J. Phys. Chem. 1993, 97, 345-3550
3545
Rates and Efficiencies of Contact-Ion-Pair Formation in Photolyzed Mixtures of TMPD with Halogenated Compounds in Nonpolar Solvents Hiroshi Shimamori,’ Kei-ichi Hanamuro, and Yoshitsugu Tatsumi Fukui Institute of Technology, 3-6-1 Gakuen, Fukui 910, Japan Received: October 28, 1992; In Final Form: January 5, I993
Time variation of microwave dielectric absorption has been examined for photolyzed solutions of N,N,N‘,N‘tetramethyl-p-phenylenediamine(TMPD) admixed with halogen-containing compounds AX (AX = CC4, C2H51, CzHsBr, C2HsC1, C6H51, C6H5BTr CsHsCl, C6H5F, and C6F6) in nonpolar Solvents (mostly benzene). In solutions with CC14, C2H5I, C6H5I, CsHsBr, and C6HsC1, the dielectric absorption signals show first-order growths with appreciable intensities, indicating formation of a contact ion pair (CIP) TMPD+X- ( X denotes a halogen atom) by reactions of these compounds with the excited triplet state of TMPD. On the contrary, no measurable amplitudes were detected for ClHsBr, C Z H ~ C IC&F, , and C6F6, showing that stable CIP cannot be formed with these compounds. Kinetic analyses indicate that the rate constants for the CIP formation are in the order CC4 (diffusion limit) > C6H5I > C2HsI > C&Br > C6H5Cl and that the efficiencies for the C I P formation also depend on the compound AX. These differences among the halogenated compounds cannot be explained on the basis of overall free-energy change of the reaction, but rather they correlate with the nature of dissociative electron attachment to the molecule AX.
Introduction Photoinduced electron transfer has been one of the extensively studied subjects during past Much work has focused on checking the validity of the Marcus theory4 and related semiempirical correlations between the rate constant and the overall free-energy change of the r e a c t i ~ n .It~has been recognized that the “reorganizational energy”, equivalent to a vertical potential-energy barrier for the reactants at the reaction coordinate where the products are in a relaxed state, is a key factor for the electron-transfer process. The effects of solvent motion can be treated as constituting the so-called outer-sphere barrier (reorganization energy), which is markedly affected by solvent polarity. On the other hand, it is also proposed that the changes in the electronic character and the geometrical configuration during the electron transfer give rise to a reorganization energy, called the inner-sphere barrier. Generally this can be regarded as solvent-independent and is often assumed to be negligible in comparison with the outer-sphereone. However, thecontribution of this barrier may become important when the electron transfer involves significant change in the molecular structures of the products, and the effect may be enhanced for processes in nonpolar solvents. Although there have been few studies showing a specific role of the inner-sphere barrier, its importance has been suggested in the electron transfer to a halogenated compound R-CI that leads to stretching of the C-Cl bond and eventual dissociation of the negative ion.6.’ A contribution from the inner-sphere reorganization has been invoked to explain the difference in the triplet andsinglet reactivities in the electron transfer from aromatic amines to chlorobenzenes.8 We do not have, therefore, many examples on this subject, and knowledge is still qualitative. A previous study9 has shown that electronically excited N,N,N’,N’-tetramethyl-p-phenylenediamine (TMPD) reacts with Ccl4, present as a solvent, to form a contact ion pair (CIP) TMPD+Cl- with near unit quantum yield. It is also evident that in benzene solvent, CC14 can acquire an electron from the excited triplet state of TMPD. These processes occur one-photonically. Such an ionization becomesenergetically possible even in nonpolar solvents with the aid of excess energy released by dissociative electron attachment to CC14 and of the energy gained by forming a CIP. These results imply that the electron-attachment property of the electron acceptor is a key factor in forming a CIP. Since the electron attachment to a compound like CCI4 involves direct
dissociation of the intermediate CCI4-* ion, there must be a significant role of the inner-sphere reorganization in this electrontransfer process. We readily expect that as for CC&, other compounds that capture electrons effectively are alsoable to form CIPs by electron transfer from the excited triplet state of TMPD. In the present study, a possibility of similar CIP formation has been examined for systems containing TMPD and a halogencontaining compound in nonpolar solvents. There are a number of data of electron attachment to molecules in the gas phase, and the attachment rates1° as well as the energetics” are established. We have intended to clarify the C I P formation in relation to the nature of the negative-ion formation in order to gain insight into the effects of inner-sphere reorganization on this type of electron transfer. Generally the presence of a cation, due to its electrostatic interaction, may significantly affect the efficiency of the process. In the present study, however, the cation is common to all the reactions, and the effects of the cation do not appear explicitly. The compounds selected are CCh, C ~ H S IC2HsBrr , C2H5CI, C6HsI, CsHsBr, GHSCI, CbHjF, and CsF6 for which the rate constants for thermal electron attachment in the gas phase are known to vary several orders of magnitude. The efficiency and kinetics of formation of C I P are analyzed in conjunction with electron-attachment properties of acceptor molecules.
