J. Am. Chem. SOC.1983, 105, 3763-3767
3763
Quantum Effects of High-Frequency Modes in Inorganic Electron Transfer: Kinetic Isotope Effects in Redox Reactions of [ Fe( H20)6I2+,[ Fe( D20)6I2+,and Fe[ ( 180H2)6]2+ Tom Guarr,+ Ephraim Buhks,l and George McLendon*+ Contributionfrom the Department of Chemistry, University of Rochester, Rochester, New York 14627, and the Department of Physics, University of Deleware, Newark, Delaware 19711. Received July 6 , 1982
Abstract: Kinetic isotope effects have been measured for redox reactions of Fe(H~0)6~+, Fe(D20):+, and Fe( 180H2)62+ with a series of M"'(bpy), oxidants (M = Fe"', Ru"', Cr"'). The rate ratios k('60H2)/k(180H2)are well predicted by the recent treatment of Buhks, Bixon, and Jortner (J. Phys. Chem.,85,3763 (1981)). Deuterium isotope effect measurementsare complicated = -0.040 V. After correcting by the difference of the Fe(aq)2+/3+reduction potential in H 2 0 and D20: &?Fc'+ H 2 ~h?Fe~+ID20 the observed rates for the change in reaction driving force, an isotope effect ofi 1.3 estimated for cross reactions involving Fe(aq)2+/3+(at AE = 0). This value is larger than predicted and -20% greater than that observed in the I60H2vs. 180H2 experiments, possibly reflecting a contribution of "frozen" 0-H modes in the reaction coordinate. Similarly, N-H modes may be involved to some extent in reductions of Co(NH3)?+
is
In the early 1960's, a number of studies of isotope effects in inorganic electron-transfer rates appeared.' These studies subsequently waned, since no appropriate theory was available to guide the design and interpretation of such experiments. However, growing interest in quantum mechanical effects (e.g., nuclear tunneling) in electron-transfer reactions2 has stimulated a search for experimental probes of quantum effects. Recently, Buhks et al. noted that kinetic isotope effects can in principle provide a probe of quantum effects in electron transfer at room temperature, and they obtained explicit expressions to predict such effects., This treatment of KIE (kinetic isotope effects) is based on nonadiabatic multiphonon quantum mechanical theory of electron transfer in solution which presents the electron-transfer transition probability as a product of electronic interaction and Franck-Condon factors for nuclear vibrational modes. The key point in this analysis is that for many redox reactions, particularly of transition metals, quantum effects can arise when high-frequency (metal-ligand) modes (with frequency h w > kT) undergo distortion during an electron-transfer reaction. Consider, for example, the outer-sphere oxidation of Fe(H20)62+.On oxidizing Fe2+(aq), the Fe-O bond lengths must decrease by ca. 0.15 A (vide infra). This nuclear reorganization necessarily precedes electron t r a n ~ f e r . ~In J ~many cases, this reorganization occurs by vibrational excitation of the appropriate mode (e.g., F d symmetric stretch, h w N 400 cm-I). However, when h w IkT the vibrational mode which allows nuclear reorganization cannot be fully populated by thermal excitation. Therefore, the electron-transfer reaction must occur (to some extent) by nuclear tunneling (Le., tunneling through the barrier separating the diabatic potential surfaces in the space of nuclear coordinates). A pictorial representation of these concepts can be found in ref 2c. Since this quantum effect depends on the metal-ligand frequency h w , it can be modulated by changing this frequency by isotopic substitution. It follows that kinetic isotope effects should be observed in outer-sphere electron-transfer reactions that involve substantial inner-sphere reorganization. Well-known examples include redox reactions involving Fe(H20):' and Co(NH3):+. Initial attempts to fit the best available experimental data on kinetic isotope effects with quantum mechanical theories seem disappointing., For the reactions CO(NH,)~,++ Cr(bpy),2+ CO(NH3)6'+ + Cr(bpy),,+ (Ia)
--
C O ( N D , ) ~ ~++C r ( b p ~ ) , ~ + Co(ND3)2+ + Cr(bpy),,+ (Ib) 'University of Rochester. 'University of Delaware. Present Address: SES, Inc., Newark, Delaware 19711.
