Extraction and Chromatographic Elution Behavior of Endohedral

J. Phys. Chem. 1996, 100, 725-729

725

Extraction and Chromatographic Elution Behavior of Endohedral Metallofullerenes: Inferences Regarding Effective Dipole Moments Dirk Fuchs and Hermann Rietschel Forschungszentrum Karlsruhe, Institut fu¨ r Nukleare Festko¨ rperphysik P.O. Box 3640, D-76021 Karlsruhe, Germany

Rudi H. Michel, Achim Fischer, Patrick Weis, and Manfred M. Kappes* Institut fu¨ r Physikalische Chemie II, UniVersita¨ t Karlsruhe, D-76128 Karlsruhe, Germany ReceiVed: June 6, 1995; In Final Form: October 10, 1995X

Chromatographic retention relationships between Ce-, Gd-, La-, and Y-containing endohedral metallofullerenes and a [2-(1-pyrenyl)ethyl]silyl-silica stationary phase were studied using toluene as eluent. Measurements are discussed in comparison to those of empty fullerenes. Both the extraction and chromatographic elution behavior of the metallofullerenes reflect their polar nature and allow inferences regarding the presence of a dipole moment in M@C82.

1. Introduction Endohedral metallofullerenes consist of up to three metal atoms1,2 (mostly of the IIIB group) trapped within a fullerene molecule. One prominent example is a C82 molecule with a La atom inside, or making use of non-IUPAC notation, La@C82. During the last three years, various Mx@Cn compounds have been prepared and isolated on a milligram-scale,3-5 thus allowing not only molecular physics experiments but also solidstate physics and chemistry studies of these molecules. Experiments on a variety of M@C82 species have provided strong evidence that the metal atoms are located inside the cage but off its center.6-12 For M@C82 it is assumed that, as a result of complexation, two or more electrons are transferred from the metal atom to the carbon cage, leading to a Coulomb interaction between both.10,13 As a result, M@C82 compounds comprising a variety of lanthanide atoms are predicted to have quite large dipole moments.13,14 However, although structural probes have recently provided unequivocal evidence for the existence11,12 of permanent moments, their magnitudes still have to be determined experimentally. Apart from possible solid-state applications, endohedrally metal-doped fullerenes and their empty cage congeners are of fundamental interest as model substances for probing transport and molecular motional dynamics in solution. Specifically, there is the unprecedented opportunity of turning on a dipolar interaction in a large polarizable Cn cage by doping it with an asymmetrically positioned metal atom. Furthermore, n can be varied over an as yet modest but finite range. One of the issues still plaguing systematic studies of endohedral fullerenes in solution is that of availability. After optimization of endohedral soot preparation, this is mainly a question of extraction and purification technology, each in turn a function of the details of the interaction between endofullerene and solvent. In this publication, we present an account of an improved extraction and purification scheme for a number of endohedral mono- and dimetallofullerenes (M@C82 and M2@C80). Detailed quantification of solubility and high-performance liquid chromatography (HPLC) retention behavior allows for conclusions regarding their polar nature. X

Abstract published in AdVance ACS Abstracts, December 15, 1995.

0022-3654/96/20100-0725$12.00/0

2. Preparation, Extraction, Separation, and Characterization Carbon soots containing higher and endohedral fullerenes were prepared by dc arc discharge of metal oxide (Y2O3, La2O3, CeO2, and Gd2O3)-carbon composite rods (1.5 atom % metal) as described elsewhere in detail.15 The absolute HPLC throughput of Mx@Cn’s has been improved relative to those in previous studies by applying a novel extraction scheme based upon selective solubility due to the different chemical nature of empty vs endohedral fullerenes. This extraction scheme, also described in ref 15 in detail, consists of two steps: (i) a preextraction of the fullerene soot with cold toluene, which removes about 70% of C60 and C70 without any significant loss of Mx@Cn’s; (ii) a Soxhlet-extraction of the soot residue using a polar solvent mixture that consists of CS2 and CH3OH (84:16 vol %). The purification of the M@C82 and M2@C80 contained in the resulting extract was done by HPLC using a PYE Cosmosil column5,16,17 (10 mm × 250 mm, Nacalai Tesque Inc.) with a [2-(1-pyrenyl)ethyl]silyl-silica stationary phase and toluene as eluent.18 Figure 1 documents sample purities achieved for Y@C82, La@C82, Ce@C82, and Gd@C82. Characterization of M@C82 purity by HPLC (Figure 1a) has been carried out on a Buckyclutcher I column19 because of its higher selectivity against neighboring eluting empty fullerenes (C86 and C88) in contrast to the commonly used PYE column. The purity obtained is further demonstrated by 337 nm laser desorption time of flight mass spectra (Figure 1b). From these data a purity of >96% can be assessed.18 Such samples were used for the systematic PYE retention time studies reported below for M@C82 and for the presented UV-vis spectra (Figure 1c). The M2@C80 (M ) La and Ce) retention behavior was studied using enriched samples. In all cases (including Cn), HPLC-resolved species were assigned on the basis of mass spectral identification. 3. Polarity and Extraction Yield Extraction with azeotropic CS2/CH3OH is preferable to the CS2 extraction procedure commonly applied. We carried out a comparison under controlled conditions to document this (Figure 2). For this, carbon soots containing La endofullerenes from the same production batch were preextracted in the same way © 1996 American Chemical Society

