13830
J. Phys. Chem. 1995,99, 13830-13833
Electronic Structure and Spectroscopy of the Five Most Stable Isomers of
cy8
Fullerene
Rajiv D. Bendale* and Michael C. Zerner" Quantum Theory Project, University of Florida, Gainesville, Florida 3261 1-8435 Received: May 24, 1995@
Of the many possible isomers of c78 fullerene, five isomers, thought to be the most stable, have been examined using the semiempirical intermediate neglect of differential overlap INDO/1 and INDO/S models. Two of these structures have C2v symmetry, two have D3h symmetry, and one has 0 3 symmetry. An equilibrium geometry has been obtained for each of these isomers, and the relative stability has been determined. The electronic spectra have been computed using the INDOIS CI-singles model. The calculated spectra have been analyzed and compared to recent experimentally obtained ~ p e c t r aconfirming ,~ that the lowest energy isomers are of C2u and D3 symmetry.
Introduction The initial discovery of has since triggered a remarkable interest in other fullerene systems. The detection of c60 in mass spectrometers has shown the simultaneous presence of a host of other carbon cage structures like c70, c78, and c80. Recently Fowler and Manolop~ulos,~ using graph theoretic algorithms6 found that, for the case of c78, there were five possible structures satisfying the isolated pentagon rule and predicted, on the basis of qualitative MO theory, that the D3h isomer would be the most stable. The five possible isomers they identified include two of C2u symmetry, two of D3h symmetry, and one of D3 symmetry. Diederich et isolated two forms of the c 7 8 isomers in a 5:l ratio with better than 98% purity and have characterized these two isomers using NMR and UV/visible spectroscopies. Their study of the isolated two isomers indicates that the most likely structures are of C2v and D3 symmetry with the major fraction isolated having C2v symmetry. The isolated C2v isomer shows 21 distinct NMR resonances, and the 0 3 isomer shows 13 distinct resonances. More recently, Kikuchi et a1.,8 have identified the presence of the two distinct C2uisomers of c78, characterized by the presence of 21 and 22 distinct NMR resonances, along with the 0 3 isomers in a 5:2:2 ratio. However, in this case too, the D3h isomers were not observed. In the present article we examine the five possible structures using the intermediate neglect of differential overlap INDO/19 and INDO/Sl0*l1models. We shall follow the naming convention of Diederich et al. for identifying the isomers under consideration.
c18 %v
Figure 1. C2visomers of
G18 C i V C7g.
c18 q h
Results and Discussion Figures 1 through 3 show the structures of the five isomers of c78. Diedrich et al. first noted that the isomers with C2vand D3h symmetry are related to each other through a very intriguing 90" rotation of a C2 unit comprised of two adjacent carbon atoms, a so-called four-electron pyracylene rearrangement, first suggested by Stone and Wales12 for Cm. This single-step rearrangement can sequentially generate four of the c 7 8 isomers C2v C'2v D'3h. The equilibrium as follows: D3h geometry for each of the five isomers was obtained using the INDO/1 model and was subsequently used for computing the electronic spectrum using the INDO/S model. Table 1 lists the relative stability of the five isomers within the INDO/l model
- - -
@
Abstract published in Advance ACS Abstracts, August 15, 1995.
