3700
NOTES
Table I: Coupling Constants (cps) for the Protons in t h e X C H T Isomers*
J1-2
Js-
6
JI- 7 JS-
7
J4-
5
J2-3,1a
Js-
3 ,,la
7-RICHT
3-MCHT
8.7 8.7 5.3 5.3
9.5
...
...
6.0 6.8 6.8
9.5
9.5
6.8 6.8
. .
6.5
3.2 3.2
...
... ...
6.8
...
3.2
a Apparent coupling constants. cycloheptatriene.
P-MCHT
1-MCHT
...
...
... 3.2
‘ M C H T stands for methyl-
case of the other isomers, involving apparent “virtual” coupling. It remains to be explained why the spectra of the 1 and 7 isomers show a triplet structure instead of a doublet for the H3-H4 band. This type of pattern can be interpreted to demonstrate the independent participation of the H3 and H4hydrogens in a virtually coupled system with Hz and Hg simultaneously. The total line separation in this triplet is 6.4 cps, meaning that the magnitude of the apparent coupling of Hz with the system is 3.2 cps. It is then not surprising that the band for H2 appears as a broad multiplet due to its virtual coupling and further perturbation by long-range coupling with the methyl group. The same type of simplified interpretation of otherwise complex spectra can be applied to the spectra of c y c l ~ h e p t a t r i e n e ~and ~ ~ ~ *lj6-cycloheptatriene dicarboxylic acid.8 Both these compounds meet the requirements of virtual coupling and the reported coupling constants and chemical shifts for the cycloheptatriene are in perfect agreement with the interpretation given in this note to the methylcycloheptatriene isomers. The information available in the literature for other substituted cycloheptatrienes2 further substantiates the assignment and interpretation given for the methylcycloheptatriene isomers.
Hq. This assignment is substantiated with the relative intensities of this absorption band in the various isomers. The remaining two hydrogens Hz and H5 can be distinctively assigned, looking a t the spectra of the 2-RICHT (€I2 missing) as compared to all the other isomers. I n addition, the assignment of the band a t 7 4.00 to H5 is verified by the measured coupling constant J 5 , e (9.5 cps) which is also seen as J6,5 in the decoupled spectra of 1-1ICHT. With confidence in the above assignment of the absorption bands, one can no\v look at the interesting aspects of the “abnormal” features evident in these spectra, i.e., the unusual splitting found in the Hz, H3, Hd, and Hg bands. The doublet of triplets for H5 found in the spectra of ( 5 ) I n the 7-MCHT isomer, the triplet is readily apparent, looking 7-, 2-, and l-methylcyclohepta-l,3,5-triene5has the a t the Hz,Hj absorption after decoupling the interaction with the hydrogen in the 7 position. same line separation in each of the triplets (3.2 cps) as (6) J. D. Roberts, “An Introduction to the Analysis of Spin-Spin the onemeasured for the H3 and H4 absorption band. Splitting in High Resolution Nuclear Magnetic Resonance Spectra,” The large doublet splitting (9.5 cps) in Hg is of course W. A. Benjamin, New York, N. Y., 1961, p 76. due to the coupling with Hg. The equal line separation (7) K. B. Wiberg and B. J. Nist, “Interpretation of NMR-Spectra,” W. A. Benjamin, Inc., New Tork, N. Y., 1961, p 21. in each of the triplets gives the appearance that Hg is (8) R. Darms, T. Threlfall, Sf. Pesaro, and A Eschenmoser, Helv. effectively equally coupled to both H3 and HI. Chim. Acta, 46, 2893 (1963). Based on reported coupling constants, one would predict J J 5 i o be of the order of 4-10 cps and J3.5 in the range of‘ 0-0.3 cps. The unusual multiplicity as The Activation Energy of Hydrated well as the apparently equal line separation measured for the proton systems H3-H4-H5 and H2-H3-H4 are Electron Reactions’ best rationalized with restricted first-order a n a l y ~ i s . ~ , ~ , These RICHT systems satisfy the conditions for “virby