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Temperature and pressure effects on charge transfer absorption bands
Volume 143, number 6
CHEMICAL PHYSICS LETTERS
5 February 1988
TEMPERATURE AND PRESSURE EFFECTS ON CHARGE TRANSFER ABSORPTION BANDS
Laura A. WORL and Thomas J. MEYER Department of Chemistry, The University of North Carolina, Chapel Hill, NC 27514, USA
Received 21 September 1987; in final form 24 November 1987
The frozen dipole approximation of dielectric continuum theory is shown to apply to the glass-to-fluid transition for charge transfer absorption bands.
In a Letter in this journal, Hammack et al. [ l] suggested that the results obtained from dielectric continuum theory by Marcus and others for the role of solvent in thermally activated electron transfer [ 2,3] have been misapplied in the study of optically induced electron transfer. In particular, they cited the case of optically induced intramolecular electron transfer in mixed-valence ions, such as the example shown in the reaction (bpy),ClRu”(pz) $+
Ru’nCl(bpy):+
(bpy),ClRu”t(pz)
Ru”Cl(bpy):+
,
(1)
where bpy is 2,2’-bipyridine and pz is pyrazine [ 41. For mixed-valence ions in fluid solution an extensive body of data have been collected concerning the dependence of metal to metal charge transfer (MMCT) absorption band energies, Eop, on solvent and the data are largely in agreement with predictions based on dielectric continuum theory [ 5-81. From dielectric continuum theory the contribution to the absorption band energy from the solvent for the symmetrical ion in eq. (1) where AG= 0 is given by (2) Here Ae is the extent of charge transfer in the electron transfer process (Ae= 1 for optically induced
electron transfer between reactants which are weakly coupled electronically), aI and a2 are the molecular radii of the electron transfer donor and acceptor sites, d is the internuclear separation between reactants, and Dop and Ds are the optical and static dielectric constants of the medium. Eq. (2) was derived for the case of non-interpenetrating, spherical donor and acceptor sites and assumes that the internal dielectric constant of the solute, Dint, is 1 [ 8-101. The evidence presented by Hammack et al. concerning the breakdown in dielectric continuum theory was based on the effect of increasing external pressure on absorption band energies and band shapes. As the pressure was increased, only slight shifts were observed in band energies and shapes through the transition from the liquid to frozen states. This was so even though the reorientation of solvent dipoles is restricted in frozen solutions which greatly decreases Ds and from eq. (2) should lead to a significant decrease in the absorption band energy. For example, for nitromethane Ds is 33.7 at 25°C increases to 36.4 just above the freezing point, and drops to 3.4 upon freezing [ 11. Because of the loss in orientational polarization, Hammack et al. pointed out that a decrease in the energy of the MMCT absorption band of between 1500 and 1300 cm-’ is predicted by eq. (2) for polar organic solvents like nitromethane when the solvent is frozen. It is, of course, true that Marcus himself has applied dielectric continuum theory to the effect of solvent on optical charge transfer absorption bands [ 91, The Marcus treatment is based on a non-equilibrium
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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Volume 143, number 6
CHEMICAL
PHYSICS LETTERS
thermodynamic approach. From his results the shift in the energy of the absorption band maximum between a polar solvent and a vacuum (A&) is given by AE,=F,
-F,,+F:!o-F
_ IO-
(3)
Here F, and F. are the contributions from the polar solvent to the Helmholtz free energy of the light absorber when the local solvent dipole environment is in equilibrium with the electronic configuration of the ground state (F,) or the excited state (F, ). F,_, is the analogous Helmholtz energy for a hypothetical chromophore having as a permanent charge distribution the charge distribution of the excited state minus that of the initial state. F:flo is the equivalent energy quantity but in which the response to the difference in electronic distribution between the excited and ground states is only through the optical polarization of the medium, D,,. The magnitudes of the terms Flmo,F’& F, and F. depend upon the charge distributions before and after electron transfer and their theoretical evaluation upon the model used to approximate the actual molecular structures. A very clear discussion of the factors involved has appeared recently in a paper by Brunschwig, Ehrenson and Sutin [ lo]. For example, for a symmetrical mixed-valence ion with spherical donor and acceptor sites, A&=do as in eq. (2) if Dint= 1 and for a charge transfer process which can be approximated as having produced a point dipole at the center of a sphere, A& is given by b3
; d-4 b3
---
1-Ds 2D,+l.