Experimental Section Thedetails of the time-resolved microwavedielectricadsorption technique used in this study were described previously: and therefore, only a brief description is made here. The sample was irradiated with the third harmonic (355 nm) of a Nd:YAG laser. An X-band microwave circuit was used. A silica cell containing a sample solution was placed within the resonant cavity (TElol mode, the resonant frequency N 8.8 MHz). Following the laser pulse, a change in the microwave dielectric absorption is detected by a crystal diode. The signal was amplified and fed to a Tektronix 2430 digital oscilloscope. The signal was mostly taken with one shot of laser pulse but in some cases averaged over two or more shots using the digital oscilloscope. The response time of the detection system was about 30 ns. TMPD (Aldrich Chemical Co.) was purified by recrystallization from ethanol or by vacuum sublimation. Carbon tetrachloride, benzene, and n-hexane (Wako Chemicals, Spectrograde) were dehydrated by contact with Molecular Sieve 3A. C2H51,
0022-3654/93/2097-3545%04.0~~0 0 1993 American Chemical Society
Shimamori et al.
3546 The Journal of Physical Chemistry, Vol. 97, No. 14. 1993
h
>
\
> E
a 8 3
i_r-i 500 ns/div
h
.1
-
' 0 -
5 E -
b x 112
a -
Y
L
v
-I
t a
z
TIME
TIME Figure 1. Timedependenceof theapparatusoutput forsolutionsofTMPD and carbon tetrachloride in benzene. The concentration of TMPD is 3.75 mM. The concentration of CC14 is (a) 0.070, (b) 0.13, (c) 0.20, and (d) 0.27 mM. The sample cell is of 3-mm optical path length (OD = 1.4); the laser intensity = 4.5 mJ/pulse.
CzHsBr, CZHsCl, C6H51, CsHsBr, C6HsC1, C ~ H S FC6H51, , and C6F6(all purchased from Wako Chemicals) were used as received. Before irradiation, all the samples were deaerated by bubbling with Ar gas for more than 20 min. In preparing a sample solution, each compound except C2HSCl has been added directly to a solution of TMPD in benzene. For CzHsCl solution, gaseous C2H5Clwas bubbled through a TMPD-benzene solution. Measurements were carried out at room temperature (298 K). The amplitude of the observed signal is expressed by9
v = KdS1Nr2)g(7)
(1) where K is a constant relating to the sensitivity of the cavity resulting from the dielectric constant of the solvent, temperature, the coupling factor and the unloaded Q of the cavity, and the filling factor of thecell in thecavity. [SIis the molar Concentration ofthe transient, A(p2) = p2-pg2 (p,dipolemomentofthetransient (ion pairs in this case); pg, dipole moment of the solute in the groundstate), andg(r) = ~ / ( i 1( ~ 7 ) ~l / )w r ( w , microwave angular frequency; I,dielectric relaxation time for the transient). When the photoabsorption produces transients that possess dipole moments larger than those of the original photoabsorbing species, one can observe increases in the signal amplitude. This is what we observe in the present study. Although the ground-state TMPD has a dipole moment of 1.3 D, it can be neglected in comparison with that of an ion pair possessing a dipole moment as large as 11 D9 because the dielectric loss is associated only with the square of the dipole nioment. Thus, A(p2)can be replaced by p 2 in this case.
