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Quantum-chemical study of C78 fullerene isomers
Volume 197, number 3
Quantum-chemical
CHEMICAL PHYSICS LETTERS
11 September 1992
study of CT8 fullerene isomers
Dirk Bakowies, Achim Gelessus and Walter Thiel Theoretische Chemie, Universitiit GH Wuppertal, W-5600
Wuppertal1, Germany
Received 9 June 1992
Semi-empirical and ab initio calculations are reported for the five Crs fullerenes with isolated pentagons. The optimized geometries and relative stabilities are discussed. The D3s structure previously favored on the basis of simple Hilckel arguments is found to be the least stable isomer at all theoretical levels applied. The most stable isomer corresponds to a Czy structure which has recently been observed experimentally together with two other isomers. Infrared spectra are predicted for all five isomers.
1. Introduction
2. Computational details
Buckminsterfullerene C& [ 1 ] can be prepared in macroscopic amounts by resistive heating of graphite [ 21. The resulting soot contains as byproducts C,,, [ 21 and higher fullerenes such as C6, C8, and Ca4 [ 31 which may be separated by high-performance liquid chromatography (HPLC) of the toluene-soluble soot extract and characterized by 13C NMR spectroscopy. This procedure yields pure CT6 [ 41, two pure CT8isomers [ 51, and a Ca4mixture with at least two major isomers [ 3 1. A third CT8 isomer has recently been detected in the CT8HPLC fraction [ 61. The most stable fullerene isomers are expected to be those with isolated pentagons [7-l 11. The preferred isomer of CT6has a chiral Dz structure [ lo] and is indeed observed experimentally [ 41. There are five CT8fullerenes with isolated pentagons [ 111 which are denoted in the original numbering scheme [ 111 as follows: 1 D3h, 2 D3,,, 3 D3, 4 CZv,and 5 CZV. The observed isomers have been identified as 3 [ 56 1, 4 [ $61, and 5 [ 61 by 13CNMR spectroscopy, and the product ratios for 3, 4, and 5 have been quoted as 1:5:0 [5] and2:2:5 [6],respectively.Inviewof these recent experimental developments, the present paper reports a quantum-chemical study of the CT8 fullerenes l-5 addressing their structures, stabilities, and infrared spectra.
Semi-empirical closed-shell SCF calculations were carried out using the standard MNDO [ 121, AM 1 [ 13 1, and PM3 [ 141 parameters and our current semi-empirical program [ 15 1. Molecular geometries were completely optimized within a given point group. The force constants and dipole moment derivatives were evaluated by finite differences at the optimized geometries. The harmonic vibrational frequencies and the infrared intensities were determined from these data by standard procedures [ 16 1. 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 [ 17 1. Single-point MNDOC [ 181 BWEN calculations (Brillouin-Wigner second-order perturbation theory with Epstein-Nesbet energy denominators) at the optimized MNDOC SCF geometries were employed to study the influence of electron correlation on the relative stabilities. In order to keep the computational effort within reasonable limits, the active space was restricted to the N,, highest occupied and NVlowest virtual orbitals, and N, = N, = 40 was chosen to include all relevant x-type orbitals in the correlation treatment. Test calculations with different N, and NVvalues (up to N, = 60, NV= 75 for isomers 4 and 5) confirmed that the relative MNDOC energies are not very sensitive to the choice of N, and NV.
Correspondence to: W. Thiel, Theoretische Chemie, Universitat GH Wuppertal, W-5600 Wuppertal1, Germany.
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CHEMICAL PHYSICS LETTERS
Volume 197, number 3
Single-point ab initio SCF calculations with the 321G basis [ 191 at the MNDO SCF optimized geometries were carried out using the TURBOMOLE program [ 201 to provide an ab initio prediction for the relative stabilities. Since these single-point SCF calculations with 702 contracted basis functions took between 11 and 43 h of CPU time (IBM RS/6000 32H), geometry optimizations were not attempted at the ab initio level.
