Theoretical study of buckminsterfullerene derivatives C60Xn (X=H, F; n=2, 36, 60)

Volume 193, number 2,3

CHEMICAL PHYSICS LETTERS

Theoretical study of buckminsterfullerene CbOXn (X=H, F; n=2, 36, 60) Dirk

Bakowies

and Walter

1 May 1992

derivatives

Thiel

Theoretische Chemie, Universitiit GH Wuppertal, W-5600 Wuppertal1, Germany Received 10 February 1992; in final form 27 February I992

Semi-empirical SCF calculations at the MNDO, AM 1, and PM3 levels are reported for the title compounds. The predicted relative stabilities are discussed for all 18 clusters studied. The calculated equilibrium geometries and vibrational spectra are presented for C6oX36( Th) and &,X& Ih ) . Contrary to a previous suggestion, C6,,He0and &,FbO prefer an icosahedral Ih structure over a distorted I structure. The calculated bond dissociation enthalpies, equilibrium bond lengths, and vibrational frequencies indicate a reduced C-X bond strength in C6oX6O (I,,).

1. Introduction Buckminsterfullerene Cbo [ 1 ] has recently become accessible in macroscopic quantities [2] which facilites the exploration of its chemistry [3-l 11. Among the simplest derivatives yet reported are GoH+ [5I, G&b [3 I, and c&60 16 I. The b drogenation of Cho to C60H36 via a Birch reduction is fully reversible, and C60H18 is detected as a byproduct [ 3 1. The fluorination of Ceo with fluorine gas proceeds in a stepwise manner [ 61, and mass spectra show a number of intermediates, the most stable one being apparently C60F36 [ 7 1. A single line 19F NMR spectrum indicates an icosahedral structure for C60F60, either of I,, or I symmetry [ 6 1, and it has been suggested that the latter alternative with a chiral equilibrium geometry should be favored due to relief of steric strain [ 12 1. On the theoretical side, the I,, equilibrium structures of C60H60 and ChOFeOhave been obtained at the ab initio SCF level [ 13,141 and by local density functional (LDF) calculations [ 151. C60H36 and other &H,, species have been studied using empirical potentials [ 151 which indicate that outward bonding for all hydrogen atoms is not always energetically preferred. Molecular mechanics MM3 calculations for a large number of inside/outside stereoisomers of &He0 predict the minimum energy 236

isomer to have ten hydrogens inside with C, symmetry [16]. In continuation of our previous work on large carbon clusters [ 17,18 ] the present paper reports semiempirical calculations on the structures, stabilities, and vibrational spectra of hydrogenated and fluorinated buckminsterfullerene species.

2. Computational

details

Closed-shell SCF calculations were carried out using the standard MNDO [ 191, AM 1 [ 20,211, and PM3 [ 221 parameters and our current semi-empirical program [ 23 1. Molecular geometries were completely optimized within a given point group. The force constants and dipole moment derivatives were evaluated by finite difference at the optimized geometries. The harmonic vibrational frequencies and the infrared intensities were determined from these data by standard procedures [ 241. The generation of the initial input geometries in a chosen point group and the symmetry assignment of the normal modes were handled automatically with the use of a program specifically designed for such purposes [ 2 5 1.

0009-2614/92/$ 05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.

1 May 1992

CHEMICAL PHYSICS LETTERS

Volume 193, number 2,3

3. Results and discussion Optimized geometries and the corresponding heats of formation were calculated at the MNDO, AMl, and PM3 levels for all 18 clusters studies, in order to assess the range and consistency of the semi-empirical predictions. This was considered to be particularly important for the fluorine-containing compounds where the errors in the semi-empirical results are usually greater than in the case of hydrocarbons [ 19-221. A force constant analysis was performed only for selected molecules, mostly at the MNDO level in analogy to previous work [ 181. Table 1 lists the calculated heats of formation. As indicated in the second column, several geometry optimizations proceeded from a lower-symmetry input structure to a higher-symmetry final structure. This applies especially to C60H60and C6,,Fb0where reasonably distorted input geometries of I symmetry always optimize towards I,, geometries. The resulting Ii, structures are confirmed to be minima on the potential surface by force constant analysis (see be-