AI, Anbar2 and Edwin J. Hart tual” ~ o u p l i n g ,ie., ~ a chemical shift of -0 between H3 and Hq and strong coupling between H3-Ha and Chemistry Division, Argonne National Laboratory, Argonne, Illinois (Received May 17, 1967) H4-H5. JIusher and Corey4 calculated a similar = example of the AA’B system, where ( Y A 0, J A ~ = B 6.5 cps, and J A A i = 10.5 cps, which also afAn activation energy, EA,of 3.5 f- 0.4 kcal/mole has forded a skewed triplet B absorption and equal line recently been reported for several hydrated electron separation with a splitting of ‘ / ~ J A ~ B . reactions that range in rate from 6 X 1O’O down to In 3-JICHT, with no possibility for this type of longrange coupling, one observes the normal nonperturbed (1) Based on work performed under the auspices of the U. S.Atomic splitting (J4.5 = 6.5 cps) which is, as expected, twice Energy Commission. as large as the corresponding coupling (3.2 cps) in the (2) The Weizmann Institute of Science, Rehovoth, Israel. YAP)
The Journal of Physical Chemistry
NOTES
3701
Table I: Activation Energies, EA, of a Number of Reactions of Hydrated Electrons Obsd lst-order decay -X 10- set-1k’soiutela
Matrix
PH
250
25’
25O
HzO
11.0 11.2 11.0 11.0 11.3
0.115 0.12 0.115 0.22 0.39
1.2 1.96 2.1 2.4 0.83
8.9 9.2 3.3 4.4 0.015
k’matrix,”
Compound
ClCHzC00 ClCHiCOO ClCHzCHzOH ClCHzCHiCOO M n E D TA2 -
ksolute,
M-* sec-1 X 10-8,’
Dz0 1120 H20 0.05 M EDTA
--EA, Matrix
koal/molec-Solute
2 . 9 i.0 . 5 4 . 0 =IC 0 . 5 2 . 9 i:0.5 3 . 6 =IC 0 . 4 4 . 0 =!= 0 . 6
‘
a k’matrix = d In [eas-]/dt; k’so~ute = d In [eag-]/dt. ksolute = ( k s o l u b- kfrnat,ix)/(concnof solute, M ) . From Debye equation assuming r(eaq-) = 2.5 A; D(e,,-) = 4.5 X cm2 sec-l.
3 X lo5 M-l sec-le3 These results, derived from the difference in temperature dependence of two processes, are open to criticism because the method is indirect. I n the present study, we use the direct method of pulse radiolysis and obtain the rate constants, k , of the reactions a t each temperature by following the decay of the optical absorption band of ea,-. Both light and heavy water were used in the chloroacetic acid studies. The rate constants were measured by the usual electron pulse t e ~ h n i q u e . ~The main departure was the use of a thermostated multiple reflection cell utilizing a 6328-L4 laser as the spectrophotometric analyzing light beam.5 With this system, 6 to 8 passes providing optical path lengths of 24 to 32 cm were readily available. With temperatures constant within *0.lo, the rates were measured a t 2, 10, 19, 28, 48, and 62”. The slopes, d In k/d(l/T), were linear within the temperature range studied, and within our experimental error of =k15yo no deviation from linearity was observed. I n each case, the rate of disappearance of ea,- in the matrix mas subtracted from the over-all rate of disappearance of eaq- in the presence of the solute. From the slope, d In k / d ( l / T ) , for the matrices we were able to obtain E A for the matrix, as well as for the solute reactions with cas-. The results are presented in Table I. The reaction, ea,ClCH2COO-, has an EA of 2.8 =k 0.4 kcal/mole. By comparing columns 8 and 9 of Table I, one sees that the rate constant, k,, for this reaction is more than an order of magnitude slower than the expected diffusion controlled rate ( k d i f f ) of 1.05 X 1O’O 1M-l sec-’. If the difference between k, and k d i f f ( s ) for this reaction is due to a difference in activation energy, this would require A E A of about 1.5 kcal/mole. Sirice the apparent EAfor diff usion-controlled reactions in aqueous solution is about 3.0 kcal/mo1e,6 the expected activation energy EA(Ca1Cd) would be about 4.5 kcal, i e . , significantly higher than the experimental value of 2.8 0.4 kcal/mole.