-
Results and Discussion Shown in Figure 1 are typical microwave dielectric absorption signals for mixtures of TMPD and CC14 in benzene solvent observed after irradiation of 355-nm laser pulses. Such measurements have been carried out for solutions with different CC14 concentrations with the TMPD concentration fixed at about 3.8 mM so that the absorbance is close to unity. In the previous study, a signal similar to that shown in Figure 1 was observed with much poorer sensitivity for the mixture of TMPD-CCI4 in benzene and was attributed to the formation of the ion pair
(500 nddiv)
Fipre2. Timedependenceof theapparatusoutput forsolutionsofTMPD and C6HsI in benzene. The concentration of TMPD is 3.83 mM. The concentration of C6HsI is (a) 0.060, (b) 0.1 1 , (c) 0.17, and (d) 0.23 mM. The sample cell is of 3-mm optical path length (OD = 1.4); the laser intensity = 3.0 mJ/pulse.
TMPD+Cl- via the reaction of the excited triplet state of TMPD with CC14. The present results support this interpretation. We can see a gradual growth of the signal in all cases. It is found that both the growth rate and the absolute amplitude increase with the concentration of C C 4 . The latter feature was not clear in the previous study.9 Measurements have been extended to other halogen-containing compounds: C2HsI,CzHsBr, CzHsCl, C6H51, C ~ H S BC~~, H S Cand ~ , C6HsF. For CzHsI, C6H51, C6H5Br, and C6H5Cl, first-order growth signals are also observed. Signals for C ~ H Swith I different concentrations are shown in Figure 2. Quite similar results have been obtained for CzHsI. For C6HSBrand C6HsC1, the observed amplitudes are relatively low so that higher concentrations as compared with those for CC4,CzHsI, and C6H51were required to obtain detectable signals. Examples of observed signals for C6H5Brand C&Cl are shown in Figure 3. It has been found that the amplitude at the plateau in each signal is proportional to the laser intensity, and the signal mostly disappears when oxygen is present in the solution. Therefore, contact ion pairs are also formed in these systems via the excited triplet state of TMPD. Following the initial growths, all the signals show gradual decays on a longer time scale. The decays for CC14, ClHJ, and C6HJ were found to be of second order. Such behavior has already been discussed in the previous study for the Ccl4 system9and was ascribed to the formation of ion-pair dimers (TMPD+Cl-)2 and their coagulations forming larger clusters. A similar fate may be true of ion pairs in C2HJ and C6HsI systems. For C&Br and C6HsCl solutions, on the other hand, the second-order decays can be observed only at a high concentration of these solutes. This can be explained by the relatively low concentration of ion pairs formed for these compounds. It should benoted that forsolutionscontainingCzHs1 or C6H5I, thecolor of solution after the photolysis turned to light blue and some precipitations appear, as in the case of CC14. Such a change was not clear for C6HsBr and C6HsCI and may be due to low yields of the ion pairs in these compounds. In contrast with CcI4, C2HsI, C6HsI, C6HsBr, and C6HsCl, negligibly small or essentially no signals have been observed for C?HsBr, C2H5C1, C6H5F, and C6F6 used as electron acceptors. Even the addition of a very high concentration of these compounds
Photolyzed Mixtures of TMPD
The Journal of rnysical Chemistry, Vol. 97, No. 14, 1993 3541
TABLE I: Amplitude of the Plateau of the Dielectric Absorption Signal and Kinetic Parameters for the Ion-Pair-Formation Processes' Determined Experimentally in Benzene Solutions, Thermal Electron-Attachment Rate and the Exothermicities Constants in the Cas Phase (kit), (EA - BD) for the Attachment Reactions in the Gas Phase RX
amplitude, mV
CClj ChH.1 C?H5I ChH5Br ChH5Cl ChHsF C2H5Br C2H:CI ChFh
IO qk, M
235 216 250 77 67
IO 'kd, s
I s I
10.4 7.8 6.0 3.4 1.6
I
2.7 3.6 3.4 1.9 2.7
0 0 0 0
k,,,, cm3 molecule Is
I
4.0 X IO 7 r l.OXIOxd 5.2 X IO q l ' 6.5 X IO 3XlOIJd
W
m TI
1
100
.-0 0)
K
O
0
5
10
15
Reciprocal Concentration (mM-') Figure 5. Plots of reciprocal amplitude of the dielectric absorption signal
as a function of reciprocal concentration of the solute, determined from the intensity of the plateau of the signal.
