J . Phys. Chem. 1987,91, 3767-3171 Although the rate constants in Table I are much larger than the typical values for E-V transfer processes (see ref 3 for some examples of NF(b) quenching by E-V mechanisms), the possibility of an E-V contribution which would give NF(a) and a vibrationally excited halogen molecule, cannot be completely ruled out. Although definitive experimental measurements of the products from NF(b) quenching by halogens are needed, we offer the opinion that chemical reaction is the process that is in competition with excitation transfer. Conclusions The NF(b) total quenching rate constants at 300 K for halogens and interhalogens are in the (0.35-15) X lo-” cm3 molecule-’ s-I range. The rate constants can be divided into two groups, those compounds (F2, ClF, and C12) with rate constants of (1.0 f 0.5) X cm3 molecule-’ s-l and those with rate constants of (1 1 f 4) X lo-” cm3 molecule-I s-l, which includes all Br- and Icontaining molecules. Three general quenching mechanisms, excitation transfer, chemical reaction, and E-V transfer, were discussed. The branching fractions for IF(B) and 12(B)formation were =0.02 and I1 > I11 > IV (>> V) at the same free energy change of the electron-transfer step (AG2&.I7 Oxidative quenching of * R u L ~ ~ + (17) AGz3 was calculated by the equation: AG23 = EIp(D*/D) - E1/2(*Ru2+/Ru+) - wP where EI12(D+/D)and E l 1 2 ( * R ~ 2 + / R are ~ + )the oxidation and reduction potentials of the quencher and *RuL,~+,respectively. wp represents the electrostatic work necessary to bring two product ions to electron-transfer distance.
3770 The Journal of Physical Chemistry, Vol. 91, No. 14, 1987
Kitamura et al.
distance A Figure 4. Relationships between the quenching rate constant and the close contact distance, d', in acetonitrile at 298 K for the quenchers TMPD (0, /3 = 0.76 .k'), TMB (0, /3 = 0.52 %.-I), and phenothiazine (A,p = 0.83 A-'). For the quenching of V (d' = 13 A), the data were taken from ref 5 .
by methylviologen has been also shown to depend on the alkyl chain length on the bpy ligands.I8 It seems to be a general trend that bulky substituents on ligands reduce the rate of luminescence quenching. As the ligands become bulkier, the radius of R u L , ~ +( r R )increases, whereas the solvent reorganization energy (A,) and, consequently, the activation free energy (AG*23)i9are expected to decreaseZo(AG23 = constant and d C 13 A):
For an adiabatic process, the rate is thus expected to increase with increasing size of reactants. On the other hand, the larger the ligands, the longer is the electron-transfer distance and, therefore, .~~ the lower the rate if the electronic factor is p r e d ~ m i n a n t . ~We will discuss these thermodynamic and electronic factors in detail in the following sections. Variation of k , with Ligand Size. The variation of Xo with R U L , ~ +(i.e., r R ) can be estimated from the equationI9
where Ae is the number of electrons transferred, and Do, and D, are the optical and static dielectric constants of the medium,22 respectively. When d = rR + rQ, however, eq 7 yields Xo to be 19.1-19.3 kcal/mol for the present R~L,~+-aromaticamine systems ( r R = 7.1-8.9 A). The change in Xo by 0.2 kcal/mol corresponds to that in AG*23 by 0.05 kcal/mol when AG23 = 0 (eq 6). It is apparent that A, based on the dielectric continuum model (eq 7) cannot account for rate retardation in the quenching of bulkier RuL,'+. It is frequently assumed that the electronic interaction energy between two reactant molecules (Hif)or the rate of electron transfer (k,,) is inversely proportional to the close contact distance, d', as expressed in the e q u a t i ~ n ~ , ~ ' HiE= Hip exp[-P(d' - d o / 2 ] k,, = k,I0 exp[-P(d' - do)] (8b) do is the most probable separation distance of the reactants and (18) Rau, H.; Frank, R.; Greiner, G. J . Phys. Chem. 1986, 90, 2476. (19) %tin, N. In Tunneling in Biological Systems; Chance, B., et al., Ed ; Academic: New York, 1979; p 201 and references cited therein. (20) Although A is the sum of the inner- and outer-sphere (A,) reorganization energies, we assumed A = A. in the present discussion. (21) Newton, M. D.; Sutin, N. Annu. Rev. Phys. Chem. 1984, 35, 437. (22) In acetonitrile, Dop= 1.807 (Techniques of Chemisfry;Riddick, J. A.; Bunger, W. B. Organic Soluenfs;3rd ed.; Wiley-Interscience: New York, 1970) and D, = 39.2 (Wurflinger, A. Ber. Bunsen-Ges. Phys. Chem. 1980, 84, 653).
-1 5 1
AGZ3 kcal/mol Figure 5. Activation enthalpies (AH*23) and entropies (AS',,) for the quenching of *RuL,~+ by aromatic amines in acetonitrile: I (0),I1 (m), 111 (A),and IV ( 0 ) .