low). When I symmetry is enforced for C60F60in a reaction path calculation where the torsional coordinate of the fluorine atoms is changed from its I,, value in increments of 2” and the remaining five geometrical variables are optimized, the calculated MNDO heats of formation rise sharply. Hence we do not find any evidence for the postulated [ 12 ] C6,,F6,, minimum with I symmetry. At the semi-empirical level both C6,,H6,,and CbOFbOprefer an I,, equilibrium structure. Table 1 includes data on the relative stability of several isomers. All methods predict for C&X2 with two neighboring atoms X = H, F that it is energetically more favourable by 15 19 kcal/mol to add these atoms to a CC bond shared by two hexagons (I) rather than to one shared by a pentagon and a hexagon (II). The most stable of the four C60X36isomers considered (X = H, F) is the proposed [ 3,151 Th species (I) with twelve isolated C=C double bonds, one in each pentagon. Shifting one of these C=C double bonds to the a position in the pentagon yields isomer (II) which is calculated to lie only 6

Table 1 Calculated heats of formation (kcal/mol) Point group ‘)

MNDO

AM1

PM3

C

Ill

C::H+ CLOHZ(1)

G-G G-G” G-K Th Cl G CZh

869.3 1039.3 828.3 844.4 232.9 238.5 242.1 261.7 286.7 166.6 756.9 771.4 -917.2 -915.5 - 903.5 -861.4 - 802.2 - 1359.0

973.3 1152.1 931.2 950.0 320.1 325.8 329.0 348.0 335.0 70.8 864.8 883.0 - 898.0 - 894.7 -887.2 -852.6 - 1409.2 - 1769.4

811.7 991.1 776.1 794.5 263.1 269.4 272.6 291.1 331.2 73.5 703.3 721.1 - 1086.4 - 1081.8 - 1073.7 - 1034.3 - 1708.2 -2073.3

Molecule

Cd2 (11) G&6 (1) GJ-L (11) C60H36

(III)

GOH36

(IV

C6OH60

(1)

C6&60

( 11)

C6ob

(1)

C6oh

(11)

C60F36

(1)

&OF36

(11)

&OF36

(III)

GOF36

(IV

C6OF60

(1)

C6OF60

(11)

)

1

I-+II, C, GG” C,-C, Th Ci C, CZh I+Ih CI

Footnote

b) b) cl d) d) e) f) b) b) c)

d) d) e) f)

‘) If there are two entries, the first one refers to the input geometry, and the second one to the optimized final geometry. b, Two vicinal atoms X=H, Fat a CC bond shared either by two hexagons (I) or by a pentagon and a hexagon (II). C) Seerefs. [3,15]. ‘) Compared with the Th structure (I) the CC double bond in one pentagon is shifted by one (II) or two (III) positions, respectively. ‘) Ten CC double bonds in ten different pentagons and two CC double bonds shared by two hexagons. f, See ref. [ 161, 10 atoms X = H, F pointing inside, same topology as in ref. [ 16 1.

237

Volume 193, number

2,3

CHEMICAL

PHYSICS

kcal/mol (X=H) or 2-5 kcal/mol (X=F) above (I). Isomer (III) with a corresponding shift to P-POsition is less stable than (I) by 9 kcal/mol (X=H) and 11-14 kcal/mol (X=F), respectively. Obviously many other such isomers can be generated by simultaneous shifts of C=C double bonds in different pentagons so that we may expect many low-energy C6oX36isomers. It seems energetically less favorable in Ce0X36to have C=C double bonds shared by two hexagons since isomer (IV) with two such double bonds lies appreciably higher than (I), by 28-29 kcal/mol for X=H and 45-56 kcal/mol for X=F. In the case of C6,,H60the semi-empirical calculations confirm the MM3 force-field prediction [ 161 that the C, isomer (II) with ten hydrogen atoms inside the cage is much more stable than the I,, isomer (I), by 120-264 kcal/mol (MM3: 402 kcal/mol). An analogous situation is encountered for &Fe,, where the calculated energy differences of 360-557 kcal/ mol are even higher. The complete fluorination of C6,,to &,FGO [ 61 will yield an all-outside isomer like (I ), of course, as long as the cage remains intact during the reaction which is normally observed in CeO chemistry [ 3- 111. Hence, the direct formation of an inside isomer would seem unlikely. Table 2 Heats of reaction

per bond: AAHr/N

(kcal/mol)