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Figure 1. Various M@C82 compounds after purification (>96%): (a) analytical HPLC traces; (b) mass spectra; (c) UV-vis spectra.

Comparing the La@C82 signal in both chromatograms, one finds that the absolute yield of La@C82 is 2-3 times higher when azeotropic CS2/CH3OH is used as the extraction solvent. For the extraction of Ce@C82, Y@C82, and Gd@C82, similar results have been obtained. The slight decrease in intensities of higher empty fullerenes like C76, C78, C84, and C90 in the azeotropic extraction can be taken as a further hint for the selectivity of this more polar solvent mixture toward metallofullerenes. This is consistent with the strongly polar character of M@C82, which has been found in a number of calculations, giving rise to dipole moments of e.g., 1.1-2.9 D for Sc@C82,14 1.1-2.6 D for Y@C82,14 and 3-4 D for [email protected],20 4. HPLC Retention Relationships of Empty Fullerenes Further information about the molecular features of endohedral fullerenes can be obtained by studying chromatographic retention relationships. Let us first consider the retention of empty fullerenes on a PYE phase. According to chromatographic theory,21 the retention time tR is related to the difference in Gibbs free energy22 between fullerene in solution and that adsorbed onto the stationary phase:

ln Figure 2. Typical HPLC chromatograms of a 4 mL xylene injection obtained using a PYE column at 20 °C: (a) fullerene mixture obtained by CS2-extraction; (b) extraction with azeotropic CS2/CH3OH as described in the text. C60 and C70 signals are off-scale.

in cold toluene. The subsequent Soxhlet-extraction of the soot residues was also identical for both samples besides the solvent. Figure 2a shows a typical chromatogram for a sample obtained upon CS2 extraction, while Figure 2b shows a chromatogram of a similar injection (same concentration and injection volume) obtained by extracting with a CS2/CH3OH (84:16 vol %) azeotropic mixture. The boiling temperatures of the extraction solvents are nearly the same (46 °C for CS2 and 37 °C for CS2/ CH3OH) so that the mean polarity of the solvents is the main difference between both extraction experiments.

()

tR ∆G° ∝ t0 RT

(1)

where t0 is the retention time of the eluent, R the gas constant, and T the temperature at which the HPLC measurement is carried out. The major retention mechanism for fullerenes on a PYE phase is based on van der Waals interactions, mainly dispersion forces resulting primarily from interactions between π-electrons on pyrene groups and fullerene analytes.16 To first order one can model this interaction in terms of the London expression describing the long range attractive potential between two polarizable Drude oscillators. In this case, ∆G° ) ∆G is proportional to the polarizability R2 of the fullerenes,

∆G )

(

)

3 I1I2 R1R2 2 I1 + I2 r6

(2)