H i t and k,: correspond to the values at d' = do. Equations 8a and 8b have been applied to various redox reactions with a known separation distance and P is known to range from 0.9 to 2.0 A-'.4,23 Although the determination of the actual close contact distance, d', is very difficult for homogeneous intermolecular electrontransfer reactions such as in the present case, we assumed d' = rR + rQ and k, was plotted against d' as shown in Figure 4. The k , values decrease exponentially with d' as expected from eq 8. 6 was calculated to be 0.7 f 0.1 A-' (Figure 4) which is slightly smaller than the values reported for the R~L,~+-methylviologen systems ( p = 1.2 A-' where L is 4,4'-dialkyl-2,2'-bipyridine).is The linear relationships in Figure 4 suggest that one of the factors responsible for the rate retardation is the change in the electron-transfer distance: rR + rQ The electronic interaction between the donor and acceptor orbitals may thus become inefficient with increasing bulkiness of the ligand. If this is the case, the present observations of the sequence of kq, I > I1 > 111 > IV (>> V), should be interpreted in terms of a S 2 3 . However, Figure 5 demonstrates that the bulkier the ligand, the more positive the value of A S * 2 3 and the more positive the AH*23. We could not find any trend of decreased transmission coefficient, K , with increasing size of the ligands from activation parameters. Does Nonadiabaticity Play a Role in the Quenching of RuL?+? According to Sandrini et al., the difference in the close contact distance between reactants leads to a change in K estimated for the I- or V-aromatic amine-acetonitrile system to be 1 X 10-'*o.s - 1 x IO-* or 5 X 10-3-10-5, re~pectively.~ We will focus our discussion on the following three subjects based on the present observations. R ~ ( b p y ) , ~ + - A r o m a tAmine ic Systems. To test the nonadiabatic behavior of the * R ~ ( b p y ) ~ ~ + - a r o m aamine t i c systems, we calculated the theoretical activation enthalpy ( A H * )and entropy (AS*)by the Marcus theory (eq 9 and 10).'9-24-26 AH* =
-m[AH2, - AGz3]
+ - [,(;: -+ m i ] + m2h
(9)
(23) Closs, G. L.; Calcaterra, L. T.; Green, N. J.; Penfield, K. W.; Miller, J. R. J . Phys. Chem. 1986, 90, 3673, and references cited therein. (24) Kitamura, N.; Kim, H.-B.;Tazuke, S.,manuscript in preparation. (25) Baggott, J. E. J . Phys. Chem. 1983, 87, 5223.
The Journal of Physical Chemistry, Vol. 91, No. 14, 1987 3771
Nonadiabaticity in Electron Transfer
AS2, + (AC2, + mA)- ds] s dT
(10)
where m = - AG2,/2X and s = Do;' - D;'. Although A is the sum of the inner- and outer-sphere reorganization energies, we assumed X = A, in the present discussion. The data for the standard enthalpy (AH23) and entropy (ASz3)of the electrontransfer step ( k 2 J are available for the quenching of *Ru(bpy)?+ by TMPD (-16.2 kcal/mol and -6.8 eu) or by T M B (-10.3 kcal/mol and -1 1.4 e ~ ) AH* . ~ thus ~ calculated by eq 9 is 0.5 or 1.4 kcal/mol for the quenching by TMPD or TMB, respectively, and is in excellent agreement with the observed value of AH*23 (0.9 or 1.7 kcal/mol). Similarly, AS* was obtained from eq 10 to be -4.6 (TMPD, A S * 2 3 = -9.4 eu) or -7.5 eu (TMB, AS*23 = -8.1 eu). If the electron transfer from the amine to *Ru(bpy)F as estimated by Sandrini et al., is nonadiabatic with K = 1 X AS*23should be more negative by 9 eu and then LU*~,(TMPD) i= -14 eu and AS12,(TMB) i= -17 eu. Our experimental errors in determining AS*23are below 2 eu. These calculations clearly indicate that both AHt2, and AS*23,at least for the quenching by TMPD or TMB, are explicable within the framework of the Marcus theory which is based on the assumption of K = l.19 We conclude that reductive quenching of *Ru(bpy),2+ at highly exoergic regions (discussed below) is adiabatic; K = 1 . Effects of the Bulkiness of Ligands on K . More positive A S * 2 3 values for R U L ~ with ~ + bulkier ligands are an opposite trend expected from the nonadiabatic behavior. If the quenching of I11 or IV by TMPD or T M B is nonadiabatic, AS*23(111 or IV) should be more negative than ASt2,(1), which requires A S 2 3 for the quenching of 111 and IV by TMPD or TMB to be more positive than +8 eu according to eq 10. Although the data for the temperature coefficient of the reduction potential (AEIl2) of 111 or IV are not available at the present time, it has been reported that AE,j2 is almost independent of the bulkiness of the ligand.27 Furthermore, the change in the electrostatic entropy accompanied by bimolecular electron-transfer reactions (ASS23)l' derived from the Born model is insensitive to the bulkiness of the ligands and, therefore, to rR:
where ZRand ZQ are the valences of R u L , ~ +and the quencher, respectively. Equation 1 1 indicates that the increase in rR from 7.1 A for I to 8.9 A for 111 or IV results in a change of ASes2, by only +1.5 eu. We cannot explain the rate retardation of 111 or IV by the change in AS*23values. The increase in AH**, for the bulkier RUL,~' will be a more probable reason for the rate retardation (Figure 5 ) . There are two possible explanations: ( 1 ) one is to assume nonelectrostatic and specific interactions of *RuL,~+with solvent molecules; (2) another is based on the large gaps between the ligands of RUL,~+. Recently, Koval et al. demonstrated that the effective radii of various transition-metal complexes estimated by the space-filling model (IsFu) were larger than those determined electrochemically, rE, based on diffusion coefficients and Stokes' law, and they interpreted the results as due to large voids in its structure.28 The discrepancies between rSFMand rE are large for nonspherical molecules. For both 1 and 2, the solvent reorganization energy (26) Reynolds, W. L.; Lumry, R. W. Mechanisms of Electron Transfer; Ronald: New York, 1966. (27) Schmits, J. E. S.; van der Linden, J. G.M. Inorg. Chem. 1984, 23, 179R
(28) Koval, C. A.; Ketterer, M. E.; Reidsema, C. M. J . Phys. Chem. 1986, 90, 4201.