(4)
Here ,u~and H are the vector dipole moments of the excited and ground states and b is the radius of the sphere. Other models have been developed and applied successfully the most notable being ellipsoidal cavity models for mixed-valence ions [ 1l-l 31. In the non-equilibrium thermodynamic treatment of Marcus it is assumed that the electronic polarization of the solvent stays in equilibrium with the initial and final electronic distributions of the ground and excited states. However, the orientational polarization is “frozen” on the timescale of the elec542
5 February
1988
tronic transition. Application of the Franck-Condon principle shows that the solvent dipoles must remain in orientations appropriate to the ele:tronic structure of the ground state during and immediately after the electronic transition. The inability of the solvent dipoles to reorient to positions appropriate to the electronic configuration of the excited state leads to a contribution to the absorption band energy of F?P,- F,_. which is the & in eq. (2). The assumption by Hammack et al. that there is a fundamental difference in the quantity FyEo F,_. between frozen and fluid solutions is incorrect. On the timescale of the optical transition, the solvent dipoles are frozen in either case. The assumption of frozen solvent dipoles is included in the underlying theory and is, in fact, demonstrated by the data of Hammack et al. [ 11. In general, solvent shifts are expected to exist between frozen and fluid solutions. One source of such shifts lies in changes in equilibrium solvent dipole orientations around the solute in its ground state. Such changes may be induced by differences in long range or local order between the frozen and fluid states. Another potential source of solvent shifts is in structural differences in the light absorber induced by the change between the frozen and fluid states. The available data, for example those of Hammack et al. in ref. [l] and those in fig. la, suggest that, at least in some cases, such effects are relatively small. Temperature variations. An experimental alternative to testing the frozen dipole approximation is available by observing changes in absorption band energies and shapes as the temperature is decreased through the fluid to glass transition. In fig. la is shown the temperature dependence of the metal to ligand charge transfer (MLCT) absorption band, d,(Re)+x*(bpy), in the complex [(bpy) Re( CO)3C1] in 4: 1 (v:v) ethanol-methanol. The ethanol-methanol mixture forms a high quality optical glass. The complex was prepared as described previously [ 141, and the temperature-dependent measurements were made by using an Oxford 1704 optical cryostat and 11 mm* glass cells. For the MLCT excited state there is a considerable radial electronic redistribution between the excited and ground states [ 151 and absorption band energies for small chromophores of this type which contain CO ligands are characteristically strongly solvent
5 February 1988
CHEMICAL PHYSICS LETTERS
Volume 143, number 6
1 .U I -
.eI
-
.? alMK bEOK c2OOK d2WK .5 , - C2QBK .I I -
a
7s. ‘d K
.I
a
225.
1SO.
TEMP
300.
CK)
.3 I .2
.l
a
aI_ I
UAVELENGTH
(ml
1.2
1
.B
.f)
a 90 K b 115K c 12’5K d 135K e 200K
cc
TEMP
.
