J. Phys. Chem. 1992, 96,7137-7145
7137
Electroreductlon of Buckminsterfullerene, CeO,in Aprotlc Solvents: Solvent, Supporting Electrolyte, and Temperature Effects Dominique Dubois, Gilles Moninot, Wlodzimierz Kutner,+ M. Thomas Jones, and Karl M. Kadish* Department of Chemistry, University of Houston, Houston, Texas 77204-5641 (Received: May 27, 1992; In Final Form: June 5, 1992)
The electroreductions of Buckminsterfullerene (c60) in aprotic solvents were examined as a function of solvent, supporting electrolyte, and temperature. Altogether, 11 different solvents and 17 different supporting electrolytes were utilized in measurements made between 223 and 348 K. The cations of the supporting electrolyteswere Li' and Na+ as well as quaternary ammonium and quaternary phosphonium cations. The anions of the supporting electrolytes were C104-, BF4-, PF6-, and Br-. Cyclic voltammograms, rotating disk electrode voltammograms, and controlled potential coulometry revealed up to five reversibleone-electron reductions. A qualitative approach is used to elucidate the effects of solvent, supporting electrolyte, and temperature on the half-wave potentials, E l / z , of the reductions of c60. E l l 2for the first reduction correlates well with the Gutmann donor number of the solvent with a positive slope, but it also shows a linear correlation with the Gutmann acceptor number of the solvent with a negatiue slope. In contrast, the third reduction E1/2correlates fairly with the Gutmann acceptor number with a positive slope. The first three reductions also correlate with the normalized Dimroth-Reichardt solvent parameter. The inorganic anions of the supporting electrolytes do not significantly affect the half-wave potentials, but these values vary substantially with the type and size of the supporting electrolyte cations. The relative magnitudes of the solvent and supporting electrolyte effects on E l I zdiffer for each redox process of Cdo,and values of shift over a range of 280-600 mV for a given redox couple. The shifts in reduction potentials were rationalized in terms of the following: (i) charge density on the fulleride anions, (ii) solvophobic effects involving Cso (aggregation), (iii) solvophobic type interactions involving Cm anions and the larger cations of the supporting electrolytes in polar solvents, (iv) ion pairing of Cdoanions with smaller cations in nonpolar solvents,and (v) the specific acceptor or donor properties of the solvents. The reversible half-wave potentials were also measured as a function of temperature in eight different solvent/supporting electrolyte systems, and the measured values of AElI2/AT were used to calculate the change of entropy associated with each electron-transfer step. The shifts in E l I zwith temperature are relatively large and indicate that an unusually large change of entropy accompanies each electroreduction step. Diffusion coefficients, Stokes radii, and apparent solvation numbers of neutral Cdowere also determined in different solvent systems, and these values are discussed with respect to the nature of the solventsolute interaction.
Introduction Fullerenes in general, and C60in particular, have generated broad interest in the scientific community,' revealing a diverse Derived from chemistry in spite of their remarkable its highly symmetric truncated icosahedron structure? and in agreement with its unusually high molecular orbital degeneracy? Cdoexhibits a very rich redox chemistry, being a weak oxidant.2J0-'4 The advent of fullerene-based superconducting m a t e r i a l ~ ' ~ J ~ underscores the importance of understanding conditions for formation of various fullerenes in different oxidation states. Electrochemistry allows for bulk generation of a given ion after which spectroscopic characterization12or chemical reactions can be carried out on the electrogenerated anionic fullerene product. A knowledge of the specific half-wave potential, Ellz,i.e. the potential at which a 1:l equilibrium of the reduced and oxidized forms of the redox couple is achieved in a given solvent system, is essential for understanding and predicting the homogeneous redox properties of Cbo. Half-wave potentials reflect, to some extent, the relative stability of the species involved in each process. For example, their variation with changes of solvent and supporting electrolyte indicate how strongly the oxidized and/or reduced forms of the fullerene couple interact with the surrounding medium. An understanding of the nature of these interactions should allow a determination of the best conditions needed for carrying out homogeneous solution redox chemistry and should also aid in isolation of a desired solid-state form of new fullerene-based products. Theory predicts that up to six electrons can be accepted by the LUMO of Cm9 Early reports showed two,2 and then three,'OJ' well-developed reversible one-electron reductions in nonaqueous media. Subsequently, our laboratory observed the fourth oneelectron-transfer process in dichloromethanelZand then the fifth Author to whom correspondence should be addressed. 'On leave from the Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01-224 Warsaw, Poland.
one in benzene.14a At first undetected, an irreversible overall four-electron electrooxidation of Cdowas also recently reported14 as was the sixth reduction in tol~ene/acetonitrile'~~ and toluene/N,N-dimethylformamide mixtures.'" These observations bring the known number of formal oxidation states of Cmto eight which, as will be seen, are respectively 0, -1, -2, -3, -4, -5, -6, and +n ( n still to be determined; see refs 14a and 17). Unusual in itself, this large number of oxidation states appears even more significant when one considers that the added electrons, in the case of neutral Ce are accepted and delocalized in pseudoaromatic orbitals encompassing the whole molecule. Electrochemical studies of Cdohave now been published from several different laboratorie~,2.'~'~ but there has yet to be a thorough examination of the Cdointeractions with the surrounding media used for the electrochemical study, Le. the solvent and supporting electrolyte. In most cases, the reductions were merely characterized as to their EY2values in a single s01vent~J'~'~J~ or measurements were made in several solvents with a single supporting electrolyte.I0 One early account suggests a trend between reversible half-wave potentials and the Gutmann donor number (DN) of the solvent, but not all of the Csoelectrode reactions were analyzed in detail.I0 In the present paper, extensive electrochemical data for the reduction of Csoare obtained in a quadridimensional space whose coordinates are C , oxidation state, the nature of the solvent, the type and size of the supporting electrolyte, and the temperature. Altogether, 11 different solvents and 17 different supporting electrolytes were utilized in measurements made between 223 and 348 K. The redox potentials are analyzed and discussed with respect to the different parameters. Experimental Section Chemicals. Fullerene mixtures were purchased from Research Materials, Inc., or provided by Prof. R. E. Smalley and his coworkers. Samples of c 6 0 were isolated and purified by gravity chromatography on an alumina column using either hexane/
0022-3654/92/2096-7137$03.00/00 1992 American Chemical Society
7138 The Journal of Physical Chemistry, Vol. 96, No. 17, 1992