TABLE 11: Parameters Determined from Plots of Reciprocal Amplitude of the Dielectric Absorption Signal at Relatively Long Times vs Reciprocal Concentrations of the Halogenated Camwunds
RX
intercept, V-'
cc14
4.7 (4.3)" 6.6 (4.6)" 3.7 (4.0)" 16 (13)" 26 (1 5)"
f'
104kd/k,M 2.6 5.0 9.7 21
(2.6)b (4.6)b (5.7)b (5.6)* 25 (19)b
I
1 GHsl 1 CzHsI 0.3 ChHsBr 0.2-0.3 ChHsCl u Directly determined from the reciprocal value of the maximum amplitude of the signals at very high concentrations of AX. The ratio calculated from the values listed in Table I. 'f = kJ(k2 + k3); the efficiency of the ion-pair formation from the intermediate complex (see text for details).
a straight line with the intercept of [TMPD*]o-I and the slope of [TMPD*Io-I(kd/k). The latter should give a value of kd/k. We have made measurements of the maximum amplitude of the signal for different concentrations of AX (=CC14, C ~ H S IC6HA , C6HsBrrand C6HsCl) under the condition that the sample cell, the optical density, and the laser intensity are kept the same. Plots based on eq 6 for these results are shown in Figure 5. As expected, the plots give good straight lines, and values of [TMPD,*Io-l and kd/k are obtained. They are listed in Table 11. ShownalsoinTableII (fifthrow) arevaluesof kdlkcalculated from values of kd and k (see the third and fourth rows in Table I) determined from the first-order growth of the signals. We can see good agreement with each other in the two sets of values for kd/k. Besides the time variation of the signal, the absolute amplitude of the signal gives valuable information on the mechanism of ion-pair formation. The intensity of the dielectric absorption signal is proportional not only to the concentration of the ion pair but also to the product of the square of its dipole moment and the dielectric relaxation function g ( r ) that is proportional to the reciprocal of the relaxation time of the ion pair (see eq 1). It is known that the dielectric relaxation time is mainly determined by the molecular volume of the polar species; a larger volume leads to a longer relaxation time (a smaller value of g ( r ) ) . The molecular length of TMPD cation along its long axis can be estimated to be about 10 A, and the ionic radii for atomic halogen anions are 1.8 1,1.96, and 2.20A for C1-, Br-, and I-, respectively. As long as we admit a model that the halogen anion resides at the center of the TMPD cation, the molecular size of the ion pair is mainly determined by TMPD cation. Thus, the relaxation time, and therefore g ( r ) ,does not change much with replacement of the halogen atom, though we expect that g ( r ) may decrease slightly in the order CI- > Br- > I- due to the difference in their
radii, On the other hand, the dipole moment of the ion pair may increase slightly in the order Cl- < Br- < I- because the separation between the positive and the negative charges increases in that order. This leads to a conclusion that the product r2g(r)does not change much with the nature of the halogen atom, and accordingly, the observed amplitude directly reflects the yield of the ion pairs. The amplitude of the signal at high concentrations of AX has been obtained from the intercept of reciprocal plots as shown in Figure 5. This value should correspond to the maximum amplitude of the signals at very high concentrations of AX. Indeed, the values from the reciprocal plots and those measured directly as the maximum amplitudes are in good agreement with each other. Both of those values are listed in Table I. One can notice from Table I that the ion pair with X = C1 from CC14 and that with X = I from C6HsIgive the same amplitude, while the ion pair with X = Cl from CCl4 and that from C6H5C1 show completely different amplitudes. This indicates that the yield of ion pairs differs significantly depending on the compound AX. However, according to reactions 2 and 3, one can expect that for any kind of AX that gives rise to production of ion pairs, the yield at a high concentration of AX should approach a value that is independent of the nature of AX, namely, [TMPD,*]o. This is contrary to the present experimental results. Therefore, there must be further processes that cause different yields of the ion pairs. Thus, we propose the following mechanism as a more detailed description of the ion-pair formation, TMPD*