l
(K)
.4
.2
0
Fig. 1. (a) Temperature dependence of the absorption spectrum of [ (bpy) Re( CO)JI] in 4 ; 1 (v :v) ethanol-methanol. At low energy the spectrum is dominated by the d, (Re) +t*( bpy) metal to ligand charge transfer absorption manifold. (b) Normalized emission intensity profilesas a function of temperature for the analogous MLCT emission from the same complex in 4: 1 ethanol-methanol. The insets show how the absorption and emission maxima vary with temperature. 543
Volume143,number6
CHEMICAL PHYSICSLETTERS
dependent [ 16,171. However, it is apparent from the data in fig. 1 that no significant shift occurs in band energy through the fluid to glass transition in the region 115- 140 K which is also in agreement with the frozen dipole approximation. Time-dependenteffects.Because of the difference in timescales involved, optical transitions occur with solvent dipoles frozen in orientations appropriate to the ground state and are free of dynamical effects arising from solvent dipole reorientations. On other timescales solvent dipole reorientational effects can play an important role either energetically or dynamically. An example of such an effect is illustrated by the data in fig. lb where the energy of the complementary LMCT (d,+x*) emission band for [ (bpy) Re( CO),Cl] is shown as a function of temperature. In contrast to the absorbance data, there is a significant shift in the emission energy of the MLCT chromophore at the fluid to glass transition. In this case, emission at low temperatures occurs from excited states which are surrounded by solvent dipoles which are frozen in orientations appropriate to the electronic distribution in the ground state. The result is a shift of the emission to higher energy. In fluid solution dipole reorientational times are rapid compared to the timescale for excited state decay. Dipole orientations in the vicinity of the excited state are at equilibrium with the electronic distribution of the excited state, and there is a significant shift to lower energy compared to the frozen solution [ 18,191. The decrease in energy gap in fluid solution leads to a decreased non-radiative lifetime in accord with a prediction of the “energy gap law” for non-radiative decay [ 19,201. In the midst of the fluid to glass transition, at z 115 to 125 K, the dipole reorientational timescale is comparable to the excited state decay time and time-dependent non-radiative lifetimes and emission energies are actually observed experimentally [21,22]. For thermally activated electron transfer, dynamic solvent dipole effects can also appear. The energy barrier to electron transfer includes contributions from the energy difference between states, solvent dipole trapping, and intramolecular vibrational modes, the latter because of the structural changes induced by the change in electron content between the reactants and products. For thermally activated electron transfer where there is sufficient electronic 544
5 February1988
coupling between the electron transfer donor and acceptor sites that electron transfer is “adiabatic”, there is growing experimental and theoretical evidence that solvent dynamical effects also play a role in determining electron transfer rates. The effects appear to arise from the temporal requirements associated with solvent dipole reorientations [ 23-281. Acknowledgements are made to the Army Research OffIce under grant No. DAAG29-85-K-012 1 and to the National Science Foundation under grant No. CHE-8503092 for support of this research.
References [ I] W.S. Hammack,H.G. Drickamer,M.D. Loweryand D. Hendrickson,Chem.Phys.LettersI32 (1986)231. [2] R.A. Marcus, Ann. Rev. Phys. Chem. 15 (1964) 155; J. Chem. Phys. 43 (1965) 679. [3] N.S. Hush, Trans. Faraday Sot. 57 (1961) 557. [4] R.W. Callahan, F.R. Keene, T.J. Meyer and D.J. Salmon, J. Am. Chem. Sot. 99 (1977) 1064; M.J. Powers and T.J. Meyers, J. Am. Chem. Sot. 102 (1980)
,1289. [ 51 C. Creutz, Progr. Inorg. Chem. 30 (1983) 1. [6] H. Taube, Ann. NY Acad. Sci. 313 (1978) 481; G.M. Tom, C. Creutz and H. Taube, J. Am. Chem. Sot. 96 (1974)7827. T.J. Meyer, Accounts Chem. Res. 1I (1978) 94; in: Mixedvalence compounds, ed. D.B. Brown (Reidel, Dordrecht, 1980) p. 75; B.P. Sullivan, J.C. Curtis, E.M. Kober andT.J. Meyer, Nouv. J. Chim. 4 (1980) 643. N.S. Hush, Progr. Inorg. Chem. 8 (1967) 391; Electrochim. Acta 13 (1968) 1005. [9] R.A. Marcus, J. Chem. Phys. 39 (1963) 1734; 43 (1965) 1261. [ IO] B.S. Brunschwig, S. Ehrenson and N. Sutin, J. Phys. Chem. 91 (1987) 4714. [ 111R.D. Cannon, Chem. Phys. Letters 49 (1977) 299: Yu.1. Kharkats, Elektrokhimya 15 (1976) 1251. [ 121 E.D. German, Chem. Phys. Letters 64 (1979) 305. [ 13] B.S. Brunschwig, S. Ehrenson and N. Sutin, J. Phys. Chem. 90 (1986) 3657. [ 141 M.S. Wrighton and D.L. Morse, J. Am. Chem. Sot. 96 (1974) 998. [ 151 E.M. Kober, B.P. Sullivan and T.J. Meyer, Inorg. Chem. 23 (1984) 2098. [ 161 P.J. Giordano and M.S. Wrighton, J. Am. Chem. Sot. 101 (1979) 2888. [ 171 R.M. Kolodziej and A.J. Lees, Organometallics 5 (1986) 450.