benzene or hexane/toluene solvent mixtures as the eluent. Voltammetric studies were carried out on solutions whose c 6 0 M. concentrations ranged from lo4 to Pyridine (py) and acetonitrile (MeCN) were distilled from CaH2 under nitrogen. Benzonitrile (PhCN) was distilled from PzOs under vacuum. Dichloromethane (DCM) was purified according to published procedures.I* Tetrahydrofuran (THF) was distilled from AlLiH4under nitrogen. Benzene was distilled from sodium under nitrogen. Nitrobenzene (PhNOJ was successively washed with 2 M aqueous NaOH, water, dilute HC1, and water, then dried over MgS04 in the dark, and finally distilled over 4-A molecular sieva under vacuum. All these solvents were purchased from Aldrich, Fischer, or Mallinckrodt. Anhydrous argon-packed N,N-dimethylformamide (DMF), chlorobenzene (PhCl), 1,2dichlorobenzene(ODCB), and 1,2-dichloroethane (DCE) were purchased from Aldrich and used as received. The cations of the supporting electrolytes were Li+ and Na+ as well as quaternary ammonium and quaternary phosphonium cations. The anions of the supporting electrolyte were ClO;, BF4-, PF6-, and Br-. Abbreviations used for the cations are as follows: TEA+ (tetraethylammonium), TPA+ (tetrapropylammonium), TBA+ (tetrabutylammonium), TPnA+ (tetrapentylammonium), THA+ (tetrahexylammonium), THpA+ (tetraheptylammonium), TOA+ (tetraoctylammonium), TDA+ (tetradecylammonium), TDdA+ (tetradodecylammonium), TBP+ (tetrabutylphosphonium), TPhP+ (tetraphenylphosphonium). All supporting electrolytes were used at a concentration of 0.1 M unless otherwise stated. These salts were purchased from Aldrich, Eluka, Johnson Matthey (Aesar, Alfa), Kodak, or Sigma. All were used as received except for (TBA)C104, (TBA)PF6, (TBA)BF,, and (THA)C104 which were recrystallized and dried in vacuum at 40 “C prior to use. Instrumentation and Procedures. All electrochemistry was carried out using a conventional three-electrodecell. A platinum disk and platinum wire served as the working and counter electrodes, respectively. The reference electrode was a saturated calomel electrode (SCE) which was separated from the working solution by a fritted glass bridge. IR compensation was used whenever possible. All potentials were measured versus SCE, but the ferricenium/ferrocene (Fc+/Fc) couple was also used as an internal standard for potential referencing and comparisons. Cyclic voltammetry (CV) and rotating disk electrode (RDE) voltammetry were performed with an IBM EC 225 2A voltammetric analyzer or with a BAS 100 electrochemical analyzer. The platinum rotating disk electrode (0.198-cm2geometric area) was purchased from Pine Instrument Co. It was driven by a Pine MSR speed control unit. Controlled potential electrolyses were carried out using an EG&G Model 173 potentiostat equipped with an EG&G Model 179 digital coulometer to record the current/time curves and the total charge transferred. All experiments were carried out at ambient temperature, 22 f 1 OC, unless otherwise indicated. Variable temperature cyclic voltammetry was performed using a constant temperature bath. Experiments of this type have been described pre~iously.’~ The SCE was separated from the working solution by a bridge of adequate size and always maintained at ambient temperature to prevent temperature variation effect. Controlled potential electrolyses of c 6 0 were performed in an inert atmosphere drybox (Vacuum Atmospheres Co.) using an “H” type cell. Both the working and counter electrodes were made of platinum gauze. The working and auxilliary compartments of the cell were separated by a sintered glass frit. Electroreductions were performed by setting the working potential at values 150-250 mV more negative than E , 2 of the considered Cso“/C,(*l)- redox couple. This allowed for h.70-99.99% completion of electrolysis in terms of the conversion of neutral c 6 0 to a given C6Ow anion ( n = 1, 2, 3, 4). The electrolyses in DMF and MeCN were performed directly with a c 6 0 suspension. Initially, only a low current was observed, but, in the course of electrolysis, the solution became colored and the current increased. As the electrolysis further proceeded, all of the substrate eventually dissolved and the solution had the expected color of the generated anion (as compared with the known colors of Cmr solutions generated in
Dubois et al. TABLE I: Utilized Solvents with Relevant Parameters solvent abbr tl(l ANb DNb ETN(30)* PhCl 5.62 c chlorobenzene c 0.188 tetrahydrofuran THF 7.58 8.0 20.0 0.207 dichloromethane 8.93 20.4 0.0 DCM 0.309 ODCB 9.93 c 1,2-dichlorobenzene c 0.225 1,2-dichloroethane DCE 10.37 16.7 0.0 0.327 py 12.91 14.2 33.1 0.302 pyridine benzonitrile PhCN 25.20 15.5 11.9 0.333 nitrobenzene PhNO, 34.78 14.8 8.1 0.324 acetonitrile MeCN 35.94 18.9 14.1 0.460 benzene C6H6 2.27 8.2 c 0.111 N,N’-dimethylformamide DMF 36.71 16.0 26.6 0.404 “Relative permittivity (dielectric constant) at 25 OC taken from ref 34. *AN, Gutmann acceptor number; DN, Gutmann donor number; ETN(30), normalized Dimroth-Reichardt parameter. All three parameters were taken from ref 25. CNotavailable.
TABLE [I: Half-Wave Potentials of the Co Redox Couples in Pyridine and Tetrahydrofuran Containing 0.1 M Supporting Electrolyte El,,, V vs SCE reduction steps supporting electrolyte solvent 1st 2nd 3rd 4th Fc+/Fc NaCIO, T H F -0.61 -1.32 0.41 LiCIO, T H F -0.51 -1.16 0.50 (TEA)C104 py -0.39 -0.82 -1.30 0.50 -0.37 -0.80 -1.29 -1.79 0.51 (TPA)C104 py 0.52 (TBA)CIO, py -0.34 -0.76 -1.28 -1.81 T H F -0.33 -0.92 -1.49 -1.99 0.57 (THA)C104 py -0.34 -0.75 -1.33 0.55 THF -0.29 -0.89 -1.51 -2.14‘ 0.55 (TOA)CI04 py -0.32 -0.75 -1.34 0.57 THF -0.24 -0.84 -1.52 0.70 (TBA)Br py -0.33 -0.76 -1.28 (TBP)Br py -0.34 -0.77 -1.29 -1.79 T H F -0.16 -0.79 -1.38 “Cathodic peak at 0.1 V/s.
other solvents where c 6 0 is more readily soluble).20
Results The electrochemical behavior of c 6 0 was investigated in 45 different solvent/supporting electrolyte systems. The supporting electrolytes contained three types of cations, as summarized in the Experimental Section. These were alkali metal, tetraalkylammonium, and tetrabutylphosphonium or tetraphenylphosphonium cations. The abbreviations and relevant parameters of the solvents used in the present work are summarized in Table I. c 6 0 is insoluble at room temperature in a number of polar solvents which might be considered most suitable for electrochemical investigations (e.g. DMF, MeCN, methanol, and DMSO). However, it was observed early in the present study that the electrogenerated Car anions are generally more soluble than neutral c60. Hence, it was possible to determine half-wave potentials in some polar solvents in which neutral Cs0 is not at all, or only sparingly, soluble. We have done this by first generating the c 6 0 B anion by controlled potential electrolysis (see Experimental Section and ref 21) after which CV experiments were carried out on these solutions. Figure la shows cyclic and rotating disk electrode voltammograms of C, in pyridine containing 0.1 M (TBA)C104. Half-wave potentials for the reduction of C, in pyridine and THF are given in Table 11, while those in other solvent/supporting electrolyte systems are listed in Tables 111-V. The listed values are in good agreement with the less extensive data given in earlier reFour reductions are generally observed by both electrochemical techniques, and the half-wave potentials measured with each technique are within experimental error of each other. Examples where neutral Cm is insoluble in a given solvent but where the voltammetry of the anions is well defined are given in
Electroreduction
The Journal of Physical Chemistry, Vol. 96, No. 17, 1992 7139
of Cb0in Aprotic Solvents
(b)
(a)
i e--'
/ C,,3-, MeCN
* 0.0
i -0.5
-1.0
-1.5
0.0
-2.0
Potential
c
] -0.5
,
, -1.0
,
,
-1.5
-2.0
, -2.5
(V vs. SCE)