+ AX
ki
(complex)*
k
-%
TMPD
+
(7)
AX
kb
A TMPD*X- + A
(8)
where (complex)* represents an intermediate, which is probably in a charge transfer state such as TMPD6+AX6-or TMPD+AX-. Here we have assumed the presence of both back electron transfer (kb)from the complex and quenching (k2)via the complex. The involvement of the latter process can explain the difference in the yield of ion pairs. The former process has been introduced because the complex is not in a relaxed state but is still capable of making the transfer of an electron back to the cation before AX- suffers bond cleavage, leading to CIP formation. It will be shown in a later section that this process is important in explaining the difference in the overall rates for the CIP formation among the halogenated compounds investigated here. According to processes 7 and 8, eq 4 can be rewritten as
i1 - exp6(gk] iAX1 + kd)t)l
(9)
where f = k3/(k2 + kj), which determines the efficiency of the ion-pair formation via the complex, and g = (k2 + k3)/(k2 + k3 kb). The rate constant for electron transfer is now expressed by gk,instead of k in eq 4, but this does not change the situation essentially. The main change is associated with the signal amplitude at t = -; namely, we have the following equation as a replacement of eq 6:
+
-
1
[TMPD+X-]
~
1
[TMPD,*lo
1
1 +
l k d
1
[TMPD,*lof g k ~[AX1
(10) Now the intercept of the reciprocal plot for the amplitude contains the factor5 This factor takes into account the difference in the yield of ion pairs depending on the nature of AX. Assuming the value offis unity for CC14,C2H51, and C&sI, those for C&Br and C6HsCl are estimated to be about 0.3. They are shown in Table 11. Low values forfin C6HsBr and C6H5C1mean that the
Photolyzed Mixtures of TMPD
The Journal of Physical Chemistry, Vol. 97, No. 14, 1993 3549 solvent with a dielectric constant t (2.3 for benzene). The term 4 / d takes into account the energy gained by bringing the two ions to an encounter distance d. For a process involving the dissociation of the negative ion, it is appropriate to use, instead of EA of the acceptor, the value EA - BD (EA, electron affinity of the halogen atom; BD, dissociation energy of bond A-X) for the exothermicity or the driving force of the negative-ion formation. Thevalues of EA - BD for acceptor moleculesstudied here are listed in Table I. The production of a cation by electron transfer, due to its electrostatic interaction with the negative ion, may affect the efficiency of the process. In the present study, however, the cation is common to all the reactions, and its effects do not appear explicitly. Then thedependenceof the rateconstant on the overall free-energy change for the reaction may reflect that on the free-energy change for the negative-ion formation. The ionization potential of TMPD in the gas phase has been reported to be 6.6,16 6.2,’’ and 5.9 eV,I8 and the energy of the triplet TMPD* is 2.9 f 0.1 eV.19920Assuming here that IP = 6.6 eV and E* = 2.9 eV and fi = 1 1 D9and p = 5.0 A (half of the molecular length of TMPD)21for the ion pair, we obtain
a)
I
TMPD’X’ Reaction Coordinate
b) I
lntemuclear Distance Figure 6. (a) Schematic representationof the potential energy variation along the reaction coordinate for the contact-ion-pair formation from TMPD’ and a halogen-containing compound AX based on the conventional picture for the photoinduced electron transfer reaction which has beencorrelatedwith the free-energychangein thereaction. (b) Schematic representation of the potentialenergy for dissociativeelectron attachment to halogen-containing compound AX. BD is the dissociation energy of bond A-X, and EA is the electron affinity of halogen atom X. The value of EA - BD represents the exothermicity of the reaction. The electron attachmentoccursvertically (Franck-Condontransition),and the unstable negative ion AX- tends to dissociate along the repulsivepotential energy curve in competition with the autodetachment of electron from AX-*.
