J. Phys. Chem. 1083, 87, 1153-1157
structure to NH.. may follow dashed-line b in Figure 4. Specifically, the proton begins to transfer from 0 toward N concomitantly with an initial reduction in the N-0 distance. The proton reaches the midpoint of its transfer simultaneously with the closest approach between the N and 0 atoms; i.e., R 2.97 A. Subsequent increase of the N-O distance and completion of the proton motion places the system in the right-hand well. The transition from N- .HO to NH. -0, both with R = 3.2 A,has thereby been accomplished with no energy barrier. Smaller N-0 vibration amplitudes of less efficient coupling between the vibration and proton transfer might lead to paths such as c in Figure 4 in which the transfer barrier, while not eliminated, is greatly reduced. It is emphasized that the conclusions drawn above from Figure 4, which represenb the POL-CI calculated data, are independent of the particular quantum chemical procedure. Hartree-Fock calculations using the 4-31G and DZP basis sets, as well as the GVB method, lead to results qualitatively quite similar to those presented in Figure 4. 0
0
-
-
Conclusions The results presented here provide clear evidence of the following trends. At the Hartree-Fock level, use of larger and more flexible basis sets leads to progressively higher energy barriers to proton transfer. Inclusion of the effects of electron correlation, on the other hand, results in a decrease of the barrier height. Both of these trends appear to be characteristic of proton-transfer processes in general as they have been observed in a number of other systems as weli. Limited treatment of electron correlation may lead to spurious results. In particular, inclusion of only intra-
1153
pair correlation via the GVB method produces effects opposite to those obtained with more complete treatments. All the quantum chemical procedures applied to (H3NHOH2)+agree on the following points. The protontransfer barrier heights, computed for fixed values of the intermolecular separation R, increase rapidly as the H3NH and OH2units are further removed from one another. The proton-transfer potential obtained at the equilibrium intermolecular distance Ro contains a single minimum, corresponding to H3NH. .OH2. The same is true of the potential for adiabatic proton transfer in which the molecular geometry is free to relax as the transfer takes place. The calculations therefore lead to the conclusion that the H3N. .HOH2 configuration is not a stable structure for (H3NHOH2)+in the gas phase. The situation is less clear-cut for NH.. SO hydrogen bonds in geometrically restricted environments. While quite substantial energy barriers may separate the NH-0 and Ne-HO minima for long hydrogen-bond lengths (e.g., 3.2 A), these barriers may be significantly reduced or even eliminated by coupling of proton transfer to molecular vibrations.
-
Acknowledgment. Grants to S.S. from the General Medical Sciences Institute of the National Institutes of Health and from the Research Corp. are gratefully acknowledged as is an allocation of computer time from the SIU Computing Center. This research was supported also by the US.Department of Energy under Contract No. W-31-109-ENG-38. Registry No. NH3, 7664-41-7;H20, 7732-18-5; (H3NHOH2)+, 56044-47-4.
Comparisons between Theoretical and Experimental Deuterium Isotope Effects for Some Outer-Sphere Electrochemical Reactions Michael J. Weaver’ and Tomi 1.-T. LI Department of Chemistry, Purdue University, West Lafayetre, Ind/ana 47907 (Received: July 21, 1982; In F/nd Form: November 8, 1982)
Experimental deuterium isotope effects upon the rates of outer-sphere electrochemical exchange reactions involving aquo and ammine complexes are compared with the predictions of contemporary theories which take into account nuclear tunneling from inner-shell vibrational modes. The isotope rate ratios calculated by considering nuclear tunneling of metal-ligand vibrational modes are in most cases much smaller than the observed rate ratios. Significant additional contributionsprobably arise from nuclear tunneling associated with internal ligand stretching modes, although this is estimated to be unlikely to account for the very large isotope effect observed for hexaaquochromium(III)/(II). The disparities seen between theory and experiment are speculated to be due to a contribution to the outer-shellreorganizationenergy from reorientation of hydrogen-boundsolvent molecules. This conclusion is supported by the marked disparities seen between the relative isotope rate ratios for correspondingelectrochemical and homogeneous reactions in comparison with the predictions of the dielectric continuum model. We have recently found that significant and even substantial rate decreases occur for a number of one-electron electrochemical reactions involving aquo and ammine complexes at the mercury-water interface upon replacing the aqueous solvent with DzO.’ Such solvent isotope effects may arise from differences in the interactions between the complex and the surrounding solvent as well as (1) M. J. Weaver, P. D. Tyma, and S. M. Nettles, J. Electroanal. Chem., 114, 53 (1980).
from changes in the inner-shell barrier to electron transfer due to replacement of hydrogen by deuterium in the reactant coordination sphere (“primary” isotope effect).’y2 The observed isotope effects are much larger than those predicted by the classical model of outer-sphere electron transfer. This treats the inner-shell (metal-ligand) contribution to the Franck-Condon barrier in terms of a harmonic oscillator, and the outer-shell (solvent repolar(2) M. J. Weaver and S. M. Nettles, Inorg. Chem., 19, 1641 (1980).