Volume 143, number 6
CHEMICAL PHYSICS LETTERS
[IS] MS. Wrighton and D.L. Morse, J. Am. Chem. Sot. 96 (1974) 998. [ 191 R.S. Lumpkin and T.J. Meyer, J. Phys. Chem. 90 (1986) 5307. [ 201L.A. Worl and T.J. Meyer, manuscript in preparation. [21] N. Kitamura, H.-B. Kim, Y. i(awanishi, R. Obata and S. Tazuke, J. Phys. Chem. 90 (1986) 1488. [ 221 E. Danielson, R.S. Lumpkin and T.J. Meyer, J. Phys. Chem. 91 (1987) 1305. [ 231 G. van der Zwan and J.T. Hynes, J. Phys. Chem. 89 (1985) 4181. [24] D.F. Calef and P.G. Wolynes, J. Phys. Chem. 87 (1983) 3387; J. Chem. Phys. 86 (1987) 3183.
5 February 1988
[ 251 M. Maroncelli and G.R. Fleming, J. Chem. Phys. 86 (1987) 6221; B. Bagchi, D.W. Oxtoby and G.R. Fleming, Chem. Phys. 86 (1986) 257. [ 261 H. Heitele, M.E. Michel-Beyerle and P. Fin&h, Chem. Phys. Letters 138 (1987) 237. [ 271 M. Sparpaglione and S. Mukamel, J. Phys. Chem. 9 1 (1987) 3938; L.A. Philips, S.P. Webb and J.H. Clark, J. Chem. Phys. 83 (1985) 5810; M.J. Weaver and T. Gennett, Chem. Phys. Letters 113 (1985) 213; J.N. Onuchi, J. Chem. Phys. 86 (1987) 3925.
545
CHEMICAL PHYSICS LETTERS
5 February 1988
TEMPERATURE AND PRESSURE EFFECTS ON CHARGE TRANSFER ABSORPTION BANDS
Laura A. WORL and Thomas J. MEYER Department of Chemistry, The University of North Carolina, Chapel Hill, NC 27514, USA
Received 21 September 1987; in final form 24 November 1987
The frozen dipole approximation of dielectric continuum theory is shown to apply to the glass-to-fluid transition for charge transfer absorption bands.
In a Letter in this journal, Hammack et al. [ l] suggested that the results obtained from dielectric continuum theory by Marcus and others for the role of solvent in thermally activated electron transfer [ 2,3] have been misapplied in the study of optically induced electron transfer. In particular, they cited the case of optically induced intramolecular electron transfer in mixed-valence ions, such as the example shown in the reaction (bpy),ClRu”(pz) $+
Ru’nCl(bpy):+
(bpy),ClRu”t(pz)
Ru”Cl(bpy):+
,
(1)
where bpy is 2,2’-bipyridine and pz is pyrazine [ 41. For mixed-valence ions in fluid solution an extensive body of data have been collected concerning the dependence of metal to metal charge transfer (MMCT) absorption band energies, Eop, on solvent and the data are largely in agreement with predictions based on dielectric continuum theory [ 5-81. From dielectric continuum theory the contribution to the absorption band energy from the solvent for the symmetrical ion in eq. (1) where AG= 0 is given by (2) Here Ae is the extent of charge transfer in the electron transfer process (Ae= 1 for optically induced
electron transfer between reactants which are weakly coupled electronically), aI and a2 are the molecular radii of the electron transfer donor and acceptor sites, d is the internuclear separation between reactants, and Dop and Ds are the optical and static dielectric constants of the medium. Eq. (2) was derived for the case of non-interpenetrating, spherical donor and acceptor sites and assumes that the internal dielectric constant of the solute, Dint, is 1 [ 8-101. The evidence presented by Hammack et al. concerning the breakdown in dielectric continuum theory was based on the effect of increasing external pressure on absorption band energies and band shapes. As the pressure was increased, only slight shifts were observed in band energies and shapes through the transition from the liquid to frozen states. This was so even though the reorientation of solvent dipoles is restricted in frozen solutions which greatly decreases Ds and from eq. (2) should lead to a significant decrease in the absorption band energy. For example, for nitromethane Ds is 33.7 at 25°C increases to 36.4 just above the freezing point, and drops to 3.4 upon freezing [ 11. Because of the loss in orientational polarization, Hammack et al. pointed out that a decrease in the energy of the MMCT absorption band of between 1500 and 1300 cm-’ is predicted by eq. (2) for polar organic solvents like nitromethane when the solvent is frozen. It is, of course, true that Marcus himself has applied dielectric continuum theory to the effect of solvent on optical charge transfer absorption bands [ 91, The Marcus treatment is based on a non-equilibrium
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
541
Volume 143, number 6
CHEMICAL
PHYSICS LETTERS
thermodynamic approach. From his results the shift in the energy of the absorption band maximum between a polar solvent and a vacuum (A&) is given by AE,=F,