formation of stable ion pairs is inefficient for these compounds. The quantum yield for the formation of the excited triplet state of TMPD has not been firmly established, but Richard and Thomasi4reported a value of 0.96 f 0.10 for the quantum yield in the photolysis of TMPD in c-C6HI2. If we adopt this value ( e l .O) for TMPD,* formation, the values off determined here can be regarded as the quantum yield for formation of respective ion pairs.
Correlation with Electron-Attachment Processes The electron-transfer process in solutions has often been discussed in terms of potential-energy or free-energy variation along the reaction coordinate, as represented in Figure 6a. The overall free-energy change for an electron transfer from an excited donor to an acceptor leading to the formation of a contact ion pair can be expressed byi5
AG = IP - EA -E* - ( p 2 / p 3 ) ( t- 1)/(2c
+ 1) -
e 2 / t d - TPS (1 1) where IP is the ionization potential of the donor molecule, EA is the electron affinity of the acceptor molecule, E* is the electronic energy of the excited donor molecule, and A S is the entropy change between the final and the initial states. The fourth term in the right side of the equation is the solvation energy for the contact ion pair (the dipole moment p and the radius p ) in a
AG (eV) = 3.56 - (EA - BD)- e 2 / d - TU3 (12) Since the value of EA - BD is less than 0.8 eV for all systems treated in this study (see Table I), the value of AG may depend very much on -e2/d. The entropy change is hard to estimate here. It is known that the value of AS is about -18 cal/deg for many donor-acceptor systems where no dissociation of the chemical bond is involved in the electron transfer. This value corresponds to-TAS = 0.23 eV a t 300 K. When the dissociation of a negative ion occurs, the entropy should increase and the value of -TAS may decrease and even become negative, but we still expect a small value for it and assume it to be negligible here. The distance d between two ions is also difficult to know. The dipole moment of 1 1 D for TMPD+Cl- suggests that d = 2.3 A for this ion pair when both charges are separated completely. Let us consider the case of ion-pair formation from the TMPD-CC4 system. As the value of EA - BD is 0.58 eV for CC14, if we use d = 2.3 A, we obtain AG = -3.28 eV. Since it is likely that the actual value of d is longer than 2.3 A, the above value for AG should be a lower limit. A similar estimate can be made for the CIP with B r or I-, because the ionic radii for C1- and I- differ only by 0.4 A. However, the situation changes if we consider C ~ H Sfor F which EA - BD is -1.95 eV. In this case, a similar estimation leads to a lower-limit value of AG of 4 . 7 5 eV. If the value of d is slightly longer than that assumed above, say 3.0 A, one obtains AG > +0.71 eV, and the formation of the contact ion pair is energetically improbable. This may be the reason why we cannot observe the formation of TMPD+F-. Of course, if we use IP = 5.9 eV, the corresponding AG is very close to zero, but we believe that the value of 5.9 eV for IP is too low. It is evident that both the values of EA - BD and -e2/d are key factors in the formation of stable CIP. However, let us consider C2H5Br and C6HSBr systems. Both have the same halogen atom Br and should have the same value for - e 2 / d(note that a similar argument can be applied to the value of -TAS), but the values of EA - BD are 0.48 and - 0 . 1 1 eV, respectively. So the value of AG is more negative for C2HSBrthan for C6HSBr. In contradiction with this expectation, the experimental results show no formation of the ion pair in the C2HSBr system. The same argument can be made for the C2HsCl and C6HsClsystems. Furthermore, in the case of C6F6, we can put the value of EA (-1.8 eV) directly into eq 1 1 because this compound does not dissociate after electron capture. Then AG becomes a large negative value even if d is around 3 A, yet we could not observe a stable CIP in this case. These results cannot be explained reasonably as long as we are basing them on the net free-energy change in the reaction. We can see from Table I that the rate constants for the formation of contact ion pairs or the electron-