0022-3654/83/2087-1153$01.50/00 1983 American Chemical Society
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The Journal of Physical Chemistty, Vol. 87, No. 7, 1983
Weaver and Li
T A B L E I: C o m p a r i s o n b e t w e e n Observed and Calculated D e u t e r i u m I s o t o p e E f f e c t s f o r E l e c t r o c h e m i c a l E x c h a n g e of Some A q u o C o u p l e s at 25 " C
va, +', + F e a q 3 +l + E u 3t/2+
craaqq3+12+
1 x 10-3 -1 x 10-4 8 x 10-5 2x
9.1 -10.5
1.5 1.5
10.6
1.1
12.8
2.8
1.16 1.18 =1.15 1.22
0.05 0.05 0 0.09
33 43 9 51
W o r k - c o r r e c t e d r a t e c o n s t a n t f o r electrochemical e x c h a n g e o f given r e d o x aq r e p r e s e n t s e i t h e r OH, o r O D , ligands. c o u p l e at m e r c u r y - a q u e o u s interface, f r o m ref 1. ' F r e e e n e r g y o f activation f o r electrochemical e x c h a n g e , d e t e r m i n e d f r o m k,, b y using AG*,, = R T In ( k e x / Z e ) ,w h e r e 2, is t a k e n a s 5 X l o 3 c m s-'. R a t i o o f observed value o f k e x determ i n e d in H,O to that in D , O , f r o m ref 1. e Calculated value o f k H/kexD o b t a i n e d b y using eq 1-3 assuming t h a t innershell c o m p o n e n t arises f r o m m e t a l - o x y g e n vibrations (see text). yDifference in f o r m a l p o t e n t i a l in D,O to t h a t in H,O a t i o n i c s t r e n g t h s 0.1-0.2, m e a s u r e d vs. a n a q u e o u s S C E ; f r o m ref 2. g E s t i m a t e d d i f f e r e n c e in average 0 - H b o n d d i s t a n c e f o r a q u o ligand b e t w e e n o x i d i z e d a n d r e d u c e d f o r m s o f r e d o x c o u p l e ; o b t a i n e d as o u t l i n e d in t e x t .
ization) component by using the dielectric continuum approximation? Moreover, even the relative isotope rate ratios for outer-sphere electrochemical and homogeneous reactions involving the same redox couples were found to differ substantially from the predictions of this model.' It was speculated that the observed electrochemical isotope effects are associated chiefly with differences in the extent of ligand-solvent hydrogen bonding in D,O and HzO.' It has recently been pointed out that contemporary models of electron transfer which provide a quantummechanical description of inner-shell r e o r g a n i ~ a t i o n ~ ~ predict significant primary isotope effects for systems with large inner-shell barriers. These effects arise from the decrease in the degree of nuclear tunneling when the ligands are deuterated.'~~In principle, the comparison of experimental isotope effects with these theoretical predictions should provide a sensitive test of the applicability of such models for describing the inner-shell vibrational modes. Such a comparison for the electrochemical kinetic isotope effects reported in ref 1 is given in the present communication. The findings implicate the importance of hydrogen bonding between the inner-shell ligands and surrounding water molecules to the electron-transfer energetics. Aquo Redox Couples Table I contains a summary of the observed rate ratios for electrochemical exchange (kexH/KexD),,bd (i.e. ratios of "standard" rate constants) for Feq3+J2+, Craq3+I2+, and EU,?/~+ (where aq represents aquo ligands) at mercury electrodes upon replacing HzO with D20 solvent. These rate ratios are taken from ref 1; they are corrected for electrostatic double-layer effects.' The uniform finding that (kexH/keP),,W> 1indicates that ligand and/or solvent deuteration yields significant increases in the intrinsic electrochemical barriers, Le., in the activation free energy in the absence of an electrochemical driving force. Listed for comparison in Table I are calculated values of kexH/kexD, (kexH/kexD)dd, obtained from a "semiclassical" treatment of outer-sphere electron transfer4 using the relationg (kexH/kexD)cdcd = (VnH/VnD) exP([AG*i,(T)D AG*in(T)Hl/RTI exP([(AG*od~ - (AG*out)~l/RT1(la) = (u,H/u,D) x ( k H / k D ) o u t ( r n H / r n D ) exP([(AG*in)D- (AG*in)~l/Rq Ob)
VaF12+,
(3) R. A. Marcus, J . Chem. Phys., 44, 679 (1965). (4) B. S. Brunschwig, J. Logan, M. D.Newton, and N. Sutin, J. Am. Chem. SOC.,102, 5798 (1980). (5) P. Siders and R. A. Marcus, J . Am. Chem. SOC.,103, 741 (1981). (6) E. Buhks, M. Bixon, J. Jortner, and G. Navon, J . Phys. Chem., 85, 3759 (1981). (7) E. Buhks, M. Bixon, and J. Jortner, J. Phys. Chem., 85, 3763 (1981). (8) T. Guarr, E. Buhks, and G. McLendon, submitted for publication.