Figure 1. (a) Room temperature rotating disk electrode cf= 2000 rpm) (top) and cyclic ( u = 0.1 V/s) (bottom) voltammograms of Cboin pyridine, 0.1 M (TBA)CI04. (b) Room temperature cyclic voltammograms (v = 0.1 V/s) of Cbo-in DMF, 0.1 M (TBA)C104 and Cm3-in acetonitrile, 0.1 M (TBA)CIO1. Initial potential, zero current, and scan direction are indicated with an arrow. The consecutive electron transfers to Cboare indicated with numbers relating to the negative charge of the reduced form at each oxidation/reduction peak pair. TABLE III Half-Wave Potentials of the Ca Redox Couples in BenzoniMle Containing 0.1 M Supporting Electrolyte E,prV vs SCE reduction steps supporting 2nd 3rd 4th Fct/Fc electrolyte oxidation" 1st NaCIOAb 1.90 -0.36 -0.82 0.47 -0.54 -0.98 L ~ C I O ~ ~ 1.76 1.78 -0.46 -0.89 -1.37 0.47 (TEA)CI04 1.80 -0.43 -0.85 -1.32 -1.78 0.50 (TPA)C104 1.82 -0.42 -0.84 -1.32 0.50 (TBA)CI04 1.91 -0.40 -0.82 -1.34 0.51 (THA)ClOp 1.82 -0.37 -0.80 -1.34 0.54 (TOA)C104 1.76 -0.45 -0.87 -1.35 -1.85 (TBA)PF6 -0.35 -0.78 (TPA)Br -0.34 -0.77 -1.27 -1.75 (TBA) Br -0.33 -0.77 -1.27' (TPnA)Br -0.33 -0.76 -1.29 (THpA)Br -0.31 -0.75 -1.28 -1.83' (T0A)Br -0.32 -0.76 -1.38' (TDA)Br (TDdA)Br -0.31 -0.78 -1.47' -0.33 -0.75 -1.24 -1.73 (TBP)Br -0.33 -0.76 -1.26 (TPhP)Br" "Anodic peak at 0.1 V/s. b0.05 M. 'Cathodic peak at 0.1 V/s. dNot fully reproducible due to adsorption. Figure l b for bulk-generated c60- in DMF and C603-in M e C N containing 0.1 M (TBA)C104. T h e formation of C6Ow where n = 1, 2 , 3 , or 4 is seen in DMF while CSowspecies with n = 1, 2, 3,4, or 5 are seen in MeCN. (Neutral Cmis insoluble in MeCN,I3 and the oxidative conversion of c60- to c 6 0 results in deposition of a solid film on the electrode.21) T h e electrogenerated Caw anions are stable in most solvents on the C V time scale (ca. 30 s), but Cm3-reacts with both D C M and DCE, as was previously reported for the case of DCM.1°J2 Under these conditions, the third and fourth reductions of c 6 0 may appear irreversible due to a n irreversible chemical transformation following electrogeneration of the tri- or tetraanion. This irreversibility, however, can be overcome a t room temperature by using sufficiently high po-
TABLE IV: Half-Wave Potentials of the Ca Redox Couples in Dichloromethane Containing 0.1 M Sumorting Electrolyte E l p V vs SCE supporting reduction steps 2nd 3rd 4th Fct/Fc electrolyte oxidation" 1st (TBA)C104 +1.83 -0.49 -0.88 -1.33 0.51 (THA)C104 -0.51 -0.92 -1.42 0.50 (TOA) C104 -0.46 -0.89 -1.40 0.53 (TBA) BF4 -0.44 -0.82 -1.25 -1.72' (TBA)Br -0.45 -0.85 -1.30 0.46 (TBA)PF, -0.56 -0.95 -1.41 (TBP)Br -0.45 -0.85 -1.29 (TPhP)Br -0.41b -0.84b -1.32b "Anodic peak at 0.1 V/s. bValues obtained from the second scan; in the first one the second wave is almost absent and an adsorption peak is present on the third wave. 'Cathodic peak at 0.1 V/s. TABLE V: Half-Wave Potentials of the Ca Redox Couples in Various Solvents Containing 0.1 M (TBA)CIO, El n, V vs SCE reduction steps solvent system oxidation" 1st 2nd 3rd 4th 5th Fc+/Fc ODCBb -0.39 -0.79 -1.29 -1.79 PhN02 1.81 -0.44 0.48 DCE 1.78 -0.48 -0.88 -1.33 0.50 C6H6C -0.36 -0.83 -1.42 -2.01 -2.60 0.47 PhCld -0.49 -0.87 -1.35 0.58 DMF -0.26 -0.72 -1.31 -1.85 0.51 MeCN -0.83 -1.32 -1.78 -2.37 0.41 "Anodic peak at 0.1 V/s. 0.5 M (TBA)Br. 'In 1.2 M (THA)C104, at 40 OC. dLarge peak separations due to low dielectric constant. tential scan rates (>5 V/s) under which conditions reversible processes a r e observed. The potential separation between the cathodic and anodic peaks for each electrode process of c 6 0 was equal to or slightly larger
Dubois et al.
7140 The Journal of Physical Chemistry, Vol. 96, No. 17, 1992 TABLE VI: Diffusion Coefncients ( D ) ,Stokes Radii (rs),and Apparent Solvation Numben (q)of Ca in Different Solvent Systems ContrininE 0.1 M (TBAICIO. D X lo6," solvent n. CP cm2 SKI rq? A r v l l v mA ,~ nid 4-1 1 3.4 7.4 0 . W 3.7 0.7 PhCl 4-1 1 7.7 3.6 2 . 6 6 1 . 1 f 0.2 ODCB 4-1 1 7.1 3.2 0.988 3.1 f 0.6 PY 2.8-3.2 5-2 1 7.5 py/MeCN, 90/10' 0.85g 3.4 0.7 2.8-3.2 5-21 7.4 py/MeCN, 80/20' 0.778 3.8 f 0.7 2.8-3.2 8-32 8.3 py/MeCN, 60/4ff 0.638 4.1 0.8 2.8-3.2 8-30 8.2 py/MeCN, 4O/6Oi 0.528 5.1 f 1.0 27-72 3.4 1.24' 1.4 0.3 12.4 PhCN 31-82 2.9 0.44* 4.4 0.9 1 1 . 1 DCM 3.2 280-760 0.55' 1.6 f 0.3 25.0 THF ~~
~
PhCN
* * *
"Determined by using the Levich equation. *Stokes radii of Cm calculated by using eq 1 with f 2 0 % standard deviation. CSolvent radius calculated from the molecular weight and density of the solvent. dSolvation number of Cmcalculated by using eq 2. 'Dynamic viscosity in absence of supporting electrolyte. /For 0.5 M tetrabutylammonium bromide solution from ref 35. BTaken from ref 36. hTaken from ref 37. 'Mole/mole ratio.
than 59 mV, the value characteristic of a CV reversible oneelectron transfer.22The exact peak-tepeak separation varied with the dielectric constant of the solvent but was always of the same magnitude as that measured for the Fc+/Fc couple, which was added as an internal standard. The latter couple is reversible in most solvents,23and the similarity in peak separation between Fc+/Fc and the various CmR-/(n+l)couples implies reversible one-electron transfers in the case of the first four Cm electrode reactions. Except for the third and fourth reductions of Cm in DCM or DCE, the ratio of each cathodic to anodic peak current, i , i,, was equal to 1. The value of i, also varied linearly with ul at scan rates between 0.02 and 0.8V/s. Both sets of data show that the four one-electron reductions of Cm are diffusion controlled.= Levich plots of the RDE limiting currents show that iL was proportional to w112 for the first four reductions (such as those shown in Figure la), also indicating that all four are diffusion controlled.24 Diffusion coefilcients of neutral Ca were determined from the RDE experiments in several pure and mixed solvent systems, and these values are summarized in Table VI. The number of electrons transferred in each reduction step was verified in several solvent/supporting electrolyte systems by controlled potential coulometry. The total charge transferred in each step was n = 1.00 f 0.05 as expected for a single one-electron transfer. Electrogenerated solutions of the mono-, di-, and trianion were stable for at least several hours and in some cases even for several days under an inert gas atmosphere. The neutral c 6 0 species could always be quantitatively recovered upon reoxidation. The fourth reduction of Cm was studied by coulometry only in PhCN, 0.1 M (TBA)PF6 and py, 0.1 M (TBA)C104, both of which solutions allowed application of a controlled potential approaching -2.0 V vs SCE. Controlled potential electrolysis in both of these solvents was characterized by a significant background current due to overlap of the Ca reduction with the reduction of the solvent at such a negative potential. Under these conditions, the Cm substrate could not be quantitatively regenerated upon reoxidation. Nevertheless, the current-time curves recorded upon direct controlled potential reduction of C60to Csoe at -1.95 V indicated an overall four-electron transfer (n = 3.85), thus further c o n f i i g addition of one electron to Ca7- in the process at Ell* = -1.81 V in py. = -1.85 V in PhCN or The fifth reduction of Ca, originally reported in benzene under rather extreme conditions,14Pis also seen in MeCN (Figure lb). The resulting peaks for this process are quite ill-defined and could not be studied in detail. Although the fifth reduction of Cm does not appear to be reversible in MeCN, the cathodic peak current is similar to currents for the second to fourth reductions (see Figure lb), indicating that the electrode reaction at EIl2= -2.37 V can be attributed to a one-electron reduction of Csoe to form C&. The half-wave potentials (measured at 0.1 V/s) for each electrode reaction of Cs0 (Tables 11-V) vary markedly upon
/
.