+
*
2 . 8 i0 . 4 3 . 2 i0 . 4 3.1 0.6 3 . 6 i:0 . 4 4.0 1 0 . 6
+
kdi f f
*x
M-1 sec -1
10-10
1.05
1.os 1.3 1.0
0.85
EA = R[d In k e / d ( l / T ) ] .
In heavy water, the activation energy for the chloroacetate ion reaction is 3.2 =!= 0.4 kcal/mole, not significantly higher than in light water. This result is not surprising, since EA of diffusion in D 2 0 inferred from viscosity6 is only 7% higher in DzO than in H20.’ Xearly identical rate constants are found for ClCH2CH20H and C1CHzCH2C00-. They are lower than that of the C1CH2C00- reaction by a factor of about 2.5, and still they all have activation energies which are equal within experimental error. Two alternative mechanisms have been suggested for haloaliphatic-hydrated electron reactions.*
+ RCl +R + C1+ RC1+ RC1- +R + C1ea,-
ea,-
(1) (11)
According to mechanism I, the R-Cl bond is broken during the rate-determining step, whereas in mechanism 11, RC1- forms as a short-lived intermediate. Comparing the difference in enthalpies for reactions of ea,- with ClCHzCOO- and with C1CHzCH2C00- gives a higher AH of about 10 kcal/mole for mechanism I.9 If the ea,-- reaction proceeded by mechanism I, this difference in AH would be reflected by a corresponding increase in EA.” Thus the equivalence in E , for both of these ea,RC1 reactions supports the idea that
+
(3) M. Anbar, 2. Alfassi, and H. Reissler, J . Am. Chem. SOC.,89, 1263 (1967). (4) J. K. Thomas, S. Gordon, and E. J. Hart, J . Phys. Chem., 68, 1524 (1964). ( 5 ) E. J. Hart, E. M.Fielden, and AT. Anbar, ibid., in press. (6) M. Eigen, W. Krase, G. YIaass, and L. dehlaeyer. Progr. Chem. Kinetics, 2, 287 (1963). (7) I. Kirshenbaum, “Physical PiopcrIips and Analysis of Heavy Water,” McGraw-Hill Bonk Go., I t i c . , Kew York, N. Y., 1951, p 33. (8) .M. Anbar, Advances in Chemistry Snries, No. 50, imerican Chemical Society, Washington, D. C., 1965, p 55. (9) T. C. Cottrell, “The Strengths of Chemical Bonds,” Butterworth and Co. Ltd., London, 1958. (10) T. 0. Edwards, “Inorganic Reaction Mechanisms,” W. A. Benjamin, Inc., New York, N. Y., 1964, Chapter 3.