-F,,+F:!o-F
_ IO-
(3)
Here F, and F. are the contributions from the polar solvent to the Helmholtz free energy of the light absorber when the local solvent dipole environment is in equilibrium with the electronic configuration of the ground state (F,) or the excited state (F, ). F,_, is the analogous Helmholtz energy for a hypothetical chromophore having as a permanent charge distribution the charge distribution of the excited state minus that of the initial state. F:flo is the equivalent energy quantity but in which the response to the difference in electronic distribution between the excited and ground states is only through the optical polarization of the medium, D,,. The magnitudes of the terms Flmo,F’& F, and F. depend upon the charge distributions before and after electron transfer and their theoretical evaluation upon the model used to approximate the actual molecular structures. A very clear discussion of the factors involved has appeared recently in a paper by Brunschwig, Ehrenson and Sutin [ lo]. For example, for a symmetrical mixed-valence ion with spherical donor and acceptor sites, A&=do as in eq. (2) if Dint= 1 and for a charge transfer process which can be approximated as having produced a point dipole at the center of a sphere, A& is given by b3
; d-4 b3
---
1-Ds 2D,+l.
(4)
Here ,u~and H are the vector dipole moments of the excited and ground states and b is the radius of the sphere. Other models have been developed and applied successfully the most notable being ellipsoidal cavity models for mixed-valence ions [ 1l-l 31. In the non-equilibrium thermodynamic treatment of Marcus it is assumed that the electronic polarization of the solvent stays in equilibrium with the initial and final electronic distributions of the ground and excited states. However, the orientational polarization is “frozen” on the timescale of the elec542
5 February
1988
tronic transition. Application of the Franck-Condon principle shows that the solvent dipoles must remain in orientations appropriate to the ele:tronic structure of the ground state during and immediately after the electronic transition. The inability of the solvent dipoles to reorient to positions appropriate to the electronic configuration of the excited state leads to a contribution to the absorption band energy of F?P,- F,_. which is the & in eq. (2). The assumption by Hammack et al. that there is a fundamental difference in the quantity FyEo F,_. between frozen and fluid solutions is incorrect. On the timescale of the optical transition, the solvent dipoles are frozen in either case. The assumption of frozen solvent dipoles is included in the underlying theory and is, in fact, demonstrated by the data of Hammack et al. [ 11. In general, solvent shifts are expected to exist between frozen and fluid solutions. One source of such shifts lies in changes in equilibrium solvent dipole orientations around the solute in its ground state. Such changes may be induced by differences in long range or local order between the frozen and fluid states. Another potential source of solvent shifts is in structural differences in the light absorber induced by the change between the frozen and fluid states. The available data, for example those of Hammack et al. in ref. [l] and those in fig. la, suggest that, at least in some cases, such effects are relatively small. Temperature variations. An experimental alternative to testing the frozen dipole approximation is available by observing changes in absorption band energies and shapes as the temperature is decreased through the fluid to glass transition. In fig. la is shown the temperature dependence of the metal to ligand charge transfer (MLCT) absorption band, d,(Re)+x*(bpy), in the complex [(bpy) Re( CO)3C1] in 4: 1 (v:v) ethanol-methanol. The ethanol-methanol mixture forms a high quality optical glass. The complex was prepared as described previously [ 141, and the temperature-dependent measurements were made by using an Oxford 1704 optical cryostat and 11 mm* glass cells. For the MLCT excited state there is a considerable radial electronic redistribution between the excited and ground states [ 151 and absorption band energies for small chromophores of this type which contain CO ligands are characteristically strongly solvent
5 February 1988
CHEMICAL PHYSICS LETTERS
Volume 143, number 6
1 .U I -
.eI
-
.? alMK bEOK c2OOK d2WK .5 , - C2QBK .I I -
a
7s. ‘d K
.I
a
225.