UVF
r
0
10
20
30
Donor Number Figure 2. Correlation of half-wave potentials for the first three electron transfers of Cm and the Gutmann donor number of the solvent in solutions containing 0.1 M (TBA)CIOI. Solvents are indicated by their respective abbreviations as assigned in Table I.
changing from one medium to another. The nature of both the solvent and the supporting electrolyte influences the measured redox potentials. Solvent and supporting electrolyte effects on El12are seen for all four Cso redox couples, but the magnitudes of the effects are not the same for each process. For example, the El12for the first reduction of Ca varies over a 450-mV potential range (-0.16 to -0.61 V vs SCE) under different experimental conditions while the second reduction occurs over a wider potential range of 600 mV (-0.72 to -1.32 V vs SCE). Some of the variations can be ascribed to liquid junction potential differences between the various media, but, as will be shown, the differences are mostly due to real physicochemical phenomena involving Cm or Cm". Solveat Effects. Solvent effects on half-wave potentials of Ca reductions were studied by making electrochemical measurements in 11 different solvents containing up to 17 different supporting electrolytes. However, not all possible combinations were studied. Half-wave potentials in py, PhCN, DCM, and T H F are summarized separately in Tables 11-IV, while less extensive data in the other seven utilized solvents are presented in Table V. The consecutive one-electron reductions of Cm lead to the formation of anions, and it was expected that the El12values would correlate best with those solvent parameters which primarily reflect the electron acceptor properties of the solvent, namely, the Gutmann acceptor number (AN) or the normalized Dimroth-Reichardt parameter (ETN(30)).25 However, correlations with donor properties of the solvent were also examined, and, as is discussed below, these analyses are also informative. Linear correlations of El12 with the Gutmann solvent donor number (DN)25are shown in Figure 2 for solutions containing 0.1 M (TBA)C104. Similar trends (not shown) are noted for the reduction of Cso in the same solvents containing (THA)C104or (TOA)C104 supporting electrolyte. The correlations are generally only fair, but the trends in the data are clear and informative. The El values for the first reduction correlate quite satisfactorily with the donor properties of the solvent (Figure 2), and the slope of the line is 0.006 f 0.001 V. The correlation of with the Gutmann acceptor number (not shown) is not as good as the correlation with the donor number, but a clear negative slope is nonetheless seen (-0.012 f 0.009 V). The potentials for the third reduction correlate only fairly with the solvent acceptor number, and, in contrast to the first reduction, the slope of El12vs AN is positive (0.013 f 0.005 V). Correlations of El,2 with ETN(30)for solutions containing 0.1 M (TBA)C104are shown in Figure 3. All three reductions exhibit a similar trend; El12are more positive as ETN(30)increases. Similar correlations (not shown) were obtained between Ell2and ETN(30) using the same solvents containing (THA)C104 or (TOA)C104 as supporting electrolyte. Because the negative limit of the potential window does not ex& -2.00 V vs SCE for most of the solvents used, very little information on solvent dependence could be obtained with respect
The Journal of Physical Chemistry, Vol. 96, No. 17, 1992 7141
Electroreduction of Cm in Aprotic Solvents
TABLE MI: Entropy Changes Due to Electron Transfer (AS,) for the C a Redox Couples in Different Solvents Containing 0.1 M Supporting Electrolyte solvent supporting ASET: J mol-’K-’ (Trange, K) electrolyte cwo/lcw1-/2cw2-13Cw3-/4Fc+/ Fc py (243-298) (TEA)CIOI -20 (4.345; 4 . 2 4 ) -120 (4.468; -1.24) -150 (4.865; -1.56) +40 (TBA)CIOI 0 (4.365; 4 . 0 2 ) -120 (4.419; -1.24) -160 (4.825; -1.64) -140 (-1.405; -1.47) +40 (T0A)CIOI +40 (-0.444; +0.36) -90 (4.506; 4 . 9 1 ) -140 (4.947; -1.40) PhCN (273-348) (TEA)CIOI -10 (4.497; 4 . 0 8 ) -80 (-0.657; 4 . 8 1 ) -90 (-1.094; -0.94) +10 (TBA)CIOI +30 (4.537; +0.31) -90 (4.584; 4 . 9 3 ) -150 (4.884; -1.56) +40 (TOA)CIO4 -30 (4.254; 4 . 3 3 ) -90 (4,505; 4 . 9 7 ) -120 (4.958; -1.24) DCM (223-293) (TBA)CIO4 -50 (4.382; 4 . 5 2 ) -140 (4.491; -1.45) -170 (4.873; -1.72) +70 DCE (243-298) (TBA)C104 +20 (-0.526; +0.17) -70 (4,679; 4 . 6 8 ) -80 (-1.104; -0.78) +60 “The parameters of the linear correlation between Ell2 and temperature are indicated in parentheses: intercept (V vs SCE); slope (mV/K).
0.60 .
F PY
t
I
c ~ ~ ~ - / c ~ ~ ~ -
phm
I
DCM
I
THF
0.20
0.30
0.40
0.50 -0.50
Figure 3. Correlationof half-wave potentials for the first three electron transfers of Cmand the normalized Dimroth-Reichardt parameter of the solvent (ETN(30))in solutions containing 0.1 M (TBA)CI04. Solvents are indicated by their respective abbreviations as assigned in Table I.
to the fourth reduction of c6@However, some EIl2data could be collected (see Tables 11-V), and the trends observed between E I l 2and the solvent parameters appeared to be consistent with those described above. Namely, the fourth reversible reduction of Ca behaves in a manner similar to the third one; i.e. the higher the solvent acceptor number, the more positive the value and the easier the reduction. Supporting Electrolyte Effects. The anion of the supporting electrolyte does not significantly affect the measured half-wave potentials for reductions of Cm if the same cation is present in solution. For example, values of E I I Zobtained in a given solvent containing a given TBA’X- salt where X- = Clod-, PF6-, BF4-, or Br- vary by less than 30 mV from each other and show no consistent trend. The cations of the supporting electrolyte have a large effect on Cm reduction potentials, and this is illustrated in Figure 4, which presents Ellz for the fmt three redox p”as a function of the number of carbon atoms in the alkyl chain of the supporting electrolyte cation. A similar plot is also shown for the Fc+/Fc couple. The behavior of the Fc+/Fc “internal standard” is not independent of the cation (as might be expected), and, in a given solvent, E l l z for the oxidation of Fc varies by up to 290 mV for different cations (see Table 11). As seen in Figure 4, there is a trend between E l l 2and the different tetraalkylammonium salts in all solvents except for THF. Solutions which contain the tetraalkylammoniumcations of larger size show a more difficult oxidation for ferrocene. In fact, the absolute magnitude of the shift of E l l z for Fc+/Fc as a function of the cation size (Figure 4a) is comparable to the effect seen upon changing the solvent while using the same supporting electrolyte (seeTable V). Liquid junction potential differences are usually accounted for, in large part, by a change of solvent (dielectric constant). Therefore, for a given solvent, the substitution of one supporting electrolyte for another at a constant ionic strength is expected to change the junction potentials only to a minor extent. Still, the supporting electrolyte effect on the E l p of the Fc+/Fc couple may be due,
2
4
6
8
2
4
6
8
Number of Carbon Atoms figure 4. Correlationof half-wave potentials for the Fc+/Fc couple and the first three electron transfers of Cw as a function of the carbon chain length of the 0.1 M tetraalkylammonium perchlorate supporting electrolyte in four solvents.