where R1 is the polarizability of the stationary phase, i.e., pyrene,

Elution Behavior of Endohedral Metallofullerenes and r is the mean center-to-center van der Waals distance between the idealized fullerene molecules and the pyrenegroup.22 I1 and I2 are the ionization potentials of pyrene and the analyte, respectively.23 To our knowledge, there exist no measurements of the static dipole polarizabilities of higher fullerenes.24,25 Therefore, we calculated the polarizabilities of C70 and C84 (D2d isomer) using the ab initio coupled perturbed Hartree-Fock (CPHF) method (second derivative of the SCF energy) as implemented in the TURBOMOLE package.25,26 The geometries were optimized at the SCF level with an optimized (7s4p)[3s2p] basis set.27,28 For the polarizabilities, a basis set was used that amounts to 1050 (C70) and 1260 (C84) basis functions,25,29 giving results typically 5-15% too low. For C70 we obtained Rxx ) Ryy ) 91.0 Å3, and Rzz ) 97.5 Å3, and for C84 (D2d) Rxx ) Ryy ) 114 Å3 and Rzz ) 112 Å3. The polarizability of C60 has been taken from ref 25 (with exactly the same basis set): Rxx ) Ryy ) Rzz ) 78.8 Å3. These data suggest that within the accuracy of our results, the polarizability of empty fullerenes is proportional to the number of carbon atoms Nc and thus to the number of π-electrons, similar to the situation for polycyclic aromatic hydrocarbons and conjugated polymers.30 In measurements on various apolar columns, several authors31 have observed a nearly linear dependence of ln(tR/t0) on Nc for fullerenes up to C96. This suggests that R2 is dominant in determining the relative retention. As a corollary, if (2) were valid, one infers that either r and Ι2 depend only weakly on Nc or there is some kind of mutual compensation (i.e., I2 decreases and r increases with increasing Nc32). Figure 3 shows the retention behavior of empty fullerenes as extracted from our measurements. Exact tR values for the various fullerenes were obtained by analysis of chromatograms determined at loadings lower than those used for preparation, which guarantees the reproducibility of the retention behavior. In Figure 3 small deviations from linearity (which, enable us to resolve certain isomers such as for the two for C78 and C86 and for at least two for C9033) likely originate from a structural dependence of tR as extensively discussed for polycyclic aromatics in previous work.34,35 Different shapes result in different molecular footprints, leading to slightly altered adsorption contributions to the overall retention. Furthermore, different topologies lead to a change of the specific diffusion coefficient, which affects the diffusion of fullerene isomers through the porous stationary phase.36 5. HPLC Retention Behavior for M@C82 and M2@C80 In Figure 3 we have also documented the retention times for various Mx@Cn compounds to facilitate a comparison between these and empty fullerenes. Before a discussion of the corresponding relationships, some comments are in order. All endohedral mono-metallofullerenes (M@C82) are plotted vs Nc ) 85. We have assumed 85 π-electrons for these fullerene species for the following reasons. (i) From X-ray photoelectron spectroscopy (XPS) measurements on Y@C82 and La@C82 it has been concluded that both metals are in a trivalent state,37 corresponding to the transfer of three additional electrons to C82 cage states and therefore increasing the nominal number of π-electrons on the cage from 82 to 85. SQUID measurements of Gd@C82 have revealed a magnetic moment consistent with a Gd3+ ion.38 (ii) UV-vis spectra of M@C82 (M ) Y, La, Ce, and Gd) as presented in Figure 1 all show the same features, i.e., two broad absorption bands near 1000 and 1400 nm (and a spectral onset at about 2000 nm39,40,41). This suggests near isoelectronic configurations for these four M@C82 species.

J. Phys. Chem., Vol. 100, No. 2, 1996 727

Figure 3. Retention time tR for various fullerenes at 20 °C vs the effective number of carbon atoms Nc (assuming M3+ for M@C82 and M2@C80 throughoutssee text). Open and filled symbols represent empty and endohedral fullerenes, respectively; more than one open symbol at one Nc value indicates different isomers of one fullerene species. The solid line represents a fit to empty cage measurements.