3. Results and discussion Table 1 summarizes the most important structural data for the CT8fullerene isomers l-5 (see fig. 1 of ref. [ 111 for a definition of these structures). According to the MNDO SCF results listed, the average bond lengths R,, are almost identical for l-5 ( 1.4475 k 0.0003 A). The extent of bond alternation is indicated by the minimum and maximum bond lengths (R,, - R,in=0.115f0.011 A for 1-S). The curvature at a given atom i may be measured with the help of the n orbital axis vector (POAV [ 2 1 ] ) which is geometrically defined such that it has equal angles Pi with the three bonds of that atom. The corresponding POAV angle is then defined as @i=pix/2 (i.e. 8i=O in the planar case). The average POAV angle e,, are fairly uniform for 1-5, with a slight increase in the series 2 < 5 < 4 x 3 < 1. Similar trends are found for the spread 0,, - Bminof POAV angles and for the measure [ 8,9] of overall curvature I@, which indicates that isomer 2 has the “most spherical” shape followed by isomer 5. According to previous correlations (see fig. 7 of ref. [ 91) consideration of strain energies should favor isomers 2 and 5 over the others.
The optimized AM1 and PM3 geometries (not listed in table 1) are quite similar to those from MNDO. the average bond lengths are somewhat shorter (AM1 1.4352f0.0004 A, PM3 1.4313+ 0.0003 A), but the bond length alternations and the POAV angles are almost the same as in MNDO. For example, the average POAV angles in AM1 and PM3 differ by at most 0.01’ from those in MNDO, and the curvature measure C 0: by about 0.01 rad2 (consistently higher in AM 1 and PM3, no change in sequence for 1-5). Hence, the three methods predict essentially the same shape for a given cluster, with a slight overall “shrinkage” in AM1 and PM3 that leads to shorter average bond lengths. The carbon atoms in the fullerenes have been classified [ 35 ] as pyrene-like (shared by three hexagons), corannulene-like (shared by two hexagons and one pentagon, not connected to another pentagon), and pyracylene-like (shared by two hexagons and one pentagon, connected to another pentagon). In the optimized MNDO SCF structures of 1-5 (as well as of ChOand C,,,), these three types of carbon atoms are associated with POAV angles that lie in typical ranges: pyrene-like usually below 9”, corannulene-like usually 10 ’ - 11 O, and pyracylene-like usually 11o- 12’. Likewise, the net atomic charges in MNDO assume typical values: pyrene-like +0.025 +O.OlO, corannulene-like -0.015 + 0.010, and pyracylene-like + 0.005 f. 0.0 15. Analogous trends are found for the POAV angles and net-atomic charges in AM1 and PM3. It would seem tempting to correlate such regular behavior with the experimental 13CNMR shifts [ 3-61 but, in the absence of definite assignments for the C8 isomers, we have only noted a rough correspondence between the calcu-
Table 1 Structural data for the C,s isomers *) Isomer
R .Y
R&
R Inax
@a”
%in
%8X
xej
1 bh
1.4478 1.4473
1.367 1.367 1.385 1.374 1.370
1.480 1.492 1.489 1.484 1.491
10.36 10.22 10.32 10.30 10.26
6.90 8.87 6.81 6.77 7.56
12.12 11.66 12.01 12.25 12.26
2.636 2.500 2.593 2.580 2.535
2 DB 3D3 4 Cl” S CZ”
1.4475 1.4475 1.4473
‘) MNDO results, see text for comparison with AM 1 and PM3. Average, minimum, and maximum bond lengths (R,,, R,i., R,) (in A); average, minimum, and maximum POAV angles (e,,, 6&, 8,,,,) (in deg); sum of squares of all 78 POAV angles ei (in radz).