in small part, to liquid junction potential differences. The large shifts in E l for the Fc+/Fc couple observed upon variation of the cation of the supporting electrolyte thus suggest that this couple may not be the best internal reference for comparisons between systems containing different cations. Accofdingly, the half-wave potentials of Cmwere also referenced to SCE for discussion. In this case the absolute magnitude of the potential shifts is somewhat decreased, but identical conclusions can be reached as compared to when the analysis is carried out versus the Fc+/Fc reference. The specific quaternary alkylammonium cation of the supporting electrolyte in THF, py, or PhCN influences the E l / zfor thz first two redox processes of Ca in an almost identical manner (see Figure 4b,c). There is a consistent positive shift of El12for the first and second reductions with an increase in the cation size of the supporting electrolyte, and this indicates a higher relative stabilization of Ca-over Ca and Cm2-over C g with larger cations (those which have a more diffuse charge). However, the trend differs for the third reduction (Figure 4d) which is facilitated (Ca3 becomes more stabilized with respect to C,,Z-) when the cation size is increased up to a medium size (TBA+) but becomes more hindered for larger cations (Ei? becomes more negative). Thus, in these cases, Cm* is less stab lzed than C,” with larger cations as compared to the stabilization which occurs in the presence of medium size cations. As seen in Figure 4, the shift of Ellz is different in the less polar solvent, DCM, than described above for the other solvents. All three reductions of Cm occur at more negative potentials in the presence of THA+ than in the presence of TBA+ or TOA’. Sodium and lithium perchlorates could be dissolved to an appreciable extent in only two of the studied solvents, i.e. THF and PhCN. Only potentials for the first and second reductions were obtained in these solutions. The E I l z values in PhCN can be compared with the other El,* values recorded using 0.1 M sup-
7142 The Journal of Physical Chemistry, Vol. 96, No. 17, 1992
porting electrolyte. However, care should be taken when interpreting correlations since the supporting electrolyte concentration (and ionic strength) was necessarily lower (0.05 M) for both the lithium and sodium perchlorates. THF solutions of 0.1 M of either of the two alkali metal cations show quite negative fmt and second C, reduction potentials (measured versus Fc+/Fc as well as versus SCE) as compared to solutions containing any of the other utilized salts of quaternary ammonium or phosphonium cations. were made in four different solvents Measurements of containing (TBP)Br or (TPhP)Br (see Tables 11-V). The E I l 2 values varied markedly from one solvent to the other. Half-wave potentials for solutions containing TBP+ or TPhP+ cations are slightly more positive than those obtained in the same solvents containing TBA+. The use of THF containing TBP+ yields the most positive El12value for the first reduction of Ca found in the present work (Table 11). Similarly, the subsequent reductions also appear at more positive potentials than for most of the solutions containing any of the other cations as supporting electrolytes. Temperature Eff& The half-wave potentials for C, reduction were measured as a function of temperature in eight solvent/ supporting electrolyte systems. The solution compositions and temperature ranges are presented in Table VII. The change of the reversible half-wave potential is directly proportional to the change of entropy upon electron transfer, defined as S E T =I Sd - Sox.For a one-electron transfer, AEIII= (A& AT)/F. Entropy changes of electron transfer were calculated from the slopes of the E I 1 2vs T plots, and these values are summarized in Table VII. Parameters for linear correlations of the half-wave potentials with temperature are also given in this table. The S E T values are strongly dependent on the nature of the solvent, the supporting electrolyte, and the redox process considered. The first reduction of c 6 0 is accompanied by either an increase or a decrease of entropy, depending upon the specific solvent/supporting electrolyte system. However, only a decrease of the entropy is associated with the m n d and thud one-electron transfers. The magnitude of this decrease is different for each process and depends upon the solution composition. In all cases, it was observed that the higher the negative charge on C60, the larger the decrease in entropy. Importantly, the changes in entropy associated with the latter two reductions of C, are quite negative as compared to values reported for redox processes of those inorganic or organometallicspecies where a change in solvent ligation does not occur upon electron transfer.26
Discussion Three principal parameters appear to affect the half-wave potentials for a given Ca redox process. These are temperature, the nature of the solvent, and the nature of the cation of the supporting electrolyte. These influences on El12are discussed in the following sections which are organized according to the oxidation state of the fullerene and preceded by a discussion of the solvent effect on the translational mobility, represented by diffusion coefficients, and solvation of neutral c60. Dihion Coefficients,Stokes Radii, and Solvation of Cm The Stokes-Einstein relation
D = RT/6rsrsNA
(1)
(where is the dynamic viscosity of the solvent (see Table VII), NA is the Avogadro number, and rs is the Stokes radius) which describes translational mobility of large-sphere molecules or ions in a continuous incompressible fluid, seemed to be appealing for the critical evaluation of diffusion coefficients of neutral C, in the solvent systems studied. The mean Stokes radius of c60 calculated from the slope of the straight line obtained (Figure S), with exclusion of the data for PhCN, THF, and DCM, was r, = 7.6 f 1.5 A. This value is appreciably larger than the van der Waals radius determined by either X-ray analysis, rvw = 5.0 A,27 or Langmuir-Blodgett measurements, ~ L = B 5.6 f 0.7 A.28 The limiting values of diffusion coefficients calculated by using eq 1 and rvw as well as rLBare also presented in Figure 5. By using the apparent volume of the solvent molecule, vi, determined from
Dubois et al. / /
/ /
/ /
x
py
PhCl
n 2 THF
0 0
50
100
150
200
250
1 1 ~( l / p o i s e ) Figure 5. Stokes-Einstein plot of the diffusion coefficient of Cm. determined by rotating disk electrode voltammetry (0.198-cmZPt area), against reciprocal of the dynamic viscosity of solvents containing 0.1 M (TBA)C104except ODCB which contains 0.5 M (TBA)Br. Open triangles (A) correspond to pure solvents (as indicated by their respective abbreviations (Table I), and filled circles ( O ) , to pyridine/acetonitrile, mole/mole, mixtures: (1) %/lo, (2) 80/20, (3) 60/40,(4) 40/60. Solid line (-) represents the linear regression of data points except for PhCN, THF,and DCM. Dashed line (- -) was calculated by using the van der Waals radius of C60,27rvw = 5.0 A, and the dotted line (--) by the Langmuir-Blodgett radius,**rLB= 5.6 A. Vertical bars indicate the standard deviations.
the molecular weight and density of the solvent, one can estimate the apparent solvation number, n , of C, in a given solvent. If electrostriction effects are neglected, then ni is given29as
As is seen in Table VI, the apparent solvation number is markedly different for different solvents. For PhCl, ODCB, and py, as well as for the py/MeCN mixtures, the ni values are small and close to those of simple inorganic ions in aprotic solvents.29 This could indicate that, upon diffusion, a monomolecular layer of the solvent is being dragged by the C, molecule. Abnormally large ni values for DCM, THF, and PhCN may also indicate the existence of some Ca aggregation rather t b n the presence of an extended solvation sheath .30 First Reduction. The increase or decrease of entropy associated with the first electron transfer indicates either a relative loss or a relative gain of overall order during the electrochemical process. Two effects, Le. the solvent and the cation of the supporting electrolyte, may compete for stabilization of the neutral and anionic forms of the couple. The overall change of entropy is governed by a superposition of the two effects. In some cases, one effect predominates while in others they are balanced. Therefore, entropy values for the fmt reduction of C, cannot lead to conclusions as to the relative magnitude of these effects in the various cases. Room temperature electrochemical studies in solvents containing different supporting electrolytes reveal the interactions which involve C, and C,-. The small negative slope (-0.012 f 0.009 V) of the line correlating the first reduction E I l 2with AN (not shown) indicates that solvents with acceptor properties seem to stabilize C, more than C,-. The for the first reduction of C, correlates astonishingly well with the Gutmann solvent donor number (see Figure 2). The positive slope of the line (0.006 f 0.001 V) indicates that solvents of higher donor abilities stabilize to a greater extent c60- than neutral Cm This trend involving donor numbers was also suggested in an earlier electrochemical study Of C6o.I' An empirical linear trend is seen between the average apparent solvation number of neutral C, and the Gutmann donor number of the solvent (with THF excluded). If one assumes, as suggested above, that the apparent solvation numbers actually indicate aggregation of Ca in solution, the correlation of the first reduction E l l 2of c 6 0 with the donor number then becomes rational. The
Electroreduction of
c 6 0
in Aprotic Solvents
The Journal of Physical Chemistry, Vol. 96, No. 17, 1992 7143