0022-3654/95/2099-13830$09.00/0
c18 4
h
Figure 2. D3h isomers of C7g. along with the number of distinct NMR resonances expected. From this table one can conclude that the C2visomer, that with 21 NMR resonances, is the most stable one. The higher energy C2v, with 22 NMR resonances, is calculated to be 2 kcaVmo1 higher in energy. The stability of the isomers that we calculate is in the order C2u > C2v> D3 > D3h > D'3h. This ordering, based on the total energy within the INDO/l model, is to be compared with the results of Raghavchari and RholfingI3from single-point calculations, C2v > D3 > C 2 v > D3h > D'3h, and Colt and Scuseria,I4C2v> C2v> D3 > D3h > D'3h. The former calculations are 6-3lG*(5d)//STO-3-21G, and the latter are DZP/ /STO-3G. Differences between the ab-initio ordering are as likely due to differences in geometry than to the relative energies calculated with these different basis sets at these optimal 0 1995 American Chemical Society
Five Most Stable Isomers of
c78
J. Phys. Chem., Vol. 99, No. 38, 1995 13831
Fullerene
.d
0
0.40
I
\
gE
z
0.00
300 350 400 450 500 550
600
650 700 750
850 900
800
h nm Figure 3. D3 isomer of
Figure 5. Calculated electronic spectrum in
c78.
c 7 8
in D3 geometry by
1
1
the INDO/S model. ,
1
1
1
1
-[ D
- .....211
300 350 400 450 500
550 600
650 700 750 800
850 900
h nm Figure 4. Calculated electronic spectrum of
in C2u and C'zU geometry by the INDOIS model. The solid line represents the computed spectrum of C2,,, and the dashed line represents the spectrum of the C2uisomer. c 7 8
TABLE 1: Relative Stabifities of the Five Isomers of C,8 Computed within the INDO/l Model. For a Comparison We List the Relative Energy for the ab-Znitio Results of Raghavachari and Rholfing13and Colt and Scuseria.14 The Cz, Isomer, Following the Convention of Diedrich et a1.: Is the Most Stable One ~~
~~~~
relative energy (kcaVmo1) isomer
I3C NMR lines
INDO/l
ref 13
ref 14
c2u
21 22 8 8 13
0.0 2.1 18.1 23.7 9.7
0.0 4.0 7.2 20.2 3.4
0.0 1.6 9.8 16.4 6.0
c 2 u
D3h
D'3h
D3
geometries. Only the relative ordering of the 0 3 h structure obtained by the INDO scheme seems at odds with these obtained through the ab-initio calculations (Table 1). On the other hand, the INDO geometries obtained for Cm are competitive with triple-5 calculations and are more accurate when compared with experiment than either STO-3G or STO-3-21G.I5 The electronic spectrum for each of the isomers has been computed using the INDOE model with the SCF followed by a CI-singles (CIS) calculation. A large density of states is observed for the C2visomers. We report only the transitions with oscillator strengths larger than 0.05 in tabular form after the first allowed transition. A more complete visualization of the data can be made in graphical form as seen from Figures 4-6. A comparison between the experimental spectrum7 for the C2visomer and the calculated spectrum for C2vand the C2v isomers examined here can be found in Table 2. The main feature that distinguishes the two isomers is the presence of the first forbidden transition for the C2vspecies at 14.7 kK (1 kK = 1000 cm-l) whereas the C 2 v species shows a weak first
............... .... ................ I I .........1.........
h nm Figure 6. Calculated electronic spectrum of
c 7 8 in D3h and D'3h geometry by the INDO/S model. The solid line represents the computed spectrum of D 3 h , and the-dashed line represents the spectrum of the D'3h isomer.