is not correctly evaluated by the dielectric continuum model (eq 7) with d = rR rQ, which predicts an almost constant Xo = 19.1-19.3 kcal/mol for all RuL32+-aromatic amine systems. Therefore, the changes in the solvent reorganization energy with the nature of the substituents on the ligands will be the primary reason for the slower quenching rate of the bulkier R u L , ~ +(111 and IV). At the present time, we tentatively conclude that bulky substituents on ligands do not necessarily bring about a large decrease in the transmission coefficient for the highly exoergic electron-transfer reactions of 111 and IV. It is apparent, however, that the comparison of the observed activation parameters with AH* and AS*(eq 9 and 10) is of primary importance to reveal the nonadiabaticity problem of the particular electron-transfer reactions. Does K Depend on AG2,? Another important consequence is that the increase in AG2, leads to the sharp decrease in A S * 2 3 for the bulkier ligands (Figure 5); AAS'23 (defined as (AS*23at AG23 -15 kcal/mol) - AS*23at +5 kcal/mol)) values are -6, 10, - 1 1 , and -12 eu = 1.8, 2.9, 3.3, and 3.6 kcal/mol, respectively) for I, 11, 111, and IV, respectively, whereas the corresponding values are constant at 2-3 kcal/mol. The present data suggest that, although favorable overlap between the donor amine and acceptor metal t2gorbitals is achieved at relatively large separations of reactants (Le., d = 12.7 %.) for highly exoergic reactions such as the quenching by TMPD or TMB ( K = l), the presence of bulky substituents in 11, 111, and IV will cause less efficient orbital overlap with increasing AC23 (K= 1). Brunschwig et al. reported that electron-transfer reactions at moderate AG2, regions (Le., normal region) have rate maxima at close contact of the reactants while those at highly exoergic regions (i.e., inverted region) proceed at larger ~ e p a r a t i o n s . ~ ~ Although the present systems are all in normal regions, the introduction of bulky alkyl substituents on bpy, which brings about a longer electron-transfer distance (from d = 10.9 A for I to 12.7 A for 111 and IV), is supposed to play a dominant role to reduce the orbital overlap with increasing AC23, in particular, at endoergic regions. The large and sharp decrease in A S * 2 3 for 11, 111, and IV will be thus ascribable to nonadiabaticity while the nonadiabaticity in the quenching of *Ru(bpy)32+at endoergic regions ( A M I 2 , = 6 eu) is marginal.24 The present results indicate that K depends on AG2, and the discussion of electron-transfer mechanisms based on a log k , vs. AG23 plot should be carefully made.
+
-
-
Concluding Remarks The present observations of k , and the activation parameters demonstrated that reductive quenching of R U L , ~ +in highly exoergic regions was adiabatic, while bulky substituents on ligands (11, 111, and IV) brought about a decrease in K with increasing AG23
In recent years, the nonadiabaticity problems in several redox reactions has been discussed on the basis of the Marcus self-exchange and cross-reaction rates.30 The K values estimated on the basis of these relations and the analysis of a log k , vs. AG2, plot for the R~L~~'-aromatic amine s y ~ t e m showever, ,~ do not agree with the activation parameters as revealed by the present study. Balzani and Scandola also pointed out that the cross-reaction may exhibit a different degree of nonadiabaticity than expected on the basis of the corresponding self-exchange reactions. It is apparent that a clearer picture on the adiabaticity problem emerges after determining activation parameters as well as the corresponding standard enthalpy and entropy. Work along this line for RuL32+-aromatic amine systems is now in progress in our laboratory. (29) Brunschwig, B. S.; Ehrenson, S.; Sutin, N. J . Am. Chem. SOC.1984, 100, 6858.
(30) Balzani, V.; Scandola, F. Inorg. Chem. 1986, 25, 4457.