accompanying the second electron transfer (Table VII) indicates lower the donor number of the solvent, the more aggregated is a pronounced gain of order under all experimental conditions. Cm and the more difficult is its reduction (e.g. in DCM), whereas Hence, one could infer that the c602-dianion interacts more the higher the donor number, the less aggregated is Cm and the strongly with solvent molecules and/or with cations of the supeasier is the first reduction (e.g. in py). Thus, it appears that for porting electrolyte than does the C, monoanion. The solvophobic a given solvent, the donor number also reflects the solvophobic dfect is not operative in the case of C,- because this anion is more effect25,31-32 to which the C, solute is submitted in solution. soluble than Cm in most solvents. Hence, the observed shifts in The size of the supporting electrolyte cation also affects El12 E I I Zfor the second reduction must be discussed in terms of a for the first reduction of Cso, as shown in Figure 4. A positive relative stabilization of Cm2-over C,- rather than in terms of shift of EIl2with an increase of the supporting electrolyte cation a destabilization of C, over Cm2-. Similar to the first reduction, size is observed in py, THF, or PhCN, and this suggests that the solvophobic interactions are observed between the supporting reduction of C, is facilitated in the presence of large ptions. The electrolyte cation and c60- and/or Cm2-,whereas the increased low charge density on C,- does not favor electrostatic interactions negative charge density of the Cm2-dianion enhances the inter(ion pairing) with cations and, accordingly, small cations do not actions of this species with the polar solvent. The dependence stabilize C,- more than C0 The more diffuse charge of the larger of EIl2on the cation type and size for the second reduction of C, cations leads to significant association with Cm-, and this results is quite similar to that observed for the first reduction. This in a stabilization by larger cations. This type of association has indicates that solvophobic interactions are still predominant, fabeen reported for aromatic hydrocarbon radical anions whose voring C6o2- over c60-a However, the fact that DCM solutions association with alkali metal cations in ethers is stronger in the show more negative values in the presence of TOA+ than presence of larger cations. For a given cation, it is also stronger TBA+ (Figure 4c)indicates that electrostatic ion pairing is more in solvents with a lower dielectric c o n ~ t a n t . ~This ~ , ~association ~ difficult to overcome by solvophobic interactions in such a low is governed by solvophobic interactions between the large cations polarity medium. and the anion of the solute. Third Reduction. The high negative values of entropy changes The solvophobic interactionr should not be confused with the upon the third electron transfer of c 6 0 indicate a large gain of solvophobic effect of a solvent on neutral Cm. The solvophobic organization. The ElI2values are practically independent of donor effect is manisfested by solutesolute interactions (associations) number (Figure 2), but the plot of Ell*vs acceptor number (not while the solvophobic interactions, although of similar origins, shown) displays a positive slope of 0.013 f 0.005 V. It must, involve the interaction (association) of two different solutes which are both quite nonpolar as compared to the s o l ~ e n t ? ~Either * ~ ~ * ~ ~ however, be noted that this small positive slope is due mainly to the THF value which has the lowest acceptor number, and in the a solvophobic effect of the solvent on c 6 0 or a solvophobic inabsence of this point no correlation is detected. Nevertheless, a teraction of the cation with Cm-, or both, will influence and correlation of EIl2with the solvent Dimroth-Reichardt parameter, the net result of these two influences, which act in the same which accounts to some extent for acceptor properties of the direction, is a relative stabilization of Cm- Over C d i.e. the electron solvents (Figure 3 ) , indicates that the potential changes for the transfer to Cmis significantly easier in donor solvents and/or in third reduction can be partially accounted for by solvent acceptor the presence of large cations. properties. Significant solvophobic interactions do not seem to The E , shift with cation size in DCM is apparently dominated occur between the supporting electrolyte cations and the CM3by two efiects. The solvophobic interactions are not as important trianion. here as in the case discussed above, and this is due to the nonpolar The general trends in Figure 4d indicate that small quaternary nature of DCM. Consequently, conventional ion pairing seems ammonium cations associate more strongly with Cm3-than with to prevail for medium size cations but is slightly overcome by Ca2-. There is very little difference in the E ! / 2values obtained solvophobic interactions in the case of the larger TOA+ cation. in solutions containing quaternary phosphonlum or quaternary The more difficult reductions of C, (Le. more negative E!/2 ammonium cations, and this contrasts with results for the first values) in THF containing LiC104 or NaC104 support the inreduction of Cm as seen in Tables 11-V. That is, there is a sizable ference regarding a strong solvophobic interaction between the increase in the stabilization of CSo3-over c602- for solutions larger cations and c60-e This is consistent with the absence of containing quaternary phosphonium cations (as compared to significant electrostatic type ion pairing. The more negative quaternary ammonium cations), but the positive shift in El12is potentials in solutions containing Li+ or Na+ (see Tables I1 and not as large as observed for the first reduction of C60under the 111) indicate a much weaker association (if any) of the small alkali same experimental conditions. metal cations with 0-than with the much larger quaternary Half-Wave Potential Prediction. As was described above, the ammonium or quaternary phosphonium cations. E I l 2values for the first reduction of c 6 0 correlate well with the The overall effect of the quaternary phosphonium cations on Gutmann solvent donor number, and this correlation can therefore the c6O/c60- redox potentials depends upon the nature of the be used to predict values in solvents where no electrochemical solvent. The potentials in py or DCM are practically the same data are available. Unfortunately, no satisfactory fits were found in the presence of TBA+ or TBP+ (see Tables I1 and IV), but the for the Cm-/Cm2-and Cm2-/c6$ couples, and therefore a single large positive shift in THF (Table 11) indicates a significantly curve fit cannot be used for prediction of their E I l 2values. larger stabilization of Cm- by TBPC. This implies either a stronger Correlations of El12with the ETN(30)parameter are shown in solvophobic interaction of the quaternary phosphonium cations order to facilitate an estimation of EI12in a given solvent. It can with c60- (as compared to the tetraalkylammonium salts for a be noted that in the case of the second reduction, the line closely given cation size) or a significant ion pairing of C,- by the fits the data points. With the exception of the El vs DN plot phosphonium cations. A systematic investigation of tetraalkylfor the first reduction and the Ell? vs ETN(30)plot #or the second phosphonium cations of different alkyl chain lengths was not reduction, no other correlation with the three solvent parameters performed in the present study, and, for this reason, unequivocal used in the present work can be considered to be sufficiently conclusions cannot be drawn as to which explanation mostly satisfactory for a confident prediction of half-wave potentials. It accounts for the results obtained in the presence of TPhP+ or is therefore recommended to simultaneously use all three of them, TBP+. However, of relevance is the observation that c60- crystallizes as a salt in the presence of the TPhP+ cation in ODCB.33 i.e. the Gutmann donor number, the Gutmann acceptor number, and the Dimroth-Reichardt parameter, if one wishes to estimate This would indicate a very strong association of C,- with the E l / *values of c 6 0 in solvents which have yet to be investigated. TPhP+ cation in agreement with the present results. In this manner, it should be possible to predict quite accurately Second Reduction. The reduction of C,- to C.& results in a the E I l 2values. doubling of the negative charge on the solute and leads to a To predict potentials at different temperatures in different behavior which is intermediate in terms of the effects for the first and third reductions of the fullerene (which are described above media, the parameters of the straight line fit indicated in Table and below, respectively). The large negative values of SETVI1 can be used directly with good confidence, since these lines
7144 The Journal of Physical Chemistry, Vol. 96, No. 17, 1992
account well for the experimental data. The second and third electron additions to C, proceed more easily at low temperature. This contrasts with the first reduction of C, which would be easier or harder, depending on the chosen combination of solvent and cation of the supporting electrolyte. Tlming the C, Homoge~~eous Redox Power. The presence of a supporting electrolyte is not required for the homogeneous redox chemistry of C,, but a knowledge of the relevant redox potentials is crucial. If one tries to suitably adjust the potential of a given C, redox couple for a solution redox reaction, one must be aware that the anionic C,"- species will not be stabilized by cations of a supporting electrolyte and one must then focus only on the solvent and temperature effects. Clearly, the first reduction will be more difficult in nonpolar media due to the solvophobic effect. Generally, all three Ca reductions will become easier in solvents with higher Dimroth-Reichardt parameters. Since the nature of the supporting electrolyte cation significantly influences half-wave potentials for all three reductions, one may consider adding a specifically selected electrolyte to the solution, even for nonelectrochemical experiments. This could shift the redox potential and result in a desired change of chemical reaction products. To put the results in perspective, a few extreme cases will be considered. If a facile first reduction of C, is desired, then a quite polar solvent (strong donor, weak acceptor) and large cation electrolytes are needed. Also, the use of the quaternary phosphonium cations over tetraakylammonium cations should render the first reduction potential more positive in almost all solvents. The first reduction can be made to occur at more negative potentials in nonpolar solvents by using low temperature and in the absence of electrolyte, but if a salt is needed, it should contain a small cation, e.g. an alkali metal. The conditions for a facile third reduction are opposite to those needed for a facile first reduction of Cb0. In this case, one needs solvents with high Gutmann acceptor number, small cations of the supporting electrolyte, and low temperature. Conversely, this reduction of C, should be harder in nonpolar, weak electron acceptor solvents, at high temperature, and in the presence of large cations (if any are to be used). The second reduction of C, is more difficult to predict in terms of extreme conditions, but E, will be more positive in solvents of high ETN(30)parameter. +he temperature effect is clearcut: the second reduction of C, becomes more facile at low temperature. Also, for solutions containing cations of equal size, this reduction will become easier in the presence of quaternary phosphonium cations than in the presence of tetraalkylammonium ones. Acknowledgment. Support of this work by the Texas Center for Superconductivity, the Robert A. Welch Foundation (Grants E-1208 (M.T.J.) and E-680 (K.M.K.)) and the National Science Foundation (Grant CHE-8822881 (K.M.K)) is gratefully acknowledged.