Volume 71, Number 11 October 1967
XOTES
3702
the rate-determining step of eaq- reactions generally involves the addition of the electron to the substrate molecule via mechanism II.8 Subsequently, the cleavage of the R-C1 bond takes place. The ethylenediaminetetraacetate complex of manganese (,11nEDTA2-) cannot be readily reduced by eaq-. Its rate constant is 1.5 X lo6 M-' sec-l at 25". Consequently, we selected it in order to see if inert solutes possessed higher activation energies than those controlled by diffusion. We find an activation energy of 4.0 0.6 ltcal/niole for this reaction and consider it to be equal, within experimental error, to the activation energies of the faster reactions cited above, and even to the diffusion-controlled ones. The slowness of the lInEDTA2- reduction cannot under any circumstances be due to an increase in EAas has been suglIn2+(aq) reaction." Even if gested for the eaqthere is a slight increase in E A for this slow reaction, it is very far from the expected increase of over 5 kcal/ mole. All eaq- reactions, including those of the matrix as well as those of the solutes, possess EAin the range from 2.8 + 0.4 to 4.0 i 0.6 kcal/niole. In view of the relatively large experimental error, me assume that the same average EA of 3.4 =t 0.4 prevails for all of these reactions. This value also agrees with that of 3.5 =t 0.4 kcal/niole obtained by competition kinetic^.^ I t should be noted that owing to the fact that kobsd = (kdiff X k ) / ( k d , i f the observed E A will remain practically constant and equal to the EA of the diffusioncontrolled reactions, E.4(diff), for any actual value of E A , ranging from zero t o EA(diff) for reactions which have a "normal" preexponential factor, of the order of 1 O I 2 JI-' sec-'. In the case EA = EA(diff) = 3.0 kcal/mole, an experimental value of EA of 3.4 kcal/mole would be observed for reactions with a "normal" preexponential factor. For reactions which have a significantly smaller preexponential factor, the measured activation energy is the actual activation energy of the reaction. This EA seems still to be the same for a great number of eaq- reactions; thus it seems to be independent of the nature of the substrate and of the free energy of activation involved. This energy of activation could be the energy required to Teorganize the hydratimi sphere around the electron. It is substantially lower than the energy of hydration of eaqand it should be equal to the energy required to create a hole in the solvent, Le., the E A of diffusion. The electron distribution in the solute ion or molecule is the principal factor determining eaq- reactivity in the primary step.8 We associated high reactivity with a
*
+
+
ready Of to a vacant' Orbital* This distribution of electrons in the molecule, which The Journal of Physical Chemistry
might be changed by electron excitation, will be unaffected by temperatures up to loo", and the parameter which determines the rate constant will thus be the probability of finding an electron vacancy on the substrate molecule. This probability, represented by the entropy of activation, is temperature independent in our range of temperatures. Our findings that EA for all eaqS S- reactions is equal supports these conclusions. One may regard eaq- reactions as electron transfer processes that involve an extra-molecular electron. These processes still obey the Franck-Condon principle, and the slow reactions of eaq- may be treated as forbidden electronic transitions having a probability much smaller than unity. Speculative as this concept niay seem, it serves as a practical working hypothesis for continuing research on the reactions of eaq-.
+
-
(11) J. H. Baxendale, E. M.Fielden, and J. P. Keene, Proc. Roy. SOC.(London), A286, 320 (1965).
A n Analysis of the Excess Charge Effect in Alternant Conjugated Hydrocarbon Radical-Ions
by James R. Bolton' Department of Chemistry, University of Minnesota, Minneapolis, Minnesota (Received M a y 26, 1967)
It is well known that in conjugated hydrocarbon radical-ions, proton hyperfine splittings are usually larger in positive ions than for corresponding positions in the negative ions. This has been called the "excess charge effect." Colpa and Bolton2 were the first to interpret this effect and ascribed it to a second-order correction in the derivation of the NcConnell r e l a t i ~ n . ~ They proposed the relation H
a,
=
[Qc"(O)
+ KCH
H
(1)
where p," is the n-electron spin density a t the carbon atom i, E," is the excess charge (el" = 1 - q," where q: is the total 9-electron density a t the carbon atom i), aiH is the hyperfine splitting constant for the proton attached to the carbon atom i, and QCHH(0)and K~~~ are constants. Although the original derivation of eq 1 was later shown to predict a positive sign for KCHH(experiment (1) Alfred P. Sloan Research Fellow. ( 2 ) J. P. Colps and J. R. Bolton, Mol. Phys., 6, 273 (1963). (3) H. M. hlcConnel1, J . Chem. Phys., 24, 633, 764 (1956); Proc. Natl. Acad. sei. u. 53, 721 (1957).
s.,