0002-7863/83/1505-3763$01.50/0
a deuterium isotope effect (kH/kD)pred = 1.12 is predicted, while the observed effect is (kH/kD)obsd = 1.35.2*5 The calculations correspond to the model where the kinetic isotope effect is due to a change of the metal-ligand vibrational frequency upon substitution of H by D. However, several explicit predictions of theory remain untested. Chief among these is the suggestion that the isotope effect should decrease as the reaction driving force ( A E ) increases. Finally, experiments have been complicated by the effect of solvent deuteration on redox potentials of many reactants. Weaver6 has suggested that most observed deuterium isotope effects could be accounted for in part by this difference. In order to clarify all these points, we have studied kinetic isotope effects in the electron-transfer reactions of Fe"(OH2)62+, Fe1'(OD2)62+,and Fe"( 180H2)62+.An explicit correction for deuterium solvent isotope effects on the thermodynamic driving force is introduced. Three major conclusions emerge from this work as detailed below. (1) Theory semiquantitatively predicts the kinetic isotope effect for substitution of I60H2by 180H2in the reaction C r ( b ~ y ) ~ , + * [Fe(OH2)612+ Fe(OH2)b3+ C r ( b ~ y ) , ~ +(2) . Theory correctly predicts a decrease in the kinetic isotope effect as the reaction driving force increases. (3) The observed isotope effect for replacement of H 2 0 by D 2 0 is significantly larger than predicted even after correcting for the solvent dependence of reaction driving force. In conjunction with data for analogous Co"' systems, the results suggest that high-frequency 0-H (or N-H) modes, which remain "frozenn during electron transfer, may dominate H / D isotope
+
-
+
(1) (a) A. M. Zwickel and H . Taube, Discuss. Faraday SOC.,29, 42 (1960). (b) A. Zwickel and H. Taube, J . Am. Chem. SOC.,83,793 (1961). (c) J. Hudis and R. W. Dodson, ibid., 78, 911 (1956). (d) J. Halpern, Q. Reu., Chem. SOC.,15, 207 (1961). (2) (a) J. J. Hopfield, Proc. Natl. Acad. Sci. U.S.A.,71, 3640 (1974). (b) P. Siders and R. A. Marcus, J . Am. Chem. SOC.,103, 741 (1981). (c) B. S. Brunschwig, J. Logan, M. D. Newton, and N. Sutin, ibid., 102, 5798 (1980). (d) E. Buhks, M. Bixon, J. Jortner, and G. Navon, J . Phys. Chem., 85, 3763 (1981). (3) E. Buhks, M. Bixon, and J. Jortner, J. Phys. Chem., 85,3763 (1981). (4) D. Stranks, Discuss. Faraday SOC.,29, 116 (1960). (5) (a) T. Guarr and G. McLendon, to be submitted for publication. (b) Y . Narusawa, M. Kimura, and K. Nakano, Bull. Chem. SOC.Jpn., 47,2017 (1974). (c) J. F. Endicott and H. Taube, J. Am. Chem. SOC.,86, 1686 (1964). (d) G. M. Waind and R. Murray, Proc. Znt. Con$ Coord. Chem., 7th, 309 (1962). (6) (a) M. J. Weaver and S. M. Nettles, Znorg. Chem., 19, 1641 (1980). (b) E. Yee, R. Cave, K. Guyer, P. Tyma, and M. Weaver, J. Am. Chem. SOC., 101, 132 (1979). (c) M. Weaver, Zsr. J . Chem., 18, 35 (1979). (d) M. Weaver, P. Tyma, and S. Nettles, J. Electroanal. Chem. Interfacial Electrochem., 114, 5 3 (1980).
0 1983 American Chemical Society
Guarr, Buhks, and McLendon
3764 J . Am. Chem. SOC.,Vol. 105, No. 12, 1983
2
7.5
7 1
0.7
05
I
21
FE
0.3
V vs. S C E Figure 1. Cyclic voltammograms of Fe2+(aq) in I6H20 and D 2 0 . Polished Pt disk working electrode, 25 OC, 0.16 M NaC104 and 0.04 M HC104; scan speed 20 mV/s.
I
I
14
I
,$
Figure 2. Stern-Volmer quenching of Cr(4,7-Me2phen),’’ by Fe2+. Stern-Volmer quenching of 2E Cr(4,7-Me2phen)33Cby Fe2+ in l60H2 (upper line) and 180H2(lower line).
effects and affect the rates of electron transfer.ls
Materials and Methods Materials. Ferrous ammonium sulfate (Baker) was recrystallized from water. F e ( b ~ y ) , ~ Fe(4,4’-Me2bpy)33t +, and F e ( ~ h e n ) ~ ,[bpy + = bipyridine; phen = phenanthroline] were prepared by addition of a stoichiometric amount of the ligand to Fe” solutions in 0.1 M H2S04, oxidation by lead dioxide, and crystallization of the Fe”’ products as perchlorate salts by slow addition of LiC104 and cooling. R ~ ( b p y ) ~( G~ .+F. Smith Chem) was oxidized as above and isolated as the perchlorate salt. Cr(bpy),”, Cr(4,7-Me2phen),’+, and Cr(3,4,7,8-Me4phen)33+were prepared by addition of anhydrous CrCI2 (or electrolytically reduced Cr”) to a degassed aqueous suspension of the ligands.’ After 5 min of stirring under N2, the solutions were oxidized by bubbling with O2 Excess Cr”’ was filtered off, and excess ligand removed by adjusting the solutions to pH >7 and filtering, or by repeated extractions with 2-pentanone. The yellow aqueous layer was concentrated on a rotovap and chilled, whereon analytically pure yellow crystals separated. All the metal(II1) bipyridyl and phenanthroline complexes were stored dessicated and frozen until use. They were dissolved in 0.04 M H 2 S 0 4solution within 30 min of use and were rigorously protected from light. D 2 0 was obtained from Aldrich and was 99.8% D. H 2 0 was doubly glass distilled. H2I80was obtained from Stohler Isotopes. Purity was >98% I8O and >98% IH. Stopped-flow measurements were made on a Durrum D-1 10 stopped flow equipped with dual detection and interfaced to a PDP 11/45. All reactions were repeated 3-4 times and then repeated with different preparations of Fe2+ and the oxidants. Emission quenching measurements were made in a Perkin-Elmer MPF-44A spectrofluorimeter. Small aliquots (
