors that contribute to the success of the correlation are the relatively nrinor perturbations caused by the variation in X on the peripheries of the ligands and the fact that the donor and acceptor orbitals remain the same throughout the series. From the quality of the correlation, it can be inferred that the electron-transfer matrix element, Hab,must remain nearly constant
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(45) (a) Hater, R. E.;Williams, K. P. J. J. Chem. Soc., Perkin Tram. 2 1981, 852. (b) Kure, B.; Morris, M. D. Takanra 1976, 23, 398.
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5857
Intramolecular Electron Transfer throughout the series. This is true, even though on the basis of molecular models, it can be shown that the center-to-center distance of separation between [4,4'-(X)2-bpy+] and pTZ'+ can vary from -6 to -9 A. The range in values exists because of the rotational flexibility introduced by the -CH2- link to PTZ, Figure 4. There is evidence for orientational and orbital pathway effects in these reactions from which it can be inferred that they are nonadiabatic in character: (1) The rate constant for back electron transfer within the association complex ([bpy'-)Re1(CO)3(4Etpy)]-, IO-MePTZ'+J following reductive quenching of [(bpy'-)Re1(CO),(4-Etpy)]+* by IO-MePTZ is faster by -3 orders of magnitude than back electron transfer in [(bpy'-)Re(CO),(py-PTZ'+)]+*.Ik The driving force is the same for both reactions. The relative orientations and distances between electron donor bpy'- and acceptor PTZ'+ can vary within the association complex, but they are restricted in [(bpy'-)Re(CO)3!pyPTZ'+)]+*. On the basis of this comparison, the restrictions imposed on the relative orientations between bpy'- and PTZ'+ by the -CH2- link greatly inhibit electronic coupling. (2) The redox-separated state [ (PTZ'+-CH2-bpy'-)Re(C0),(4-Etpy)]+* is reached following Re bpy excitation and intramolecular quenching in [(PTZ-CH2-bpy)Re(CO)3(4-Etpy)]+. Back electron
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B
I Q Figure 5. Energy-coordinate diagram illustrating electron transfer in the inverted region, (A) with the involvement of a high- or medium-frequency mode of quantum spacing hw as the energy acceptor, and (B) in the limit that hw