References and Notes (1) Kroto, H. W.; Allaf, A. W.; Balm, S.P. Chem. Rev. 1991, 91, 1213 and references cited therein. (2) Haufler, R. E.; Conceicao, J.; Chibante, L. P. F.; Chai, Y.; Byrne, N. E.; Flanagan, S.; Haley, M. M.; OBrien, S. C.; Pan, C.; Xiao, Z.; Billups, W. E.; Ciufolini, M. A,; Hauge, R. H.; Margrave, J. L.; Wilson, L. J.; Curl, R. F.; Smalley, R. E. J. Phys. Chem. 1990, 94, 8634. (3) Hawkins, J. M.; Meyer, A,; Lewis, T. A,; Loren, S.; Hollander, F. J. Science 1991, 252, 312. (4) (a) Holloway, J. H.; Hope, E. G.;Taylor, R.; Langley, G.J.; Avent, A. G.;Dennis, T. J.; Hare, J. P.; Kroto, H. W.; Walton, D. R. M. J . Chem. Soc., Chem. Commun. 1991, 966. (b) Selig, H.; Lifshitz, C.; Peres, T.; Fischer, J. E.; McGhie, A. R.; Romanow, W. J.; McCauley, J. P., Jr.; Smith, A. B., 111. J. Am. Chem. SOC.1991, 113, 5475. (c) Olah, G.A.; Bucsi, I.; Lambert, C.; Aniszfeld, R.; Trivedi, N. J.; Sensharma, D. K.; Surya Prakash, G.K. J. Am. Chem. SOC.1991, 113, 9385. (5) (a) Bausch, J. W.; Surya Prakash, G.K.; Olah, G. A,; Tse, D. S.; Lorents, D. C.; Bae, Y. K.; Malhotra, R. J. Am. Chem. Soc. 1991, 113, 3205. (b) Olah, G. A.; Bucsi, 1.; Lambert, C.; Aniszfeld, R.; Trivedi, N. J.; Sensharma, D. K.;Surya Prakash, G.K. J . Am. Chem. Soc. !991,113,9387. (c) Susuki, T.; Li, Q.; Khemani, K. C.; Wudl, F.;Almarson, 0. Science 1991, 254, 1186. (d) Kmsic, P. J.; Wasserman, E.; Parkinson, B. A.; Malone, B.; Holler,
Dubois et al. E. R., Jr.; Keizer, P. N.; Morton, J. R.; Preston, K. F. J. Am. Chem. SOC. 1991, 113, 6274. (e) Krusic, P. J.; Wasserman, E.; Keizer, P. N.; Morton, J. R.; Preston, K. F. Science 1991, 254, 1183. (6) (a) Fagan, P. J.; Calabrcse, J. C.; Malone. B. Science 1991,252, 1160. (b) Roth, L. M.; Huang, Y.; Schwedler, J. T.; Cassady, C. J.; Ben-Amotz, D.; Kahr, B.; Freiser, B. S. J. Am. Chem.Soc. 1991,113,6298. (c) Phicaud, A.; Hsu, J.; Reed, C. A,; Koch, A.; Khemani, K. C.; Allemand, P.-M.; Wudl, F. J. Am. Chem. SOC.1991,113,6698. (d) Huang, Y.; Freiser, B. S. J . Am. Chem. SOC.1991, 113, 8186. (e) Koefcd, R.S.;Hudgens, M. F.; Shapley, J. R. J. Am. Chem. Soc. 1991,113,8957. (f) Balch, A. L.; Catalano, V. J.; Lee, J. W. Inorg. Chem. 1991,30, 3981. (g) Fagan, P. J.; Calabrese, J. C.; Malone, B. J. Am. Chem. SOC.1991,113, 9408. (7) Chai, Y.; Guo,T.; Jin, C.; Haufler, R. E.; Chibante, L. P. F.; Fure, J.; Wang, L.; Alford, J. M.; Smalley, R. E. J . Phys. Chem. 1991, 95, 7564. (8) Liu, S.; Lu, Y.-J.; Kappas, M. M.; Ibers, J. A. Science 1991, 254,408. (9) (a) Haddon, R. C.; Brus, L. E.; Raghavachari, K. Chem. Phys. Lett. 1986,125,459. (b) Haymet, A. D. J. Chem. Phys. Lett. 1985, 122,421. (c) Hale, P. D. J. Am. Chem. SOC.1986, 108, 6087. (IO) Allemand, P.-M.; Koch, A.; Wudl, F.; Rubin, Y.; Diederich, F.; Alvarez, M. M.; Anz, S. J.; Whetten, R. L. J . Am. Chem. Soc. 1991, 113, 1050.
I 1 I ) Cox. D. M.: Behal. S.:Disko. M.: Gorun. S. M.: Greanev. M.: Hsu. C. S.; Kollin, E. B.; Millar, J.; Robbins, J.; Robbins, W.; Sherw&d, R. D.1 Tindall, P. J. Am. Chem. Soc. 1991, 113, 2940. (12) Dubois, D.; Kadish, K. M.; Flanagan, S.; Haufler, R. E.; Chibante, L. P. F.; Wilson, L. J. J . Am. Chem. SOC.1991, 113, 4364. (13) Jehoulet, C.; Bard, A. J.; Wudl, F. J . Am. Chem. Soc. 1991, 113, 5456. (14) (a) Dubois, D.; Kadish, K. M.; Flanagan, S.; Wilson, L. J. J . Am. Chem. Soc. 1991,113,7773. (b) Xie, Q.;Perez-Cordero, E.; Echegoyen, L. J . Am. Chem. SOC.1992.114, 3978. (c) Ohsawa, Y.; Saji, T. J . Chem. SOC., Chem. Commun. 1992, 781. (15) (a) Hebard, A. F.; Rosseinsky, M. J.; Haddon, R. C.; Murphy, D. W.;
Glarum, S. H.; Palstra, T. T. M.; Ramuez, A. P.; Kortan, A. R. Narure 1991, 350,600. (b) Stephens, P. W.; Mihaly, L.; Lee, P. L.; Whetten, R. L.; Huang, S.-M.; Kaner, R.;Deiderich, F.;Holczer, K. Nature 1991, 351, 632. (c)
Holczer, K.; Klein, 0.;Huang, S.-M.; Kaner, R. B.; Fu, K.-J.; Whetten, R. L.; Diederich, F. Science 1991, 252, 1154. (d) Kelty, S. P.; Chen, C.-C.; Liebcr, C. M. Nature 1991,352,223. (e) Tanigaki, K.; Ebbescn, T. W.; Saito, S.; Mizuki, J.; Tsai, J. S.; Kubo, Y.; Kuroshima, S. Nature 1991, 352, 222. (f) McCauley, J. P., Jr.; Zhu, Q.;Coustel, N.; Zhou, 0.; Vaughan, G.; Idziak, S. H. J.; Fischer, J. E.; Tozer, S. W.; Groski, D. M.; Bykovetz, N.; Lin, C. L.; McGhie, A. R.; Allen, B. H.; Romanow, W. J.; Dcnenstein, A. M.; Smith, A. B., I11 J . Am. Chem. SOC.1991, 113,8537. (g) Zhou, 0.;Fischer, J. E.; Coustel, N.; Kycia, S.; Zhu, Q.; McGhie, A. R.; Romanow, W. J.; McCauley, J. P., Jr.; Smith, A. B., 111; Cox,D. E. Nature 1991, 351, 462. (16) (a) Wang, H. H.; Kini, A. M.; Savall, B. M.; Carlson, K. D.; Williams, J. M.; Lykke, K. R.; Wurz, P.; Parker, D. H.; Pellin, M. J.; Gruen, D. M.; Welp, U.; Kwok, W.-K.; Fleshler, S.; Crabtree, G. W. Inorg. Chem. 1991, 30, 2838. (b) Wang, H. H.; Kini, A. M.; Savall, B. M.; Carlson, K. D.; Williams, J. M.; Lathrop, M. W.; Lykke, K. R.; Parker, D. H.; Wurz, P.; Pellin, M. J.; Gruen, D. M.;Welp, U.;Kwok, W.-K.; Fleshler, S.; Crabtree, G. W.; Schirber, J. E.; Overmyer, D. L. Inorg. Chem. 1991, 30, 2962. (17) The overall oxidation observed implies four electrons, but it is not known which fullerene cation is initially generated upon heterogeneous electron transfer. (18) Kadish, K. M.; Anderson, J. E. Pure Appl. Chem. 1987, 59, 707. (19) Kadish, K. M.; Das, K.; Schaeper, D.; Merrill, C. L.; Welch, B. R.; Wilson, L. J. Inorg. Chem. 1980, 19, 2816. (20) The colors of the solutions of the anions are as follows: Cm', dark red-purple; Ca2-, red-orange; Cm3, dark red-brown. (21) Koh, W.; Dubois, D.; Kutner, W.; Jones, M. T.; Kadish, K. M. J. Phys. Chem. 1992, 96, 4163. (22) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 713. (23) Kadish, K. M.; Ding, J. Q.; Malinski, T. Anal. Chem. 1984,56, 1741. (24) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; Wiley: New York, 1980. (25) Reichardt, C. Solvents and Solvent Effects in Organic Chemistry; VCH: New York, 1988, and references cited therein. (26) (a) Hupp, J. T.; Weaver, M. J. Inorg. Chem. 1984, 23, 3639 and references cited therein. (b) Sahami, S.; Weaver, M. J. J. Solution Chem. 1981, 10, 199. (27) (a) Kratschmer, W.; Lamb, L. D.; Fostiropoulos, K.; Huffman, D. R. Nature 1990,347, 354. (b) Hawkins. J. M.; Lewis, T. A.; Loren, S. D.;
Meyer, A.; Heath, J. R.; Saykally, R. J.; Hollander, F. J. J . Chem. SOC., Chem. Commun. 1991, 775. (28) Obeng, Y. S . ; Bard, A. J. J . Am. Chem. SOC.1991, 113, 6279. (29) Physical Chemistry of Solvents; Covington, A. K., Dickinson, T., Eds.; Plenum Press: London, 1973; Chapter 5. (30) Krishnan, V.; Moninot, G.;Dubois, D.; Kutner, W.; Kadish, K. M. Manuscript in preparation. (31) Aten, A. C.; Dieleman, J.; Hoijtink, G. J. Discuss. Faraday Soc. 1960, 29, 182. (32) Peover, M. E. In Electroanalytical Chemistry; Bard, A. J., Ed.; Dekker: New York, 1967; Vol. 2, pp 1-53.