3550
The Journal of Physical Chemistry, Vol. 97, No. 14, 1993
transfer reactions vary in the order C c l 4 > C6HsI > C2HsI > C6HSBr> C6HsC1. This order is in accord with that of the magnitude of rate constants for thermal electron attachment to those compounds in the gas phase. The latter values are also listed in Table I. The rate and the efficiency of the electron attachment to a molecule are well-characterized by where the potential energy surface of the neutral molecule overlaps with or crosses that of the corresponding negative ion. In the resonant captureof an electron by a molecule, a vertical (Franck-Condon) transition occurs from a system comprising a free electron and a neutral molecule to a negative-ion state. The negative ion is energically unstable in itself, so unless some stabilization process is present, the electron will suffer autodetachment. If the attachment involves dissociation of the molecular negative ion, thedissociation competes with the autodetachment. This situation can be understood from Figure 6b, where the potential energies for a neutral molecule AX and the corresponding negative ion AX- are shown as a function of the internuclear distance f A - X or f A - X . The formation of a stable negative ion is completed when the internuclear distance extends beyond the crossing point between two potential energy surfaces. A scheme of dissociative electron attachment to molecule AX is written as ka
ks,
e-+AXsAX-*+A+X-
(13)
kad
where the k's are rate constants. Then, the overall rate constant k,,, for the attachment reaction producing a negative ion X- is expressed by
Shimamori et al. process through a factor of ks,/(kad + ks,).We suggest that the overall efficiency for the formation of stable contact ion pairs determined by a factor of/(=kj/(kl + k3)) can be correlated also with the factor kst/(kad + ks,) because in theattachment of free electrons the autodetachment process with the rate constant kad controls both the overall attachment rate and the attachment efficiency, but in the contact-ion-pair formation, the rate and the efficiency can be determined separately through different factors g a n d f. We conclude that the efficiency and the rates for the formation of stable contact ion pairs are mainly governed by the nature of the electron-transfer (attachment) process in the interacting regions and are not controlled by the free-energy change of the reaction. Such a nature may be a result of the occurrence of the dissociation of negative ions after electron transfer. Acknowledgment. This work was partly supported by a Grantin-Aid for Special Project Research and that for Scientific Research (C) from the Ministry of Education, Science and Culture. References and Notes ( I ) See, for example: Photoinduced Electron Transfer; Fox, M. A., Channon, M., Eds.; Elsevier Science: Amsterdam, 1988; Parts A-D. (2) Photoinduced Electron Transfer; Mattay, J., Ed.; Springer-Verlag: Berlin, 1990; Vols. I and 11; 1991; Vol. 111. (3) Kavarnos, G.J.; Turro, N. J. Chem. Reo. 1986, 86, 401. (4) Marcus, R. A. Annu. Reo. Phys. Chem. 1964. I S . 155. (5) Rehm, D.; Weller, A. Isr. J. Chem. 1970, 8, 259. (6) Andrieux, C. P.; Blocman, C.; Dumas-Buchiat, J.-M.; Saveant, J.M. J . Am. Chem. Soc. 1979, 101, 3431. (7) Chesta, C. A.; Cosa, J. J.; Previtali, C. M. J . Photochem. 1986, 32, 203.