1May 1992

LETTERS

Table 2 lists the heats of several formal reactions per bond, i.e. per broken C-X bond in reactions ( l)( 12) and per transferred C-X bond in reactions ( 13)-( 18). It should be noted that the semi-empirical heats of formation for atoms (see reactions ( l)( 11) are correct by definition [ 191 and that the experimental heat of formation is also used for H+ in reaction ( 12) following the usual practice [ 261. For the reference reactions ( 1 ), (2), ( 7 ) and (8) involving small molecules, there is excellent agreement between the theoretical and experimental [ 27,281 heats. The observed proton affinity of C6,, [ 51 from reaction ( 12) is reproduced with acceptable accuracy. Comparing the results for reactions (2)-( 5) the calculated C-H bond dissociation enthalpies for C60H36are similar to those for the reference molecule CzHs, while those for Cb0H2 are slightly higher and those for CbOHhOappreciably lower. The C-H bonds in C6,,HS6are predicted to be stronger than in &H6,, by 7-8 kcal/mol, in agreement with the LDF value of 7 kcal/mol [ 151 which is based on LDF bond dissociation energies of 72 and 65 kcal/mol for reactions (4) and ( 5 ), respectively. It has been stated in the LDF study [ 15 ] that the C-H bond strenghts are reduced by 44% in going from CH4 to C60H60

‘)

No.

Reaction

N

MNDO

AM1

PM3

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18)

CH4+C+4H C2H6+C2H4+2H CG0H2-+C6,,+2H C60H36+C60+ 36H C60Hh0-’ C6,, + 60H CF,+C+4F CH3-CHF2+C2H4+2F CH2F-CH2F+C2H4 + 2F C6,,F2-+&,+2F Ce,~F36+C~~+36F C60F,0+C60+60F C60H+--Z6,+H+ C60+ 18C2H6-+C6,,H36+ 18C2H4 &+ 18C2F6+C60F36+ 18C2F4 GoHx + 6W+GoFx + 6CzH6 C6,,+ 30C2H6+C60H60+ 30C2H4 C60+3OC2F6-+C@JF60+ 30CzF4 C60Hb0+ 10C2F6+C6,,F6,,+ lOCzH6

4 2 2 36 60 4 2 2 2 36 60 1 36 36 36 60 60 60

97.8 69.1 72.6 69.8 61.8 115.2 83.3 81.6 75.1 68.5 46.1 197.2 -0.1 12.3 14.7 7.9 34.1 28.5

97.0 69.0 73.2 70.2 62.7 118.0 86.4 84.3 73.2 70.8 58.6 188.4 -1.2 17.1 15.5 6.3 29.3 20.2

98.1 69.5 69.9 67.3 60.1 117.9 83.2 78.2 73.1 71.6 60.9 187.8 2.1 22.1 12.5 9.4 32.8 16.0

‘) The entries for &,X2,

C60X36, and C6,,X6,, (X = H, F) always refer to isomer (I) in table 1.

b, From refs. [27,28] unless noted otherwise. ‘) At the lower end of the range 204-207

238

kcal/mol,

see ref.

[ 51.

Exp. ” 99.3 68.4

117.4 84.5

204 ‘)

1 May 1992

CHEMICAL PHYSICS LETTERS

Volume 193, number 2,3

which, in our opinion, is misleading since reaction ( 5 ) should properly be compared with reaction ( 2 ) and not with reaction ( 1). Relative to CzH6 the CH bonds in C6,,Hh0are found to be weaker by only 9- 13%. Similar comparisons for reactions (7 )- ( 11) show that the calculated C-F bond dissociation enthalpies are always significantly lower in the fluorinated clusters than in difluoroethane, with larger differences than in the corresponding C-H bond dissociation enthalpies (see above) which reflects the higher steric strain associated with fluorine. The C-F bonds in CbOFeO are calculated to be particularly weak. The results for the exchange reactions ( 13 )- ( 18 ) again indicate that, in a relative sense, hydrogenation of Ceo to CeOH,,(n = 36,60) is energetically more favorable than the analogous fluorination to C6,,Fn.For the isodesmic reaction ( 18) the ab initio 6-3 lG** SCF value of 16.8 kcal/mol [ 141 is close to the PM3 value of 16.0 kcal/mol. The corresponding MNDO value of 28.5 kcal/mol thus appears to be too high probably due to an exaggeration of the nonbonded repulsions between the fluorine atoms. Table 3 and 4 contain the calculated equilibrium geometries for C60X60and C60X36 (X=H, F) in I,, and T,, symmetry with four and thirteen indepen-