(iii) From thermodynamic calculations it has also been deduced that lanthanide atoms such as Ce and Gd exhibit a +3 oxidation state in [email protected] In addition, ab initio calculations by Nagase et al. for M@C82 (M ) Sc, Y, La, and Ce) again predict a +3 oxidation state for Y and La. However for Sc and Ce they find a +2 oxidation state.43 Besides these M@C82 data, we have also plotted the retention times for two later eluting M2@C80 (M ) La and Ce), assuming Nc ) 86 (86 π-electrons). This assumption is supported less strongly by experiment, theory and previous speculation as indicated below. (i) Surface collisional probes of La2C80- have been rationalized in terms of a structure consisting of an Ih-C80-related fullerene cage with six additional electrons delocalized over the entire fullerene cage.44 This structure can be described as (La3+)2@C806-, meaning that each lanthanum atom is in a La3+ state as it is in [email protected] It has been suggested that this IhC80 cage (the neutral molecule is open shell) is highly stabilized by such charge transfer.45 (ii) The postulation of extensive charge transfer is not unprecedented for M2@Cn; for example Nagase has shown in ab initio calculations that Sc2@C84 can in fact be formally described as (Sc2+)2(C844-) having four extra electrons on the C84 cage distributed almost uniformly on the surface.46 Furthermore, cyclic voltametry experiments on La@C82 show that up to five additional electrons can be transferred onto the cage without dissociation.41 From Figure 3 we see that the retention times for M@C82 are only slightly different from each other and obviously shorter than those for M2@C80 on this column. Evidently, all Mx@Cn compounds studied here have significantly longer retention times than their homologous empty cage fullerenes (i.e., the pseudo “C85” and C86), indicating an additional contribution to the retention mechanism beyond the dispersion term invoked above.

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Such a chromatographic elution behavior can be discussed in terms of additional polar contributions to the solute-column interaction. Dipole-induced dipole interactions between a polar metallofullerene and the polarizable PYE phase would cause a further contribution ∆(∆G) to the change of the Gibbs free energy between fullerene in solution and that adsorbed on the stationary phase, thus increasing the retention time21 ∆G° ) ∆G + ∆(∆G). Such interactions can again be modeled in terms of an idealized gas-phase picture:49

1 R1µ2 + R2µ1 4π0 r6 2

∆(∆G) )

2

(3)

Here, R is the polarizability and µ the dipole moment of the pyrene group() ˆ 1)/metallofullerene() ˆ 2) and r is the mean center-to-center van der Waals distance between both. A dipole induction from the nonpolar PYE phase in the analyte can be negleted (µ1 ) 0). In this model, the difference in retention between doped and undoped fullerenes having the same polarizability (which we regard as determined by the number of π-electrons) is proportional to the square of the dipole moment µ2 of a metallofullerene as shown by (4a) and (4b) (assuming empty and filled cages to have the same mean separation from the pyrene group and the same ionization potential):47,48 empty fullerenes (µ2 ) 0)

()

ln

( )

tR daR1 )c+ R2 t0 T

(4a)

doped fullerenes (µ2 + 0)

() ( ) ( )

tR* daR1 b daR1 2 ln )c+ R2 + µ2 t0 T a T

(4b)

where

a)

3 I1I2 1 1 , c ) constant, and d ) 6 ,b) 2 (I1 + I2) 4π0 Rr

From (4a) and (4b) one finds for µ2

µ2 )

[( ( ) ( )) ln

tR* tR - ln t0 t0

R2)const

×

( )] T a daR1 b

1/2

(5)

The factor (daR1)/T can be determined from the slope of the retention line for empty fullerenes in Figure 3. From this Figure, the additional average energy contribution ∆(∆G) for M@C82 turns out to be about 360 J/mol. Note that ∆(∆G) is larger than deviations between empty cage isomers but still only about 7% of ∆G°. This means that the additional dipole moment affects ∆G° only slightly. It is of interest to note in passing that, in the case of M2@C80, the additional free energy contribution is about twice that of the M@C82. Assuming separate metal cations diametrically oriented in a symmetric cage, these fullerenes should be nonpolar. As described by Yeretzian et al.50 for La2@C80, two metal atoms in a 3+ oxidation state can be well accomodated in a C80 cage with Ih or D5h symmetry when displaced symmetrically along a C5 axis by about 4 Å relative to each other. This is also consistent with recent ab initio calculations51 on the isolated molecule. The two local dipoles originating from the two cations would then be oppositely directed with a mean distance of about 6 Å if a cage diameter of 8 Å is assumed. It is not clear whether polar surroundings could induce significant

Figure 4. Retention time t*R for various M@C82 at 20 °C vs effective dipole moment µ. See text for a discusion of error bars/sensitivity analyses.