In eq la, A.G*,(T), and AG*i,,(T)Hare the (temperaturedependent) inner-shell intrinsic barriers4for the deuterated and protonated reactants, and (AG*in)Dand (AG*in)Hin eq l b are the corresponding "classical" barriers; the former quantities include the effects of nuclear tunneling4 which is expressed separately in eq l b as a ratio of nuclear tunneling factors4 (rnH/rnD). The terms (AG*ouJD and (AG*,,,JH in eq l a represent the outer-shell barriers in D20 and HzO solvent; in eq l b the outer-shell contribution to the isotope effect is expressed instead as the preexponential ratio (kH/kD),,,. The remaining term in eq 1, unH/unD, is the corresponding ratio of the nuclear frequency factors u,. On the basis of a "preequilibrium" model of outer-sphere reactions, u, is related closely to the frequency of inner-shell vibration^.^ The quantity unH/unD can therefore be taken as approximately equal to the ratio of the symmetric metal-oxygen frequencies4 for OH2 and ODz, i.e., (20/18)1/2= 1.05. The outer-shell contribution (kH/kD)outis estimated to be 1.06 from the dielectric continuum model, using the typical reactant radius of 3.5 A and a reactant-electrode distance of 7 A." The inner-shell barriers were calculated from4 AG*i,(T) = AG*in(
z)
tanh
(2)
(2)
where uin is the effective (average) frequency of the in(9) Although the contemporary treatments of outer-sphere electron transfer described in ref 3-7 have been applied almost exclusively to homogeneous reactions, they are also applicable with minor modification to electrochemical processes.'0 In particular, the relations derived for homogeneous self-exchange reactions can be transposed directly to describe the corresponding electrochemical "exchange" reactions, Le., the kinetics determined at the formal potential for the redox couple under consideration. Relations such as eq 1 will apply to nonadiabatic as well as adiabatic processes on the basis of a semiclassical model: provided that the transmission coefficient for electron tunneling is equal in the protonated and deuterated systems. Minor differences in the contributions of the preexponential factor to the isotope ratio between adiabatic and nonadiabatic pathways arise when using the model described in ref 6. (10) M. J. Weaver in 'Inorganic Reactions and Methods", J. J. Zuckerman, Ed., Verlag Chemie, Weinheim, West Germany, in press. (11) In ref 7, the outer-shell solvent contribution to the isotope ratio kH/kDfor homogeneous self-exchange was calculated to be -0.90 by using the dielectric continuum model. This result appears to be in error, being apparently based on an inappropriate value for the refractive index ni for liquid D20. The original literature values for for DzOare slightly higher than those for HzO over a range of temperatures at the same wavelength of light.l2 Thus, at 25 OC,ni = 1.3329 (HzO) and 1.3288 (DzO) using the NaD line.'* Combining these with the correspondin static dielectric constants D = 78.3 (HzO) and 77.95 (D,O) at 25 OC,' yields values for the quantity B ( = n C z of 0.5500 (HzO)and 0.5535 (DzO), which, using the usual dielectric continuum expression: leads to kH/kD 1.08. A somewhat smaller value of kH/kD (1.06) is obtained for electrochemical exchange' because only one reactant is activated, rather than a pair of reactants for homogeneous self-exchange. (12) D.Eisenberg and W. Kauzman, "The Structure and Properties of Water", Oxford University Press, Oxford, 1969, p 198; E. Reisler and H.Eisenberg, J. Chem. Phys., 43, 3875 (1965); H.Eisenberg, ibid.,43, 3887 (1965).(13) G. Nemethy and H.A. Scheraga, J . Chem. Phys., 41,680 (1964).
f!