allowed transition at 12.2 kK. The oscillator strengths and transition energy for the C2v species, especially between 250 and 450 nm, are in good agreement with experiment with the calculated energies being somewhat higher. The experimental spectrum for the C2vspecies is still not known. It is interesting to see the effect of a single rotation of a C2 unit on the computed electronic spectrum of the two C2visomers. From Table 2 one notices that the first computed transition energy for the lower energy C2v isomer is an electric dipole forbidden transition, whereas the first transition in the case of C2vis an allowed one, although lower in energy by 2.5 kK. The transition at 18.3 kK (labeled I11 in Table 2), in the case of C 2 v isomer appears to be five times more intense when compared to the one at 18.5 kK for C2v. The two isomers show the same bands at 22,25.5, and 26 kK with approximately the same intensities as can be' seen from Table 2 (bands labeled IV, V, and VI) and Figure 4. Beyond 30 kK however the C2, isomer has the more intense transitions (bands labeled VII-IX in Table 2). The computed electronic spectrum for the 0 3 species is in reasonable agreement with experiment. Table 3 shows the computed spectrum compared with the experimental one. The main differences lie in the 820 to 700 nm region. The first transition computed is an allowed one at 10.6 kK (940 nm) followed by a reasonably strong transition at 14.6 kK (685 nm) (see Figure 5). The corresponding transition is not observed with the same intensity in the experiment. The broad weak bands observed between 768 and 734 nm are not reproduced by these calculations. The computed spectrum shows the transitions at 27.7 and 28.0 kK to be in agreement with experiment. The peak at 3 1.1 kK seen experimentally appears
13832 J. Phys. Chem., Vol. 99, No. 38, I995
Bendale and &mer
TABLE 2: CIS Spectrum of the CzUIsomers Computed within the INDOlS Model in kK. The Size of the Active Space Used for the CIS Calculation is 23 Occupied Orbitals for Both Species, 23 Virtual Orbitals for the Czu,and 22 Virtual Orbitals for C'zu. The Numbers in Parentheses Are Oscillator Strengths for the Computed Spectra and Are Extinction Coefficients in L mol-' for the Ex~eriment~ C'2e C2" experiment kK nm kK nm kK nm 12.22 (0.27) 15.61 (0.018) 17.45 (0.003) 18.33 (0.085) 18.40 (0.042) 18.96 (0.036) 19.90 (0.011) 22.13 (0.057) 23.72 (0.028) 23.80 (0.015) 24.07 (0.030) 25.07 (0.022) 25.31 (0.081) 25.48 (0.088) 26.37 (0.031) 26.89 (0.035) 27.67 (0.048) 28.23 (0.031) 29.34 (0.058) 29.78 (0.039) 29.91 (0.037) 30.11 (0.037) 31.26 (0.031) 32.42 (0.073) 32.78 (0.047)
I I1
818 64 1 573 545 544 528 502 452 422 420 416 399 395 393 379 372 361 354 34 1 336 334 332 320 308 305
111
IV
V
VI VI1 VI11
IX X
14.64 15.98 (0.013) 17.19 (0.13) 18.48 (0.016) 21.52 (0.057) 23.16 (0.016) 24.06 (0.017) 24.18 (0.055) 25.67 (0.080) 25.93 (0.027) 26.70 (0.012) 26.94 (0.018) 27.16 (0.010) 29.19 (0.087) 29.84 (0.074) 30.06 (0.035) 30.52 (0.025) 30.69 (0.126) 30.77 (0.045) 32.21 (0.048) 32.39 (0.038) 33.00 (0.030) 33.15 (0.027)
TABLE 3: Comparison between Experiment' and the computed CI-Singles-Only Spectrum of Cn 0 3 Isomer Using 23 Occupied and 30 Virtual Orbitals. The Experiment Shows a Number of Very Weak Bands between 820 and 700 nm of Which Only a Weak Transition Is Calculated at 940 nm. For Transitions Higher in Energy Than 28 kK, Only Those Transitions with Oscillator Strengths Larger Than 0.050 Are Shown computed spectrum experiment kK A2 E E A2 A2 A2 E A2 E E E E E E E