reorientation of these dipoles thus leading to enhanced dipoleinduced dipole interactions relative to M@C82 From eq 5, gross estimates of the effective dipole moments of the M@C82 may be obtained. Assuming (i) IP (Mx@Cn) ) 6.5 eV, IP (pyrene) ) 9 eV, (ii) R(Cn) ) 1.32 Nc Å3, (iii) R(M@C82) ) R(“C85”), and (iv) µ1(pyrene) ) 0 D, we find the effective dipole moments as presented in Figure 4. Vertical error bars in Figure 4 reflect instrumental uncertainities. The relative retentions of Y@C82 and Gd@C82 could not be differentiated. Asymmetric boundaries on µeff are meant to show sensitivity to limiting assumptions. Assuming a 20% contribution of higher multipole interactions to ∆(∆G) reduces µeff by the amounts shown. Alternatively, positive deviations reflect the typical extent of isomer variation in empty cage retentions (M@C82 species corresponding to specific empty cage isomers that fall below the best fit of Figure 3 would have appropriately larger effective moments). The M dependent trends observed for µeff are of particular interest because preliminary IR and Raman measurements of La@C82 and Y@C82 indicate that at least two of the four M@C82 species studied here have the same cage structure.52 Note that the µeff values determined here are significantly larger than those resulting from ab initio calculations. This is not suprising given the many gross assumptions made in this analysis (see above). A quite different retention behavior of metallofullerenes is obtained when columns with polar stationary phases are used such as the Buckyclutcher column,17 which is also often employed for separating endohedral fullerenes in multistep HPLC.3,4,53,54 This column shows strong dipole-dipole interactions with polar fullerenes that are about 10 times greater than the dipole-induced dipole interactions on a PYE column so that the retention now also depends on the effective dipole moment of the stationary phase. Interestingly, in a comparison of M@C82 and M2@C82 (M ) Sc, Y, La) on this column it was found that the dimetal species are more weakly retained.54 Systematic measurements of M2@C80 retention on a Buckyclutcher column have yet to be performed. A clear understanding of such differences between columns will ultimately require definite measurements of the dipole and higher multipole moments of M@C82 species. Such measurements are in progress.55 6. Conclusions HPLC retention relationships between empty and doped fullerenes and a PYE stationary phase were studied in detail. As has previously been observed for this and other apolar