Theexothermicity, EA- BD, for the electron-attachment reaction is listed in Table I. Based on the schematic potential energy diagram shown in Figure 6b, a large negative value for EA - BD corresponds to a large positive energy at the dissociation limit, which generally leads to a large Franck-Condon resonance energy for the electron attachment. In this case, we may have a significantly low value for the overall rate constant, because not only the initial attachment rate constant k, becomes lower but also the autodetachment rate k,d increases due to the longer time taken for AX-* to reach the crossing point. On the other hand, a large positive value for EA - BD, like the CC14 case, results in a very large attachment rate constant since the potential energy curve of the negative ion crosses that of the neutral molecule at a point very close to the equilibrium internuclear distance of the latter. The same argument can be made for the electron attachment in the liquid phase except that the potential energy surface of the negative ion becomes lower than that in the gas phase due to the polarization energy of the ion in the liquid phase. It should be noted that expression 14 resembles the rate constant for the ion-pair formation, gkl = kl(k2 + k3)/(k2 + k ) + kb). Thus, the difference in the rate constants among the halogencontaining compounds that stems from a factor of g can be correlated with that in the initial electron-transfer (attachment)
(8) Avila, V.; Cosa, J. J.; Chesta, C. A,; Previtali, C. M. J . Photochem. Photobiol. 1991, 62, 83. (9) Fessenden, R. W.; Carton, P. M.; Shimamori. H.; Scaiano. J. C. J. Phys. Chem. 1982, 86, 3803. (IO) See, for example: Chirstophorou, L. G.;McCorkle, D. L.; Christodoulides, A. A. In Electron-Molecule Interactions and Their Applications; Christophorou, L. G . ,Ed.; Academic Press: New York, 1984; Vol. I , Chapter 6.
( I I ) For electron affinities of atoms and molecules, see: Christophorou, L. G.;McCorkle, D. L.; Christodoulides, A. A. In Electron-Molecule Interactions and Their Applications; Christophorou, L. G . , Ed.; Academic Press: New York. 1984; Vol. 2, Chapter 5. (12) Yokoyama, K. Chem. Phys. Lett. 1982, 92, 93. ( I 3) Nakamura, S.; Kanamaru, N.; N0hara.S.; Nakamura, H.; Saito, Y.; Tanaka, J.; Sumitani, M.; Nakashima, N.; Yoshihara, K. Bull. Chem. SOC. Jpn. 1984, 57, 145. (14) Richard, J. T.; Thomas, J. K. Trans. Faraday Soc. 1970, 66, 621. (15) Weller, A. Z . Phys. Chem. 1982, 133, 93. (16) Briegleb, G.;Czekalla, J. Z.Elektrochem. 1956, 63, 6. (17) Holroyd, R. A.; Russel, R. L. J. Phys. Chem. 1974, 78, 2128. (18) Faidas, H.; Christophorou, L. G.;Datskos, P. G.;McCorkle, D. L. J . Chem. Phys. 1989, 90, 6619. (19) Kalantar, A.; Albrecht, A. C. Ber. Bunsen-Ges. Phys. Chem. 1964, 68. 36 I . (20) Yamamoto, N.; Nakato, Y.; Tsubomura, H. Bull. Chem. Soc. Jpn. 1966, 39, 2603. (21) The molecular size of TMPD can be estimated from known lengths of the constituent bonds in the molecule. The atomic halogen negative ion with radius of about 2 A is assumed to be located near the center of the benzene ring so that its size has been neglected in estimating the molecular size of the ion pair.