1SO.
TEMP
300.
CK)
.3 I .2
.l
a
aI_ I
UAVELENGTH
(ml
1.2
1
.B
.f)
a 90 K b 115K c 12’5K d 135K e 200K
cc
TEMP
.
l
(K)
.4
.2
0
Fig. 1. (a) Temperature dependence of the absorption spectrum of [ (bpy) Re( CO)JI] in 4 ; 1 (v :v) ethanol-methanol. At low energy the spectrum is dominated by the d, (Re) +t*( bpy) metal to ligand charge transfer absorption manifold. (b) Normalized emission intensity profilesas a function of temperature for the analogous MLCT emission from the same complex in 4: 1 ethanol-methanol. The insets show how the absorption and emission maxima vary with temperature. 543
Volume143,number6
CHEMICAL PHYSICSLETTERS
dependent [ 16,171. However, it is apparent from the data in fig. 1 that no significant shift occurs in band energy through the fluid to glass transition in the region 115- 140 K which is also in agreement with the frozen dipole approximation. Time-dependenteffects.Because of the difference in timescales involved, optical transitions occur with solvent dipoles frozen in orientations appropriate to the ground state and are free of dynamical effects arising from solvent dipole reorientations. On other timescales solvent dipole reorientational effects can play an important role either energetically or dynamically. An example of such an effect is illustrated by the data in fig. lb where the energy of the complementary LMCT (d,+x*) emission band for [ (bpy) Re( CO),Cl] is shown as a function of temperature. In contrast to the absorbance data, there is a significant shift in the emission energy of the MLCT chromophore at the fluid to glass transition. In this case, emission at low temperatures occurs from excited states which are surrounded by solvent dipoles which are frozen in orientations appropriate to the electronic distribution in the ground state. The result is a shift of the emission to higher energy. In fluid solution dipole reorientational times are rapid compared to the timescale for excited state decay. Dipole orientations in the vicinity of the excited state are at equilibrium with the electronic distribution of the excited state, and there is a significant shift to lower energy compared to the frozen solution [ 18,191. The decrease in energy gap in fluid solution leads to a decreased non-radiative lifetime in accord with a prediction of the “energy gap law” for non-radiative decay [ 19,201. In the midst of the fluid to glass transition, at z 115 to 125 K, the dipole reorientational timescale is comparable to the excited state decay time and time-dependent non-radiative lifetimes and emission energies are actually observed experimentally [21,22]. For thermally activated electron transfer, dynamic solvent dipole effects can also appear. The energy barrier to electron transfer includes contributions from the energy difference between states, solvent dipole trapping, and intramolecular vibrational modes, the latter because of the structural changes induced by the change in electron content between the reactants and products. For thermally activated electron transfer where there is sufficient electronic 544
5 February1988
coupling between the electron transfer donor and acceptor sites that electron transfer is “adiabatic”, there is growing experimental and theoretical evidence that solvent dynamical effects also play a role in determining electron transfer rates. The effects appear to arise from the temporal requirements associated with solvent dipole reorientations [ 23-281. Acknowledgements are made to the Army Research OffIce under grant No. DAAG29-85-K-012 1 and to the National Science Foundation under grant No. CHE-8503092 for support of this research.