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lated POAV angles and the measured [22,23] r3C NMR shifts for CTO. Table 2 contains theoretical data on the relative stabilities of the CT8isomers 1-5. According to simple Htlckel theory [ 111 the D3,, structure 1 should be favored because it has the highest n: delocalization energy and the largest HOMO-LUMO gap of the live isomers, and because it is the only one with a closedshell electronic configuration (positive LUMO energy ). In contrast to this “unambiguous” prediction [ 111 from qualitative MO theory, 1 has not yet been observed experimentally [ 5,6] and is calculated to be the least stable isomer by all methods applied presently (see table 2). This failure of the simple Htlckel approach can be overcome by introduction of a curvature correction [ 9 ] for the resonance integral, i.e. &= (Sc/So)& where Sc is the average MNDO xrc overlap integral in the cluster, So the MNDO ICXoverlap integral in a graphite sheet, and & the resonance integral for graphite [ 9 1. This correction accounts for the reduced rtrr interactions due to the curvature of the cluster, in the spirit of the POAV/ 3D HMO model [ 24 1. Upon introduction of this correction, 1 becomes the least stable isomer also at the Htickel level (see last column of table 2). This example emphasizes our previous conclusion [ 9 ] that a suitable curvature correction is essential for realistic stability estimates at the Htlckel level. All methods listed in table 2 predict the CZvstructure 5 to be the most stable isomer, and they agree in the energy ordering 5x4~ 3 < 1 whereas the po-
11 September 1992
sition of 2 differs for different methods (between 51 4, 413, or 3/l). Some of the calculated energy differences are so small that they cannot be regarded as conclusive. It is reassuring, however, that the theoretically most stable isomer 5 has been observed experimentally [ 61, as well as the isomers 3 and 4 [ 5,6] which are calculated to lie only a few kilocalories per mole above 5. A comparison of the MNDOC SCF and BWEN results in table 2 indicates that electron correlation has only a minor influence on the relative stabilities of l-5, at least at the semi-empirical level. The ab initio 3-2 1G SCF results in table 2 yield and energy ordering 5 < 4 < 3 < 2 < 1, and differ from the semiempirical results mainly in predicting a relatively low energy of 4 and a relatively high energy of 2. The present ab initio results refer to optimized MNDO SCF geometries, of course, but a reoptimization at the ab initio SCF level should not lead to drastic changes in the relative stabilities. This expectation is based on preliminary results from a Cs4 study [ 25 ] and on the very small changes in relative stabilities for l-5 when using MNDO SCF geometries instead of the corresponding optimized geometries with AM 1 or PM3 (see columns 3 and 4, and 8 and 9 in table 2 ). In view of the small energy difference between 4 and 5 at the 3-21G//MNDO level, however, additional ab initio calculations with geometry optimization and with the use of larger basis sets would seem desirable to check more reliably whether 5 is indeed the most stable CT8isomer.
Table 2 Relative heats of formation and relative energies for the CT8isomers ‘) Isomer
1 Da 2 Dx, JD, 4 Clv S Cl”
MNDO b,
23.4 1.6 10.5 7.1 0.0
AM1 b’
21.3 5.1 7.1 5.3 0.0
PM3 b,
17.5 5.6 6.3 3.8 0.0
MNDOC ‘) SCF
BWEN
20.5 3.8 9.2 5.4 0.0
23.4 3.7 9.5 6.5 0.0
3-2lG*’
AM1 d’
PM3 d’
MM3 =’
HMO” corr.
13.9 11.1 4.7 0.5 0.0
21.1 5.2 7.1 5.1 0.0
17.5 5.4 6.4 3.8 0.0
8.0 3.5 3.5 1.4 0.0
9.9 2.5 8.0 2.7 0.0
a) In kcal/mol, SCF values unless noted otherwise. b, At the corresponding optimized geometries. c, At the optimized MNDOC SCF geometries, N, = N, = 40 (see text ). d, At the optimized MNDO SCF geometries. =) MM3 force-field results from ref. [ 5 1. see ref. [ 9 ] for definitions. f, Curvature-corrected HMO results from AE.= nDCREPE,
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CHEMICAL PHYSICS LETTERS
Volume 197, number 3
&h (2)
c,,15)
! I,
03
I
1500
I
1000
I
I
I
I
I
so0
II
t
I
[cm-l]
Fig. 1. Calculated infrared spectra for C,, fullerene isomers 1-5 (MNDO SCF, no scaling).