dent geometrical variables, respectively. A comparison between the available ab initio SCF [ 13,141 and LDF [ 15 ] structures for C6,,Xsoand our current semiempirical results in table 3 shows a reasonable overall agreement. All methods predict a significant lengthening of the CC bonds when going from CbOHeO to CeOFeO(by 0.06 kO.03 A) and almost identical XCC bond angles. MNDO yields extremely long CC bonds in CeOFeOwhich are considered to be overestimated judging from the known error in C2F6 [ 221, even though the best ab initio estimate of 1.627 8, for these CC bond lengths is also quite high [ 141. The predicted semi-empirical structures for C60X36in table 4 are expected to be of similar accuracy as those for C6,,X60in table 3. The calculated bond lengths and bond angles appear to be reasonable. The C-X bonds in C6,,XJ6are somewhat shorter than in C60X60, by about 0.005-0.019 A for X=H and 0.015-0.028 A for X = F which is consistent with the trends in the calculated bond strengths. The nonbondes X...X distances between neighboring X atoms are significantly larger in C&XJ6 than in C60X6o,on the average by 0.19-0.22 A for X = H and by 0.24-0.32 8, for X=F. Obviously the X atoms can avoid each other much better in the sterically less demanding C6oX36species. The associated reduction of the non-

Table 3 Calculated equilibrium 1s structures of C&&, (X = H, F) X

Variable a)

MNDO

AM1

PM3

dzP SCF b’

6-31G” SCF =’

6-3 lG** extrap ‘)

LDF *)

H

C-C (pent) C-C (hex) C-H HCC (hex) H...H (pent) H...H (hex)

1.554 1.537 1.132 100.9 2.027 1.964

1.530 1.504 1.146 101.3 1.999 1.954

1.527 1.508 1.122 100.1 2.014 1.901

1.565 1.553 1.082 101.3

1.561 1.552 1.080 c) c) c)

1.568 1.560 1.088 c) c)

1.55 1.54 1.10

C-C C-C C-F FCC F...F F...F

1.645 1.633 1.362 101.1 2.209 2.157

1.584 1.565 1.412 101.3 2.164 2.118

1.585 1.569 1.381 101.5 2.147 2.118

1.597 1.591 1.339 101.4

1.602 1.601 1.336 c) c) c)

1.627 1.627 1.339 c) c) c)

F

(pent) (hex)

(pent) (hex)

1.977

2.120

-

Cl

1.61 1.60 1.35

a) Distances in A and angles in deg. The designations pent and hex refer to the pentagons and hexagons in the I,, structure. There are 60 X...X (pent) and 30 X...X (hex) interactions between vicinal atoms X=H, F. b, Ref. [13]. ‘) Ref. [ 141. Angles HCC are quoted as lOl”-102”, distances H...H as 1.97-2.01 A and F...F as 2.12-2.16 A. d, Ref. [ 151.

239

Volume 193, number 2,3

1May 1992

CHEMICAL PHYSICS LETTERS

Table 4 Calculated equilibrium T,, structures of C60X36(X = H, F) Variable ai

C=C C--C? C-C6 c”-Cs @-CB C”-X” c*-xs CCt?S CCC*6 CC%? CC”6X” C%?X” CeCsXs X9..X” [email protected]

X=H

X=F

MNDO

AM1

1.348 1.526 1.499 1.580 1.564 1.117 1.120 112.2 124.9 116.2 108.8 108.0 103.8 2.218 2.099

1.338 1.509 1.472 1.563 1.535 1.127 1.131 112.1 125.1 115.7 109.3 108.2 104.0 2.201 2.083