References [ I] W.S. Hammack,H.G. Drickamer,M.D. Loweryand D. Hendrickson,Chem.Phys.LettersI32 (1986)231. [2] R.A. Marcus, Ann. Rev. Phys. Chem. 15 (1964) 155; J. Chem. Phys. 43 (1965) 679. [3] N.S. Hush, Trans. Faraday Sot. 57 (1961) 557. [4] R.W. Callahan, F.R. Keene, T.J. Meyer and D.J. Salmon, J. Am. Chem. Sot. 99 (1977) 1064; M.J. Powers and T.J. Meyers, J. Am. Chem. Sot. 102 (1980)
,1289. [ 51 C. Creutz, Progr. Inorg. Chem. 30 (1983) 1. [6] H. Taube, Ann. NY Acad. Sci. 313 (1978) 481; G.M. Tom, C. Creutz and H. Taube, J. Am. Chem. Sot. 96 (1974)7827. T.J. Meyer, Accounts Chem. Res. 1I (1978) 94; in: Mixedvalence compounds, ed. D.B. Brown (Reidel, Dordrecht, 1980) p. 75; B.P. Sullivan, J.C. Curtis, E.M. Kober andT.J. Meyer, Nouv. J. Chim. 4 (1980) 643. N.S. Hush, Progr. Inorg. Chem. 8 (1967) 391; Electrochim. Acta 13 (1968) 1005. [9] R.A. Marcus, J. Chem. Phys. 39 (1963) 1734; 43 (1965) 1261. [ IO] B.S. Brunschwig, S. Ehrenson and N. Sutin, J. Phys. Chem. 91 (1987) 4714. [ 111R.D. Cannon, Chem. Phys. Letters 49 (1977) 299: Yu.1. Kharkats, Elektrokhimya 15 (1976) 1251. [ 121 E.D. German, Chem. Phys. Letters 64 (1979) 305. [ 13] B.S. Brunschwig, S. Ehrenson and N. Sutin, J. Phys. Chem. 90 (1986) 3657. [ 141 M.S. Wrighton and D.L. Morse, J. Am. Chem. Sot. 96 (1974) 998. [ 151 E.M. Kober, B.P. Sullivan and T.J. Meyer, Inorg. Chem. 23 (1984) 2098. [ 161 P.J. Giordano and M.S. Wrighton, J. Am. Chem. Sot. 101 (1979) 2888. [ 171 R.M. Kolodziej and A.J. Lees, Organometallics 5 (1986) 450.
Volume 143, number 6
CHEMICAL PHYSICS LETTERS
[IS] MS. Wrighton and D.L. Morse, J. Am. Chem. Sot. 96 (1974) 998. [ 191 R.S. Lumpkin and T.J. Meyer, J. Phys. Chem. 90 (1986) 5307. [ 201L.A. Worl and T.J. Meyer, manuscript in preparation. [21] N. Kitamura, H.-B. Kim, Y. i(awanishi, R. Obata and S. Tazuke, J. Phys. Chem. 90 (1986) 1488. [ 221 E. Danielson, R.S. Lumpkin and T.J. Meyer, J. Phys. Chem. 91 (1987) 1305. [ 231 G. van der Zwan and J.T. Hynes, J. Phys. Chem. 89 (1985) 4181. [24] D.F. Calef and P.G. Wolynes, J. Phys. Chem. 87 (1983) 3387; J. Chem. Phys. 86 (1987) 3183.
5 February 1988
[ 251 M. Maroncelli and G.R. Fleming, J. Chem. Phys. 86 (1987) 6221; B. Bagchi, D.W. Oxtoby and G.R. Fleming, Chem. Phys. 86 (1986) 257. [ 261 H. Heitele, M.E. Michel-Beyerle and P. Fin&h, Chem. Phys. Letters 138 (1987) 237. [ 271 M. Sparpaglione and S. Mukamel, J. Phys. Chem. 9 1 (1987) 3938; L.A. Philips, S.P. Webb and J.H. Clark, J. Chem. Phys. 83 (1985) 5810; M.J. Weaver and T. Gennett, Chem. Phys. Letters 113 (1985) 213; J.N. Onuchi, J. Chem. Phys. 86 (1987) 3925.
545