The Journal of Physical Chemistry, Vol. 87, No. 7, 1983 1155
Deuterium Isotope Effects
ner-shell motion in the two oxidation states, the classical component AG*i, being determined from AG*in = 0.5nvi,27r2c2mAu2
(3)
where n is the number of bonds required to be stretched (or compressed), m is the ligand mass, and Au is the difference in bond distances between the oxidized and reduced forms of the complex. Note that AG*in will be unaffected by ligand deuteration provided that the force constants remain the same (i.e., muh2 = constant), as is normally 0b~erved.l~The sole contribution to the isotope effect upon AC*,(T) is then contained in the nuclear tunneling ratio rnH/rnD (eq lb). (The presence of the factor 0.5 in eq 3 arises because only one reactant has to be activated for electrochemical exchange, rather than a pair of reactants as for the more commonly encountered4 homogeneous self-exchange process.) The values of (ke,H/kexD)cdedgiven in Table I were obtained by assuming that the only contribution to AG*J T) arises from metal-oxygen (M-OH2) vibrations. The average stretching frequency vi, was taken as 430 cm-’ for M-OH2;4 Au is known to be 0.14 A for Fe,93+/2+ (ref 15) and 0.20 A for Cr, 3+/2+ (ref 16 and 17), which enables ( k e x H / k e x D ) d d for tkese two couples to be found from eq 1-3, given that n = 6, and p = 18 or 20 for M-OH2 or M 4 D 2vibrations, respectively. Reliable values of Au are as yet unavailable for the remaining redox couples VW3+I2+ and E u , ~ + / ~ +Nevertheless, . the values of AG*h required for eq 2 were obtained instead from the calculated value of AG*i, for FeaF/2+(4.2 kcal mol-l) by assuming that the variations in the observed values of k,, between Fe,q3+/2+ and these two couples were due only to differences in AG*kls The overall free energy barriers to electrochemical exchange, AG*ex, used for this purpose (Table I) were obtained from k, by using AG*, = -RT In (kex/Ze),taking the frequency factor 2, to be 5 X lo3 cm s-1.18J9 In each case vin for M-OH2 was taken as 430 cm-’; variations in this quantity with the nature of the metal ion are only moderateMand unlikely to influence the result substantially. Comparison of corresponding values of (kexH/kexD)obsd and (kexH/kexD)c&d in Table I reveals that the observed values are substantially larger than the calculated quantities for V,q3+I2+, Fe,q3+/2+,and especially for Cr,q3+/2+, although the relatively small value of (kexH/kexD)obsd for (1.1)is close to (kexH/keXDldd(=1.15). We have E~,q3+/~+ previously suggested that a major part of the observed isotope effects could be due instead to a larger outer-shell reorganization barrier in D20arising from ligand-solvent hydrogen b0nding.l These aquo redox couples are known to involve a substantial diminution in the extent of out~
~
~~~~
(14) K. Nakamoto, “Infrared and Raman Spectra of Inorganic and Coordination Compounds”, 3rd ed., Wiley, New York, 1978. (15) N. J. Hair and J. K. Beattie, Inorg. Chem., 16, 245 (1977). (16) B. S. Brunschwig, C. Creutz, D. H. McCartney, T.-K. Sham, and N. Sutin, Discuss. Faraday Soc., in press. (17) The estimate Aa = 0.20 A for Cr, 3+/2+ obtained from EXAFS data is an average value taken over all six & O H z bonds.16 Since Cr,2+ exhibits a noticeable Jahn-Teller distortion from octahedral symmetry, a pair of C d H 2 bonds have a markedly larger value of Aa (and probably a slightly smaller value u,) than the remaining four bonds.16 Nevertheless, the use of the single value Aa = 0.20 A is adequate for the present purposes since only the overall value of AG*h appears in eq 2 rather than the individual values of n and Aa. (18) Strictly speaking, the differences in he, between the various redox couples may be due to variations in AG*,(T), AG* and also in the electronic transmission coefficient Q. However, the praominant variable is likely to be AG*h. (19) M. J. Weaver, J. Phys. Chem., 84, 568 (1980). (20) I. Nakagawa and T. Shimanouchi, Spectrochim. Acta, 20, 429 (1964).