Elution Behavior of Endohedral Metallofullerenes stationary phases, the retention times of empty fullerenes show a linear relationship with regard to the number of π-electrons. The retention mechanism for M@C82 (M ) La, Y, Ce, and Gd) can be quite well understood in terms of charge-induced dipole and dispersion interactions, allowing inferences about the charge transfer in these molecules and their effective dipole moments. This knowledge is of use for further improvements regarding the separation of new endohedral metallofullerenes on a PYE stationary phase. Acknowledgment. Financial support by the Bundesministerium fu¨r Bildung und Forschung under the “Pilotprogramm Fullerene” is gratefully acknowledged. We thank H. Shinohara and S. Nagase for providing preprints prior to publication. References and Notes (1) Shinohara, H.; Inakuma, M.; Hayashi, N.; Sato, H.; Saito, Y.; Kato, T.; Bandow, S. J. Phys. Chem. 1994, 98, 8597. (2) van Loosdrecht, P.; Johnson, R.; de Vries, M.; Kiang, C.; Bethune, D.; Horn, H.; Burbank, P.; Stevenson, S. Phys. ReV. Lett. 1994, 73, 3415. (3) Shinohara, S.; Yamaguchi, H.; Hayashi, N.; Sato, H.; Ohkohchi, M.; Ando, Y.; Saito, Y. J. Phys. Chem. 1993, 97, 4259. (4) Kikuchi, K.; Suzuki, S.; Nakao, Y.; Nakahara, N.; Wakabayashi, T.; Shiromaru, H.; Saito, K.; Ikemoto, I.; Achiba, Y. Chem. Phys. Lett. 1993, 216, 67. (5) Yamamoto, K.; Funasaka, H.; Takahashi, T.; Akasaka T. J. Phys. Chem. 1994, 98, 2008. (6) Park, C. H.; Wells, B. O.; DiCarlo, J.; Shen, Z. X.; Salem, J. R.; Bethune, D. S.; Yannoni, C. S.; Johnson, R. D.; deVries, M. S.; Booth, C.; Bridges, F.; Pianetta, P. Chem. Phys. Lett. 1993, 213, 196. (7) Wang, X.; Hashizume, T.; Xue, Q.; Shinohara, H.; Saito, Y.; Nishina, Y.; Sakurai, T. Chem. Phys. Lett. 1992, 216, 409. (8) Shinohara, H.; Hayashi, N.; Sato, H.; Saito, Y.; Wang, X.; Hashizume, T.; Sakurai, T. J. Phys. Chem. 1993, 97, 13438. (9) Wang, X.; Xue, Q.; Hashizume, T.; Shinohara, H.; Nishina, Y.; Sakurai, T. Phys. ReV. B 1993, 48, 15492. (10) Ru¨bsam, M.; Plu¨schau, M.; Schweitzer, P.; Dinse, K. P.; Fuchs, D.; Rietschel, H.; Michel, R. H.; Kappes, M. M. Chem. Phys. Lett. 1995, 240, 615. (11) Takata, M.; Umeda, B.; Nishibori, E.; Sakata, M.; Saito, Y.; Ohno, M.; Shinohara, H. Nature 1995, 377, 46. (12) Shinohara, H.; Inakuma, M.; Kishida, M.; Yamazaki, S.; Hashizume T.; Skurai, T. J. Phys. Chem. 1995, 99, 13769. (13) Laasonen, K.; Andreoni, W.; Parrinello, M. Science 1992, 258, 1916. (14) Nagase, S.; Kobayashi, K.; Kato, T.; Achiba, Y. Chem. Phys. Lett. 1993, 201, 475. (15) Fuchs, D; Rietschel, H.; Michel, R. H.; Benz, M.; Fischer, A.; Kappes, M. M. in Physics and Chemistry of Fullerenes and DeriVatiVes, Proceedings of the IWEPNM 1995; Kuzmany, H., Fink, J., Mehring M., Roth, S., Eds.; World Scientific: Singapore, New Jersey, London, and Hong Kong, 1995; p 105. (16) Kimata, K.; Hosoya, K.; Araki, T.; Tanaka, T. J. Org. Chem. 1993, 58, 282. (17) Achiba, Y. Private communication. (18) For a sample purity of >96%, a second separation step must be carried out. For this we have again used either a PYE column (for the separation of La- and Ce@C82) or a Buckyclutcher I column (for the separation of Y- and Gd@C82), depending on the endohedral fullerene and its retention time relative to close lying empty cage fullerenes. (19) Welch, C. J.; Pirkle, W. H. J. Chromatogr. 1992, 609, 89. (20) Poirier, D. M.; Knupfer, M.; Weaver, J. H.; Andreoni, W.; Laasonen, K.; Parrinello, M.; Kikuchi, K.; Achiba, Y. Phys. ReV. B 1994, 49, 17403. (21) Kaliszan, R. QuantitatiVe Structure-Chromatographic Retention Relationships in Chemical Analysis; Winefordner, J. D., Ed.; John Wiley & Sons: New York, 93, 1987; Vol. 93. (22) ∆G° originates from intramolecular interactions between the analyte and the two separation phases, e.g., stationary and mobile phases. In the case of nonreversed phase HPLC, molecular interactions with the eluent can be neglected to first order.