PM3

MNDO

AM1

1.333 1.507

I .337 1.554

1.329 1.530

1.478

1.527

1.493

1.562 1.545 1.117 1.117 112.2 125.1 115.9 108.4 109.3 102.4 2.237 2.026

1.647 1.643 1.347 1.347 113.6 126.3 115.8 109.9 108.9 105.5 2.469 2.362

1.613 1.593 1.384 1.387 113.3 126.4 114.9 111.3 107.6 104.6 2.409 2.293

PM3 1.322 1.524

1.495 1.616 1.620 1.363 1.362 113.4 126.7 115.1 109.5 110.9 103.3 2.510 2.246

‘) Distances in A and angles in deg. The live symmetry inequivalent atoms [ 151 are denoted as follows: C is in a double bond shared by a pentagon and a hexagon, and the groups C”-X” and Cs-Xs are in a- and /%position to C, respectively. A tilde designates an adjacent symmetry equivalent atom (e.g. in C-c). For a given atom C, the two CC” bonds in the pentagon and the hexagon are not equivalent so that C?” and Cn6are used for distinction, if necessary. There are 24 X”...XOand 6 Xs...@ interactions between vicinal atoms Xr H, F.

bonded repulsions will stabilize C&X36 relative to C6oX60,for X =H and particularly for X=F (see above ) . The normal modes transform according to 13a, + 1la,+ 13e,+ 1le,+34t,+36tU for C6eXS6 (point group Th), and 4a,+2a,+-7t,,+8t2g+9tlu+ 10tz,+ 1Zg,+ 12g, + 16h,+ 14h, for C60X60(point group I,,) . Only the t,, transitions in C60X36 and the ti, transitions in C6,,X60are infrared allowed. The predictions for the corres~ndin8 harmonic wavenumbers and infrared intensities are gathered in table 5. The Raman allowed transitions in C60X60 (a,, hg) are listed in table 6 while those in C&XJ6 (+, e,, tp) are omitted due to their large number. Tables 5 and 6 contain the MNDO results for X=H, F. AM1 results are given for X = F only to indicate how much related semi-empirical methods may differ in their predictions (the differences for X = H being smaller). In analogy to previous work on the vibrational spectra of carbon clusters [ 18,29,30] only the MNDO results will be discussed in the following. The theoretical data in tables 5 and 6 are mainly intended to provide a qualitative picture of the expected infrared and Raman spectra, especially with 240

regard to the overall distribution of the allowed transitions within the spectra and the distinction between strong and weak infrared bands. The calculated MNDO wavenumbers are subject to the usual uncertainties [ 18, 29-311. Based on a systematic comparison between MNDO and experiment [ 3 1] improved estimates for the C-H, C-F, and C-C stretching vibrations should be obtainable by multiplying the corresponding MNDO wavenumbers in tables 5 and 6 (i.e. C-H above 3000 cm-‘, C-F 1466-1610 cm-‘, C=C 1866-1935 cm-‘) by scale factors of 0.901, 0.752 and 0.894, respectively. For the other vibrations a standard scale factor around 0.9 should be appropriate [ 18 ] (possibly somewhat lower [ 321). The unscaled MNDO wavenumbers for the C-X stretching vibrations (X = H, F) show some regular trends. Considering both allowed and forbidden transitions and using the notation from table 1, the stretching frequencies for Cs0H60 f I ) , 3089-3 154 cm-‘, are considerably below those for &Hz (I), 3249-3259 cm-‘, for C&,HJ6 (X), 3190-3233 cm-‘, and for C&He0 (II), 3174-3269 cm-‘. The same holds for the C-F stretching frequencies of G0F6,,

Volume

193, number

Table 5 Infrared-allowed

CHEMICAL

2,3

transitions

in C.&&, (Ih, t,,) and in C&&

PHYSICS

(Th,

1”) a’ X=H, a,

MNDO 1,

X=F, Wi

MNDO 1,

X=F, W,

AM1 1,

1 May 1992

LETTERS

Table 6 Harmonic wavenumbers tions in C60X60 ( Ih)