er-shell solvent polarization in going from the oxidized to the reduced state,2*21 so that significant cleavage of ligand-solvent hydrogen bonds is probably necessary in order to approach the transition state for reduction of the tripositive aquo cation. Such a component of the intrinsic reorganization energy is expected to be greater in DzO as a result of the tendency of the deuterated solvent to form stronger and more extensive hydrogen bonds. Such an effect is not considered in current theoretical models which uniformly assume that the outer-shell solvent reorganization can be described in terms of a dielectric continuum. An alternative explanation of the unexpectedly large values of (kexH/kexD)&d is that they arise from nuclear tunneling associated with 0-H ligand vibrational modes. Although these modes probably constitute only a minor component of the overall Franck-Condon barrier, their high frequencies (ca. 3200-3400 cm-’ (ref 22)) can result in substantial contributions to the nuclear tunneling factor and hence to the observed isotope rate ratios7v8(eq 2). This possibility was explored in the following manner. Estimates of the difference in the 0-H bond distance, AUGH, for the aquo ligands in the reduced and oxidized complexes were obtained by assuming that the differences between and (kexH/kexD)dd corresponding values of (kexH/kexD)om are due entirely to inner-shell 0-H vibrations. This entailed inserting trial values of A u ~ Hinto eq 3, assuming that n = 12, vin = 3200 cm-l, until agreement was reached between the observed isotope rate ratios and the values of (k,H/k,D)dd arising from this component together with the other factors considered above. The resulting estimates of AuGH are also listed in Table I. By and large, these values are somewhat greater than the usual variations in 0-H bond distances (ca. 0.02-0.03 8)determined by neutron diffraction for coordinated water, including that hydrogen bound to surrounding water, for a variety of crystalline hydrates containing multivalent metal cati o n ~ Admittedly, . ~ ~ ~ ~ the 0-H bond in coordinated water will probably be significantly elongated upon increasing the charge of the central metal ion as a result of the combined effect of the larger polarizing charge and greater hydrogen bonding with surrounding water molecules oriented in the enhanced local fieldaZ4 Nevertheless, in particular the estimated value of AUGH for Craq3f/2+,0.09 A, seems unreasonably large.25i26 These results suggest (21) E. L. Yee, R. J. Cave, K. L. Guyer, P. D. Tyma, and M. J. Weaver, J. Am. Chem. SOC.,101, 1131 (1979). (22) I. Gamo, Bull. Chem. SOC. Jpn., 34, 760, 765 (1961). (23) (a) W. C. Hamilton and J. A. Ibers, “Hydrogen Bonding in Solids”. W. A. Beniamin. New York. 1968. D 212 (b) M. Falk and 0. K ~ O D in ‘‘Water: A Comprehensive Treatise”,’Vol. 2, F: Franks, Ed., Plenum Press, New York, 1973, Chapter 2. (24) Although the 0-H bond distances for coordinated water in the large numbers of crystalline hydrates for which neutral diffraction data are available vary over the range ca. 0.95-1.03 A, these values refer to water molecules in a variety of electrostatic and stereochemical environmenta.23 The bond distances of greatest relevance to Mnq3+I2+redox couples clearly will involve coordinated water that is also hydrogen bonded to surrounding water molecules. From the average 0-0 bond distances noted for various divalent and trivalent cations, 2.82 and 2.68 A, respectively,23bcombined with the correlation seen between the 0-H and 0-0 bond distances (Figure 10 of ref 23b), it is deduced that the 0-H bond length will typically increase by ca. 0.02 A from the dipositive to tripositive oxidation state. (25) The result Aa = 0.09 A for Cr8?/*+ represents an “average” value since it was obtained by assuming n = 12. If the predominant changes in the 0-H bond distance occur for a air of trans ligands, then n effectively equals 2, yielding Aa = 0.15 (26) If indeed such large values of Aa occur for these redox couples, then one would expect the 0-H stretching frequencies in the higher oxidation state to be noticeably smaller than the ‘typical“ values in the . ~would ~ ~thereby , ~ decrease the effective range ca. 32CC-3400 ~ m - ~This frequency vin in eq 3, yielding even larger estimates of Aa from this relation. (27) See, for example, M. D. Newton, J. Chem. Phys., 67,5535 (1977).