10.64(0.0005) 14.60 (0.081) 16.17 (0.013) 21.58 (0.011) 22.09 (0.041) 22.70 (0.027) 24.78 (0.025) 25.67 (0.261) 27.74(0.135) 28.02 (0.049) 29.88 (0.093) 30.36 (0.052) 32.20 (0.078) 32.58 (0.05 1) 32.91 (0.096)
E
33.47 (0.088)
E E A2 E A2 A2 A2 E
34.10 (0.147) 34.85 (0.175) 34.99 (0.059) 35.33 (0.061) 35.45 (0.123) 36.48 (0.057) 37.14 (0.142) 37.47 (0.263)
nm I
940 I1 685 618 I11 464 453 44 1 IV 404 390 V 361 357 VI 335 329 311 307 304 299 VI1 293 287 286 283 VI11 282 274 269 267
kK
nm
12.20 I 14.29 I1
820,768,757,734 700
21.19
111
472
27.62 28.09
IV V
362 356
36.23
322
VI1 276
at 32.2 kK in the computed spectrum. The observed transition at 37.14 kK is calculated at 36.23 kK. The computed spectra for the two D3h isomers are reported in Table 4 and in graphical form in Figure 6. There are several features that are immediately noticeable from Table 4. The calculated spectrum for the D3h isomer contains a first transition
683 626 582
I1 111
14.37 (3400) 15.67 (4000)
696 638
I I1
18.94 (11500)
528
111
23.59 (23800)
428
IV
25.64 (25500)
390
V
27.17 (30300) 27.86 (30800)
368 359
VI VI1
30.77 (42700)
325
VI11
32.47 (44400)
308
IX
541
IV
465 432 416 414 390 386 375 371 368 343 335 333 328 326 325 311 309 303 302
V
VI
VI1 VI11
IX
TABLE 4: Computed CI-Singles Spectrum for the Two Isomers with Du, Symmetry, Not Yet Seen in the Experiment. The Calculation Uses 23 Occupied orbitals for Both Species and 22 and 24 Virtual Orbitals for the D'u,and Du, Species, Respectively Dr3h
D3h
B2 E" E" B2 E' BI E' BI E' BI E' E'
E' 31.06 VI
I
BI E' E' BI BI
kK
nm
16.30 17.76 18.57 18.80 19.17 (0.006) 26.93 (0.306) 30.82 (0.1 12) 32.86 (0.130) 33.05 (0.403) 33.58 (0.152) 33.59 (0.210) 34.81 (0.313) 36.17 (0.124) 36.69 (0.292) 37.92 (0.352) 38.34 (0.181) 38.70 (0.131) 39.32 (0.668)
614 563 539 532 521 371 324 304 303 298 298 287 277 273 264 26 1 258 254
E" A2
E" BI B1 BI E' E' E' E' BI BI E' BI E' B1 E'
kK
nm
11.36 12.49 14.96 15.10 (0.116) 16.36 (0.146) 23.31 (0.109) 24.46 (0,149) 25.70 (0.188) 31.83 (0.147) 33.67 (0.318) 35.67 (0.768) 37.16 (0.117) 37.57 (0.158) 38.51 (0.131) 39.07 (0.494) 39.50 (0.346) 40.01 (1.005)
880 801 668 662 61 1 429 409 389 314 297 280 269 266 260 256 253 250
at 16.3 kK which is electric dipole forbidden. This might be compared to the much lower energy forbidden transition of 11.4 kK for the D'3h isomer. The f i s t allowed transition for the D3h isomer is 4 kK higher in energy compared to that of D'3h. Considering the one-step pyracylene rearrangement which yields the D3h from (see Figure 7), we see some similarity between their two spectra. In agreement with ab-initio calculations, the three most stable structures we calculate are of CZ,, CzU,and D3 symmetry. Although the computed spectra of the Czu and D3 structures agree remarkably with experiment, we find it difficult to use the spectrum to identify or distinguish between the two species. Our predictions are generally within 2000 K of the experimental
Five Most Stable Isomers of
c78
J. Phys. Chem., Vol. 99, No. 38, 1995 13833
Fullerene
References and Notes
T
?3h
ClScLv
Figure 7. Representation of the one-step pyracylene rearrangement transforming isomers of from C2”into D3h symmetry.
value, but this is not fine enough resolution to make assignments of spectra to individual species. Acknowledgment. This work was supported in part through a grant from the Office of Naval Research.
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JP95 1450U