Force constant analysis confirms that the CT8isomers l-5 are local minima on the MNDO SCF potential surface. Figs. 1 and 2 show the complete calculated infrared spectra for l-5 and an expanded view of the region below 1200 cm-‘, respectively. Fig. 2 is included for convenience since MNDO is known to exaggerate the relative intensities of the
hip-f~quency bands in the fullerenes [ 26,271 so that details in the low-frequency region may be obscured in fig. I. Figs. 1 and 2 are intended to provide a qualitative picture of the expected infrared spectra, especially with regard to the overall distribution of the allowed transitions and the distinction between strong and weak bands. The calculated MNDO 327
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CHEMICAL PHYSICS LETTERS
11 September 1992
03 (3)
v ‘I
CZ”(51 800
400
Fig. 2. Calculated infrared spectra for the CT8ftilerene isomers l-5 in the region below 1200 cm-’ (MNDO SCF, no scaling).
wavenumbers are subject to the usual uncertainties [ 26-29 ] and should be scaled by a factor of about 0.9 [26,27 ] when comparing with experiment. The normal modes for the five CT8isomers transform as follows: 1 2 1a; + I 7a; + 38e’+ 18a;’+ 2Oa;’ +3gefl, 2 2la;+18a;+39e’+18a;+19al+37e”, 3 39a, +37a2+76e, 4 59a, + 56a,+ 56b, +57b2, 5 60a, 328
+55a2f56b,+57bt. Hence, there are 58, 58, 113, 172, and 173 infrared-allowed bands for 1-5, respectively [ 111. Inspection of figs. 1 and 2 indicates that it will be hard to distinguish between the fairly congested infrared spectra of the two CzVisomers 4 and 5. To some extent, this also applies to the D3 isomer 3 whereas the computed spectra of the two Dsh
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CHEMICAL PHYSICS LETTERS
isomers 1 and 2 have a simpler appearance. It is hoped that the predicted infrared spectra in figs. 1 and 2 will be helpful in the further characterization of the experimentally accessible CT8isomers [ 5,6].
Acknowledgement This work was supported by the Fonds der Chemischen Industrie and the Alfred-Krupp-Fiirderpreis. The semi-empirical calculations were carried out using the NEC SX-3 computer at RRZK Cologne.
References [ 1] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl and R.E. Smalley, Nature 3 18 ( 1985) 162. [2] W. Kr&chmer, L.D. Lamb, K. Fostiropoulos and D.R. Huffman, Nature 347 (1990) 354. [ 31 F. Diedetich and R.L. Whetten, Accounts Chem. Res. 25 ( 1992) 119, and references therein. [4] E. Ettl, I. Chao, F. Diederich and R.L. Whetten, Nature 353 (1991) 149. [ 51F. Diederich, R.L. Whetten, C. Thilgen, R. Ettl, I. Chao and MM. Alvarez, Science 254 (1991) 1768. [6] K. Kikuchi, N. Nakahara, T. Wakabayashi, S. Suzuki, H. Shiromaru, Y. Miyake, K. Saito, I. Ikemoto, M. Kainosho and Y. Achiba, Nature 357 (1992) 142. [ 71 H.W. Kroto, Nature 329 (1987) 529. [S] T.G. Schmalz, W.A. Seitz, D.J. Klein and G.E. Hite, J. Am. Chem.Soc. 110(1988) 1113. [ 91 D. Bakowies and W. Thiel, J. Am. Chem. Sot. 113 ( I99 1) 3704.
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[lo] D.E. Manolopoulos, J. Chem. Sot. Faraday Trans. 87 (1991) 2861. [ 111 P. W. Fowler, R.C. Batten and D.E. Manolopoulos, J. Chem. Soc.FaradayTrans. 87 (1991) 3103. [ 121 M.J.S. Dewar and W. Thiel, J. Am. Chem. Sot. 99 (1977) 4899. [ 13 ] M.J.S. Dewar, E.G. Zoebisch, E. Healy and J.J.P. Stewart, J. Am. Chem. Sot. 107 (1985) 3902. [ 141 J.J.P. Stewart, J. Comput. Chem. 10 (1989) 209,221. [ 15 ] W. Thiel, program MND09 1, version 3.2. 161 E.B. Wilson Jr., D.C. DEcius and P.C. Cross, Molecular vibrations (MC Graw-Hill, New York, 1955). 17 ] D. Bakowies and W. Thiel, to be published. 181 W. Thiel, J.Am. Chem.Soc. 103 (1981) 1413,142O. 19 ] J.S. Binkley, J.A. Pople and W.J. Hehre, J. Am. Chem. Sot. 102 (1980) 939. 201 R. Ahlrichs, M. B&r, M. H&r, H. Horn and C. Kolmel, Chem. Phys. Letters 162 ( 1989) 165. [ 2 I] R.C. Haddon and L.T. Scott, Pure Appl. Chem. 58 ( 1986) 137. [22 ] R. Taylor, J.P. Hare, A.K. Abdul-Sada and H.W. Kroto, J. Chem. Sot. Chem. Commun. ( 1990) 1423. [23] R.D. Johnson, G. Meijer, J.R. Salem and D.S. Bethune, J. Am.Chem.Soc. 113 (1991)3619. [24] R.C. Haddon, J. Am. Chem. Sot. 108 (1986) 2837. [ 25 ] R. Ahhichs, S. Richard, D. Bakowies, M. Kolb and W. Thiel, to be published. [ 26 ] D. Bakowies and W. Thiel, Chem. Phys. 151 ( 199 1) 309. [27] 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. [28] R.E. Stanton and M.D. Newton, J. Phys. Chem. 92 (1988) 2141,5314. [29]D.S. Bethune, G. Meijer, W.C. Tang, H.J. Rosen, W.G. Golden, H. Seki, C.A. Brown and M.S. de V&s, Chem. Phys. Letters 179 (1991) 181.