3114 1524 1445 1427 1329 1142 577 564

604 0 0 14 50 335 0 5 1

1482 1461 1172 1054 722 582 462 392 282

2304 32 2 13 667 1 1 1 145

1376 1359 1305 1124 757 490 448 328 275

578 24 10 16 342 1 0 0 59

CSOX36

3231 3229 3227 3205 3190 1888 1866 1510 1486 1447 1398 1385 1360 1340 1329 1315 1286 1251 1238 1211 1197 1163 1082 997 963 898 831 762 672 631 576 546 465 342 331 300

182 8 6 54 3 2 1 41 5 97 1 5 13 27 3 0 0 7 49 4 4 9 0 47 34 0 83 0 4 2 1 0 23 0 1 0

1922 1897 1607 1588 1573 1566 1561 1404 1366 1331 1195 1178 1151 1106 1003 942 876 828 799 713 645 614 593 548 464 421 373 366 344 322 279 254 243 204 196 154

12 9 1210 994 99 66 1118 184 28 682 15 2 40 0 9 9 12 87 29 388 3 9 17 0 31 0 5 4 19 67 0 28 0 0 6 0

2004 1968 1504 1483 1477 1457 1449 1432 1394 1345 1213 1193 1157 1120 1024 942 886 853 811 741 663 634 612 566 484 381 351 315 305 298 280 251 237 198 186 152

5 9 763 661 75 9 79 556 5 174 44 2 5 1 5 0 1 10 1 364 8 0 3 0 25 0 0 3 11 31 3 1 0 0 3 0

‘) Harmonic intensities entry.

vibrational wavenumbers wi in cm- ’ and infrared 1; in km/mol. For 1,<0.5 km/mol there is a zero

’ ) for Raman-allowed

transi-

X

Method

Symmetry

Wavenumbers

H

MNDO

a,

3154,1545,1443,491 3143,3128,3104, 1498,1493, 1449,1434, 1414, 1353,1338, 1245,1000,748,720,430,234 1493,1183,586,281 1487,1475, 1467,1221, 1166, 1047,1026,824,575,558, 521,467,382,312,299, 154 1383,1322,453,294 1381,1369, 1358,1316,1282, 1128,1090,875,600,452, 426,394,366,287,274,160

h,

C6OX60 3145

wi (cm-

F

MNDO

a, h,

F

AM1

a8 hB

(I), 1466-1506 cm-‘, in comparison with C6,,F2(I), 1583-1591 cm-‘, and C60F36(I), 1561-1610cm-‘. The calculated wavenumbers for the C-X stretching modes in icosahedral (&,X6,, (I) are thus approximately 100 cm-’ lower than those in the other C&,Xn species studies presently, including the case of Ce0H6,, (II) with ten hydrogens inside the cage. Experimentally, such a difference of the order of 100 cm- ’ has been found for the strongest infrared-active C-F stretching bands in C60F60 [6] and partly fluorinated material [ 71. The low C-X stretching frequencies in C6oX60 (I) are obviously another indication for the reduced C-X bond strengths in these icosahedral compounds.

Acknowledgement This work was supported by the Fonds der Chemischen Industrie and the Alfried-Krupp-Fiirderpreis. The calculations were carried out using the NEC SX-3 computer at RRZK K61n.

References [ 1] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl and R.E. Smalley, Nature 318 (1985) 162. [2] W. Kr;itschmer, L.D. Lamb, K. Fostiropoulos and D.R. Huffman, Nature 347 ( 1990) 354. [ 31 R.E. Haufler, J. Conceicao, L.P.F. Chibante, Y. Chai, N.E. Byrne, S. Flanagan, M.M. Haley, S.C. O’Brien, C. Pan, 2. Xiao, W.E. Billups, M.A. Ciufolini, R.N. Hauge, J.L.