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The Journal of Physical Chemistry, Vol. 87, No. 7, 1983
that other factors are at least partly responsible for the observed isotope effects, most likely from specific outershell reorganization as noted above. Both these explanations for the observed isotope effects invoke the specific involvement of outer-shell solvent molecules. In this context it is interesting to note that the electrochemical isotope rate ratios for Cr,q2+ and Vaq2+ oxidation are substantially (factors of 3-4-fold) larger than expected from the observed solvent isotope ratios for their homogeneous oxidation by Co(NH3)2+on the basis of the usual Marcus electron-transfer model.' This model presumes that the inner- and outer-shell components of the overall free energy barrier arise from separable contributions due to each reactant that are the same (or similar) in the electrochemical and homogeneous environments. While this should be approximately correct for the inner-shell barrier since the metal-ligand vibrations are unlikely to be affected greatly by the surroundings, the reorganization energy of the nearby solvent is likely to be sensitive to the chemical and electrostatic environment in which the reactant undergoes activation.28 The structure of the surrounding solvent is indeed expected to be markedly different for related electrochemical and homogeneous processes. Thus, the latter reactions involve close approach of a pair of multicharged cations which is expected to disrupt the aquo ligand-solvent hydrogen bonding in the region between two reactants. The mercury surface should exhibit a milder perturbation upon the reactant solvation since the interfacial region contains only a small net charge density at the electrode potentials at which the electrochemical kinetics were monitored. Indeed there is evidence from studies of electrochemical doublelayer effects that the secondary hydration sphere surrounding the aquo complexes remains at least partly intact in the transition state at the mercury-aqueous interface.29v30 Consequently, the magnitude of the isotope effect arising from ligand-solvent hydrogen bonding is expected to be quite different in these homogeneous and heterogeneous environments. The relative magnitude of the effect is difficult to predict. However, the observed larger kH/kD ratios obtained in the latter environment are consistent with greater changes in the solvent polarization required to surmount the Frank-Condon barrier for electrochemical processes arising from the more extensive hydrogen bonding in the electrochemical compared with homogeneous transition states. It is interesting to note that the magnitude of the observed isotope rate ratios (kexH/kexD)oMare related closely to the size of the thermodynamic isotope effects as measured by the difference in the formal potentials, for a redox couple in DzO and H 2 0 solvents. Thus, the substantially larger value of (kexH/kexD)obad for Cr,q3+12+ (2.8) compared with that for Eu,q3+I2+(1.1)is mirrored by differences in aEfDH of 57 and 9 mV, respectively3' (Table I). These thermodynamic isotope effects appear to be due at least in part to an entropic destabilization of the tripositive oxidation state upon deuteration associated with ligand-solvent hydrogen bonding,2 yielding greater differences in solvent polarization ("ordering") between the oxidized and reduced forms in D20. As noted above, such (28)M.J. Weaver and E. L. Yee, Inorg. Chem., 19, 1936 (1980). (29)M.J. Weaver and T. L. Satterberg, J. Phys. Chem., 81, 1772 (1977). (30)M.J. Weaver, H. Y. Liu, and Y. Kim, Can. J. Chem., 59, 1944 (1981). (31)Such differences in thermodynamic driving force for a given electrochemical reaction in DzO and H 2 0 are themselves taken into account by evaluating the rate constants at the appropriate formal potential in each solvent.
Weaver and Li
enhanced structural differences could also yield larger intrinsic barriers in DzOresulting from the need to undergo greater changes in solvent polarization in order to form the nonequilibrium configuration appropriate for electron transfer.' The values of (kexH/kexD)obsdand AEWH for Eu, 3+/2+ are surprisingly small in comparison with those for h e other aquo couples. A possible explanation is that V,F/'+, Feap3+/2+,and Cr,q3+/2+involve electron transfer into 3d orbitals, yielding significant differences in the electron density of the aquo hydrogens,32and hence the extent of ligand-solvent hydrogen bonding (and the 0-H bond length), between the two oxidation states. These differences should be smaller for the Eu,g3+12+couple since the electron is transferred into a 4f orbital which is shielded from the ligand orbitals.