7145
J. Phys. Chem. 1992,96,7145 (33) Allemand, P.-M.; Srdanov, G.;Koch, A,; Khemani, K.; Wudl, F.; Rubin, Y.;Diederich, F.; Alvarez, M. M.; Anz, S. J.; Whetten, R. L. J . Am. Chem. SOC.1991, 113, 2780. (34) Handbook of Chemistry and Physics, 66th ed.; CRC Press: Boca Raton, FL, 1985; pp E50-52. (35) Miller, B.; Rosamillia, J. M. Presented at the Symposium Fullerenes: Chemistry, Physics and New Directions of the 180th Meeting of The Elec-
trochemical Society, Phoenix, AZ, 1991. (36) Gill, D. S.; Singh, B. J. C h .Soc., Faraday Trans. I 19%8,84,4417. (37) Svorstd, I.; Sigvartsen, T.; Songstad, J. Acta Chem. Scand. 1988, B42, 133. (38) The effective donor numbers of the pyridine/acetonitrile mixtures were approximated as the weighed average of the donor numbers of both pure solvents.
COMMENTS Comment on "Accuracy of Counterpoise Corrections In Second-Order Intermolecular Potential Calculatlons. 1. Helium Dimer" Sir: A recent paper on the validity of counterpoise corrections in the intermolecular energy calculations was published by Yang and Kestner.' We are particularly interested in this work since we previously worked on the same topic with a different approach.* While we generally agree with their arguments and conclusions in the paper, we have found a few problems in some of the calculational results. It is the purpose of this comment to point out the possible errors in that paper. On the basis of our experience in the interaction energy calculations for "true" van der Waals molecules such as noble gases, we feel that it is impossible to reach the large depth of the He, interaction potential with the second-order theory of electron correlation with the contracted basis set [8s4p2d/2s4p2d]. To convince ourselves of this, we have repeated the same calculations and obtained the results shown in Table I. Since the paper did not mention which was the uncontracted single s gaussian function in the [8~4p2d/h4p2d]basis set, we have chosen the most diffuse one (with the smallest exponent) as the uncontracted s function accordii to common practice. (Other choices did not significantly change the results.) The calculations were carried out on a V A X mainframe with the GAUSSIAN 86 package. It is clear from Table I that considerable discrepancies exist between their results and ours. First the Hartree-Fock (HF) interaction energies are noticeably different: theirs are consistently larger than ours. For the correlation interaction energy calculations, they used the second-order localized orbital pair approach while we directly used the MP2 method. The two formalisms are not essentially different (the unitary transformation of molecular orbitals does not affect the total energy). So the large difference in the total interaction energies (HF plus correlation contribution) between theirs and ours is hardly understandable. Their values at the attractive region are almost twice ours. In order to confirm the reliability of our results, we have performed further calculations at higher levels of M~ller-Plesset perturbation theory and with use of a series of larger basis sets formed by gradual decontraction of the 8s primitive Gaussian functions. The HF and MP2 interaction energies remain nearly unchanged. The MP3, MP4SDQ, and MP4SDTQ values a t R = 3.0 A with [8s4p2d/2s4p2d] are -7.803, -8.064, and -8.843 K, respectively, and they remain nearly the same for the other basis sets. The slow convergence of the calculated interaction energy with the level of electron correlation theory for the noble gases was noted in our previous studies on Ne, and is consistent with other calculations in the l i t e r a t ~ r e . ~In- ~addition to the inadequacy of the MP2 theory, the basis set of spd quality is also likely far from sufficient for the accurate calculations. A study by Sauer et al.3 showed that hardly more than 65% of the stabilization energy could be recovered by the second-order theory, even if very extended basis sets are used. A possibility might be that the discrepancies of the reported values are due to random errors since they do not yield an upper
0022-365419212096-7 145$03.00/0
TABLE I: Comparison of the Calculated Interaction Energies at the HartreeFock and Second-Order Correlated Levels (BasisSet 18s4pM/Zs4pMl or ~~l/l:l:l:l/l:ll, Full CP Corrections for BSSE) results of Yang and Kestner' our results R(& HF(K) MP2(K) HF(K) MP2 (K) 2.0 734.430 609.211 724.604 598.649 2.5 78.666 35.931 77.782 40.242 -10.588 3 .O 9.736 7.864 -5.485 3.5 1.638 -7.953 0.762 -4.447 4.0 0.138 -4.450 0.0717 -2.183 -2.134 0.006 4.5 0.010 -1.070 5.0 0.001 -0.966 0.0003 -0.558 ~~
bound (the interaction energy by the perturbation theory is not a variational quantity). However, a study of the component contributions in the second-order theory showed that the major attractive contribution to the interaction energy is the dispersion energy evaluated at the second-order uncoupled HF level, which is advantageously a variational q ~ a n t i t y .As ~ a result, the second-order interaction energies should not allow such large random errors as those shown in the reported He, potential in that paper. As our frank conclusion, we consider that the reported He, potential in that paper is not possible under the described computational conditions and that the errors may be caused by some technical reasons. Note added in proof from the original authors (Yang and Kestner): This present study confirms that the counterpoise correction can lead to accurate results. The method of analysis used by Yang and Kestner is a good way to provide proof of its accuracy. However, in our helium work we modified an old version of the Gaussian program and something was not correct with our modifications, as this note has pointed out. The relative sizes of the components is valid but not their absolute values. The conclusions are also valid. The original program could not be checked as it will no longer run on our present computer. It is important to realize that this is not the program used in our paper part IL6 Those values are not subject to this problem. Registry No. He,, 12184-98-4.
References and Notes (1) Yang, J.; Kestner, N. R. J . Phys. Chem. 1991, 95, 9214. (2) Tao, F.-M.; Pan, Y.-K. J . Phys. Chem. 1991, 95, 3582; 9811. (3) Sauer, J.; Hobza, P.; Carsky, P.; Zahradnik, R. Chem. Phys. Lett. 1981, 134, 553. (4) Chalasinski, G.; Szczesniak, M. M. Mol. Phys. 1988, 63, 205. (5) Cybulski, S. M.; Chalasinski, G.; Moszynski, R.J . Chem. Phys. 1990, 92, 4357. ( 6 ) Yang, J.; Kestner, N. R. J. Phys. Chem. 1991, 95, 9221.
Department of Chemistry Brown University Providence, Rhode Island 0291 2 Department of Chemistry Boston College Chestnut Hill, Massachusetts 02167
Fu-Ming Tao Yuh-Kang Pan'
Received: April 30, 1992; In Final Form: June 24, 1992 0 1992 American Chemical Society