241

Volume 193, number 2,3

CHEMICAL PHYSICS LETTERS

Margrave, L.J. Wilson, R.F. Curl and R.E. Smalley, J. Phys. Chem. 94 ( 1990) 8634. [4] J.M. Hawkins, T.A. Lewis, S.D. LorenA. Meyer, J.R. Heath, Y. Shibato and R.J. Saykally, J. Org. Chem. 55 ( 1990) 6250. [5] S.W. McElvany and J.H. Callahan, J. Phys. Chem. 95 (1991) 6186. [6] J.H. Holloway, E.G. Hope, R. Taylor, G.J. Langley, A.G. Avent, T.J. Dennis, J.P. Hare, H.W. Kroto and D.R.M. Walton, J. Chem. Sot. Chem. Commun. ( 1991) 966. [ 71 H. Selig, C. Lifshitz, T. Peres, J.E. Fischer, A.R. McGhie, W.J. Romanow, J.P. McCauley Jr. and A.B. Smith, J. Am. Chem. Sot. 113 (1991) 5475. [ 81 P.J. Krusic, E. Wasserman, B.A. Parkinson, B. Malone, E.R. Holler Jr., P.N. Keizer, J.R. Morton and K.F. Preston, J. Am.Chem.Soc. 113 (1991) 6274. [9] J.W. Bausch, G.K.S. Prakash, G.A. Olah, D.S. Tse, D.C. Lorents, Y.K. Bae and R. Malhotra, J. Am. Chem. Sot. 113 (1991) 3205. [IO] J.M. Wood, B. Kahr, S.H. Hoke, L. Dejarme, R.G. Cooks and D. Ben-Amotz, J. Am. Chem. Sot. 113 ( 1991) 5907. [ 111 A. Penicaud, J. Hsu, C.A. Reed, A. Koch, K.C. Khemani, P.-M. Allemand and F. Wudl, J. Am. Chem. Sot. 1I 3 ( 1991) 6698. [ 121 P.W. Fowler, H.W. Kroto, R. Taylor and D.R.M. Walton, J. Chem. Sot. Faraday Trans. 87 ( 1991) 2685. [ 131 G.E. Scuseria, Chem. Phys. Letters 176 (1991) 423. [ 141 J. Cioslowski, Chem. Phys. Letters 18 1 ( 1991) 68. [ 151 B.I. Dunlap, D.W. Brenner, J.W. Mintmire, R.C. Mowrey and C.T. White, J. Phys. Chem. 95 (1991) 5763. [ 161 M. Saunders, Science 253 (1991) 330. [ 171 D. Bakowies and W. Thiel, J. Am. Chem. Sot. 113 ( 199 1) 3704.

242

1 May 1992

[ 181 D. Bakowies and W. Thiel, Chem. Phys. I5 1 ( 1991) 309.

[ 191 M.J.S. Dewar and W. Thiel, J. Am. Chem. Sot. 99 (1977) 4899.

[ 201 M.J.S. Dewar, E.G. Zoebisch, E. Healy and J.J.P. Stewart, J. Am. Chem. Sot. 107 (1985) 3902.

[ 211 M.J.S. Dewar and E.G. Zoebisch,

J. Mol. Struct. THEOCHEM 180 (1988) 1. [22] J.J.P. Stewart, J. Comput. Chem. 10 (1989) 209,221. [ 231 W. Thiel, program MND09 1, version 3.2. [24] E.B. Wilson Jr., D.C. Decius and PC. Cross, Molecular vibrations (MC Graw-Hill, New York, 1955). ]25 1D. Bakowies and W. Thiel, to be published. 126‘I M.J.S. Dewar and K.M. Dieter, J. Am. Chem. Sot. 108 (1986) 8075. ]27 M.W. Chase, C.A. Davies, J.R. Downey, D.R. Frurip, R.A. McDonald and A.N. Syverud, JANAF Thermochemical Tables, 3rd Ed., J. Phys. Chem. Ref. Data 14 ( 1985) Suppl. 1. 128 J.B. Pedley, R.D. Naylor and S.P. Kirby, Thermochemical data of organic compounds, 2nd Ed. (Chapman and Hall, London, 1986). 1291R.E. Stanton and M.D. Newton, J. Phys. Chem. 92 ( 1988) 2141,5314. [30‘I K. Raghavachari and C.M. Rohlting, J. Phys. Chem. 95 (1991) 5768. [31] M.J.S. Dewar, G.P.Ford,M.L. McKee,H.S.Rzepa, W.Thiel and Y. Yamaguchi, J. Mol. Struct. 43 (1978) 135. [ 321 J.P. Hare, T.J. Dennis, H.W. Kroto, R. Taylor, A.W. Allaf, S. Balm and D.R.M. Walton, J. Chem. Sot. Chem. Commun. (1991) 412.