Ammine Redox Couples Redox couples containing ammine ligands are of particular interest in studies of isotope effects since, in contrast to aquo complexes, the ammine hydrogens can be deuterated independently of the surrounding solvent.' Substantial rate decreases were obtained for one-electron reduction of Co(NH3)$+, Cr(NH3)$+, and related complexes at a constant electrode potential E at the mercury-aqueous interface upon deuterating the ammine ligands. Thus, for CO(NH&~+/'+the observed isotope rate ratio (kNH/kND)fbadequals 2.3 in aqueous solution.' Theoretical interpretation of these results is hampered by an absence of information on the formal potentials for these couples on account of the instability of the divalent ammines, so that the required values of k,, are unknown. However, there is evidence that the difference in formal potentials, AEfmNH,for Co(ND3)2+12+ vs. Co(NH3)2+12+ is small and positive (x7 mV).' Although the formal potentials themselves are uncertain, accurate knowledge of Ef is unnecessary since the values of (kNH/kND)fbsd were found to be essentially independent of potential.' (Decreasesin isotope ratios are predicted as the driving force is increased since the extent of nuclear tunneling will thereby be dimini~hed.~ However, this dependence should be scarcely detectable for the moderate range of overpotentials over which the electrochemical kinetics in ref 1 were monitored.) Therefore, the required value of the isotope rate ratio for electrochemical exchange of C O ( N H & ~ + / ~(kexNH/ +, kexND)obsd,can be estimated from the observed value of (kNH/kND)fbadby correcting for the isotope effect upon the driving force using1 (kexNH/kexND)obsd = (k NH / k ND)
Ssd+ exp(aFA&ND-NH /R T )
(4)
where a is the electrochemical transfer coefficient for C O ( N H ~ )reduction. ~~+ Inserting the above values of (kNH/kND)tbadand AEfNPNHinto eq 4 and assuming that a = 0.5 yields the estimate (kexNH/kexND)obsd = 2.5. The corresponding theoretical prediction using eq 1-3 is obtained from (vnH/vnD) = (20 17)'12 = 1.08, Aa = 0.22 win= 409 cm-l,%yielding (ke,L/k,,m)dd = 1.18. (No (32)This effect has indeed been obtained from a theoretical study of inner-shell bonding in the Fea,3C/z+couple: J. A. Jafri, J. Logan, and M. D. Newton, Isr. J. Chem., 19 340 (1980). (33)The value Aa = 0.22 has recently been obtained from EXAFS measurements; a similar value (0.21 A) has also been obtained from EXAFS and X-ray crystallography for the closely related C ~ ( e n ) ~ ~ + / ' + ~ o u p l e . ' ~This ~ ~ ' estimate for Aa is considered to be more reliable than the earlier value of Aa for Co(NHJ3+/*+of 0.18A.3J (34)D. A. Geselowitz, P. R. Jones, and H. Taube, unpublished results. (35)H. C. Stynes and J. A. Ibers, Inorg. Chem., 10, 2304 (1971). + / ~data + ; given (36)Average stretching frequency for C O ( N H ~ ) ~ ~from in T. Shimanouchi and T. Nakayawa, Spectrochim. Acta, 18.80 (1962).
A
J. Phys. Chem. 1983, 87, 1157-1160
1157
(The square root arises from the involvement of only one outer-shell contribution is included in this estimate since C O ( N H J ~ ~ +couple / ~ + in the exchange reactions rather than the solvent was not deuterated.) Again, this calculated a pair of reactants as in homogeneous self-exchange?) The isotope ratio is much smaller than the experimental value difference between this value of (kexNH/k,xm)&d and that of 2.5. noted above (1.18)arises chiefly from the larger value of We have noted previously that the corresponding isotope Au for CO(NH,):+/~+ used here.% Buhks et al. noted that ratio (kNH/km)!gzfor the homogeneous reduction of Cotheir predicted value of (kexNH/kexND)cdcd is significantly (NH3):+ by Cr(bpy)gS+in aqueous solution (where bpy = smaller than the experimental value (1.36) for Co(NH3)r 2,2’-bipyridine) is markedly smaller (1.35) than reduction by C r ( b p ~ ) , ~and + , also suggested that the dis(kNH/km)tbd for Co(NH3),3+electroreduction (2.3) even crepancy may be due to an additional contribution to the though the Marcus model predicts equal isotope ratios latter from high-frequency N-H modes.7 Similarly to the under these conditions.’ This discrepancy seems likely to electrochemical isotope ratio for C O , + ( N H ~ )reduction ~~+ be due to the same causes as those discussed above in (kNH/kND)zbsd that is discussed above, this experimental connection with the observed similar behavior of the aquo value for homogeneous reduction using a fixed reductant couples. The observation that (kexNH/kexND)obsd> will differ from that for true homogeneous “exchange” of (kexNH/kexND)calcd for electrochemical exchange may CO(NH,):+/~+ on account of the change in the driving force therefore be again due to the effects of specific ligandupon deuteration of the ammine ligands. Assuming that solvent hydrogen bonding,’ although the extent of such for CO(NH,),~+/~+ equals 7 mV, using eq 439one interactions appears to be smaller than for otherwise simobtains a value of (kexNH/kexND)obsd equal to 1.55 for Coilar aquo couples.21 Unfortunately, there appears to be no (NH3)63+/2+ exchange with Cr(bpy)2+/2+,again noticeably direct information on the effect of complexation and hylarger than the calculated values. drogen bonding on N-H bond distances. The N-H bonds are presumably lengthened slightly in going from Co(NH3),2+to Co(NH3)2+in view of the minor (ca. 100 cm-l) N o t e Added i n Proof. Newton* has recently estimated decrease in the N-H stretching freq~encies.,~However, the possible contribution to AaGHfor Fea,3+/2+from hythere appears to be little influence on these bonds from drogen bonding between the inner shell and surrounding hydrogen bonding with the surrounding solvent on the water molecules. He notes that A u ~ Hvalues as large as basis of the very similar N-H stretching frequencies obca. 0.07 A can arise under these conditions, although this served in crystalline solids and in aqueous solution.38 is probably only an upper limit (see footnote 24). Buhks et al. have recently calculated an isotope ratio of 1.26 for the effect of ligand deuteration upon CO(NH,),~+/~+ Acknowledgment. We are grateful to Ephraim Buhks, homogeneous self-exchange at 25 “C using a similar apGeorge McLendon, and Henry Taube for communicating proach based on a quantum-mechanical model.7 This some results (ref 8 and 34) prior to publication. This work result corresponds to a value of approximately (1.26)1/2= is supported in part by the Office of Naval Research and 1.12 for either electrochemical exchange or homogeneous the Air Force Office of Scientific Research. “exchange” of C O ( N H ~ ) ~ with ~ + / an ~ +inert c o r e a ~ t a n t . ~ ~ ~ ~ Registry No. Fe,q3+, 15377-81-8;V,?, 21374-21-0; Craq3+, 14873-01-9;Fe, 2+, 15365-81-8;Vaq2+,15696-18-1;Cr,?, 20574(37)K.H.Schmidt and A. Muller. Coord. Chem. Res.. 19.41 (1976). 26-9; Co(NHJ>, 14695-95-5; CO(NHJ,~+,15365-75-0; D20, (38)T. W.Swaddle, P. J. Craig, and P. M. Boorman,’ Sbectrochim. 7789-20-0; deuterium, 7782-39-0. Acta, Part A , 26, 1559 (1970). (39)The electrochemical isotope rate ratio (kNH/kND)fM, Le., that determined at a constant electrode potential, is analogousto the use of a fixed reducing agent, such as Cr(bpy)32+in the present case.
(40)M.D.Newton, Discuss. Faraday Soc., in press.
Neutral Gaseous Molecules with Molecular Weights Higher Than 4000 J. P. Bell, R. H. Hauge, J. L. Margrave,* Department of Chemistry, Rice Unlversi@’, Houston, Texas 7700 1
and J. 0. Edwards Department of Chemistry, University of Toledo, Toledo, Ohio 43606 (Received: June 9, 1982; In Final Form: October 29, 1982)
Gaseous molecules with very high molecular weights in the range 4000 to over 6000 have been detected in vaporization studies of a series of perfluoro polyethers by both Knudsen-effusion and simultaneous, Knudsen-effusion,dynamic-torsion-effusionmethods. For example, data on the DuPont Krytox MD-15-4 oil indicate that the equilibrium vapor initially has a molecular weight in excess of 4000 which increases to over 6000 as the lighter components are boiled off. Torsion-effusiondata on two other types of Krytox oils indicate similarly large molecular weights in the vapor.
Neutral gaseous molecules with molecular weights higher than 4000, even in excess of 6000, have been detected in vaporization studies of perfluoro polyethers! We believe there are no previous literature reports of congruently 0022-365418312087-1 I57$0l.50/0
vaporizing liquids with a rigidly established gas-liquid equilibrium for which molecular weights of this magnitude have been reported. Nonequilibrium fragmentation of chlorophyll and other biological reactants have been re0 1983 American Chemical Society