J. Phys. Chem., Vol. 100, No. 2, 1996 729 (23) See for example, the following. Ruoff, R.; Hickman, A. J. Phys. Chem. 97, 1993, 2494. Han, K.-Li; Lin, H.; Gallogy, E.; Jackson, W. Chem. Phys. Lett. 1995, 235, 211. (24) There is an experimental determination of the molecular polarizability of C60 (90.6 Å3) from solid state probes: Hebard, A.; Haddon, R.; Fleming R.; Kortan, A. Appl. Phys. Lett. 1991, 59, 2109. This is in reasonably good agreement with the ab initio calculation for the isolated species (78.8 Å3)ssee ref 25. (25) Ha¨ser, M.; Ahlrichs, R.; Baron, H. P.; Weis, P.; Horn, H. Theor. Chim. Acta 1992, 83, 455. (26) Ahlrichs, R.; Ba¨r, M.; Ha¨ser, M.; Horn, H.; Ko¨lmel, C. Chem. Phys. Lett. 1989, 154, 165. (27) Bakowies, D.; Kolb, M.; Thiel, W.; Richard, S.; Ahlrichs, R.; Kappes, M. M. Chem. Phys. Lett. 1992, 200, 411. (28) Scha¨fer, A.; Horn, H.; Ahlrichs, R. J. Chem. Phys.1992, 97, 2571. (29) Spackman, M. H. J. Chem. Phys. 1993, 93, 7594. (30) Wang, F.; Jiang, Y.; Jiang, D.; Wang, W. J. Chromatogr. Sci. 1995, 33, 71. (31) Anacleto, J. F.; Quilliam, M. A. Anal. Chem. 1993, 65, 2236. Klute, R. C.; Dorn, H. C.; Mc Nair, H. M. J. Chromatogr. Sci. 1992, 30, 439. (32) Steger, H.; Holzapfel, J.; Hielscher, A.; Kamke, W.; Hertel, I. V. Chem. Phys. Lett. 1995, 234, 455. (33) We plot only these isomers resolved on the semipreparative Cosmosil column. (34) Cox, D. M.; Behal, S.; Disko, M.; Gorum, S. M.; Greany, M.; Hsu, C. S.; Kollin, E. B.; Millar, J.; Robbins, W.; Sherwood, R. D.; Tindall, P. J. Am. Chem. Soc. 1991, 113, 2940. (35) Wise, S. A.; Bonnett, W. J.; Guenther, F. R.; May, W. E. J. Chromatogr. Sci. 1981, 19, 457. (36) Haselmeier, R.; Holz, M.; Kappes, M. M.; Michel, R. H.; Fuchs, D. Ber. Bunsenges. Phys. Chem. 1994, 98, 878. (37) Weaver, J. H.; Chai, Y.; Kroll, G. H.; Jin, C.; Ohno, T. R.; Haufler, R. E.; Guo, T.; Alford, J. M.; Concaicao, J.; Chibante, L. P. F.; Jain, A.; Palmer, G.; Smalley, R. E. Chem. Phys. Lett. 1992, 190, 460. (38) Funasaka, H.; Sugiyama, K.; Yamamoto, K.; Takahashi, T. J. Phys. Chem. 1995, 99, 1826. (39) Shinohara, H.; Kishida, M.; Nakane, T.; Kato, T.; Bandow, S.; Saito, Y.; Wang, X.; Hashizume, T.; Sakurai, T. Proceedings of the Symposium on Recent Advances in the Chemistry and Physics of Fullerenes and Related Materials. Electrochem. Soc. Proc. 1994, 94-24, 1361. (40) Kikuchi, K.; Suzuki, S.; Nakao, Y.; Nakahara, N.; Wakabayashi, T.; Shiromaru, H.; Saito, K.; Ikemoto, I.; Achiba, Y. Chem. Phys. Lett. 1993, 216, 67. (41) Kikuchi, K.; Nakao, Y.; Suzuki, S.; Achiba, Y. J. Am. Chem. Soc. 1994, 116, 9367. (42) Wang, Y.; Tomanek, D.; Ruoff, R. S. Chem. Phys. Lett. 1993, 208, 79. (43) Nagase, S.; Kobayashi, K. Chem. Phys. Lett. 1993, 214, 57. (44) Yeretzian, C.; Hansen, K.; Alvarez, M. M.; Min, K. S.; Gillan, E. G.; Holczer, K.; Kaner, R. B.; Whetten, R. L. Chem. Phys. Lett. 1992, 196, 337. (45) Fowler, P. W. Chem. Phys. Lett. 1986, 131, 444. (46) Nagase, S.; Kobayashi, K. Chem. Phys. Lett. 1994, 231, 319. (47) Microscopically the r’s in expressions 2 and 3 are different for the same cage-stationary phase separation. We treat them as identical for simplicity. (48) Measurements and calculations suggest that endohedral metallofullerenes have IP’s that are about 1 eV lower than those of empty cage congeners. For invariant r’s this would make the dipole-induced dipole effect stronger. (49) Maitland, G. C.; Rigby, M.; Smith, E. B.; Wakeham, W. A. Intermolecular Forces; Clarendon Press: Oxford, 1981. (50) See, for example, Handbook of Chemistry and Physics, 60th ed.; CRC Press: Boca Raton, FL, 1976. (51) Kobayashi, K.; Nagase S.; Takasaka, T. Chem. Phys. Lett. 1995, 245, 230. (52) Michel, R. H.; Benz, M.; Fischer, A.; Fuchs, D.; Rietschel H.; Kappes, M. M. In preparation. (53) This column was also studied by our group. (54) Dorn, H.; Stevenson, S.; Burbank, P.; Sun, Z.; Glass, T.; Harich, K.; Loosdrecht, P. V.; Johnson, R.; Beyers, R.; Salem, J.; De Vries, M.; Yannoni, C.; Kiang, C.; Bethune, D. MRS Proccedings, 1994. (55) Fuchs D. In preparation.

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