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Quantum-chemical
CHEMICAL PHYSICS LETTERS
11 September 1992
study of CT8 fullerene isomers
Dirk Bakowies, Achim Gelessus and Walter Thiel Theoretische Chemie, Universitiit GH Wuppertal, W-5600
Wuppertal1, Germany
Received 9 June 1992
Semi-empirical and ab initio calculations are reported for the five Crs fullerenes with isolated pentagons. The optimized geometries and relative stabilities are discussed. The D3s structure previously favored on the basis of simple Hilckel arguments is found to be the least stable isomer at all theoretical levels applied. The most stable isomer corresponds to a Czy structure which has recently been observed experimentally together with two other isomers. Infrared spectra are predicted for all five isomers.
1. Introduction
2. Computational details
Buckminsterfullerene C& [ 1 ] can be prepared in macroscopic amounts by resistive heating of graphite [ 21. The resulting soot contains as byproducts C,,, [ 21 and higher fullerenes such as C6, C8, and Ca4 [ 31 which may be separated by high-performance liquid chromatography (HPLC) of the toluene-soluble soot extract and characterized by 13C NMR spectroscopy. This procedure yields pure CT6 [ 41, two pure CT8isomers [ 51, and a Ca4mixture with at least two major isomers [ 3 1. A third CT8 isomer has recently been detected in the CT8HPLC fraction [ 61. The most stable fullerene isomers are expected to be those with isolated pentagons [7-l 11. The preferred isomer of CT6has a chiral Dz structure [ lo] and is indeed observed experimentally [ 41. There are five CT8fullerenes with isolated pentagons [ 111 which are denoted in the original numbering scheme [ 111 as follows: 1 D3h, 2 D3,,, 3 D3, 4 CZv,and 5 CZV. The observed isomers have been identified as 3 [ 56 1, 4 [ $61, and 5 [ 61 by 13CNMR spectroscopy, and the product ratios for 3, 4, and 5 have been quoted as 1:5:0 [5] and2:2:5 [6],respectively.Inviewof these recent experimental developments, the present paper reports a quantum-chemical study of the CT8 fullerenes l-5 addressing their structures, stabilities, and infrared spectra.
Semi-empirical closed-shell SCF calculations were carried out using the standard MNDO [ 121, AM 1 [ 13 1, and PM3 [ 141 parameters and our current semi-empirical program [ 15 1. Molecular geometries were completely optimized within a given point group. The force constants and dipole moment derivatives were evaluated by finite differences at the optimized geometries. The harmonic vibrational frequencies and the infrared intensities were determined from these data by standard procedures [ 16 1. 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 [ 17 1. Single-point MNDOC [ 181 BWEN calculations (Brillouin-Wigner second-order perturbation theory with Epstein-Nesbet energy denominators) at the optimized MNDOC SCF geometries were employed to study the influence of electron correlation on the relative stabilities. In order to keep the computational effort within reasonable limits, the active space was restricted to the N,, highest occupied and NVlowest virtual orbitals, and N, = N, = 40 was chosen to include all relevant x-type orbitals in the correlation treatment. Test calculations with different N, and NVvalues (up to N, = 60, NV= 75 for isomers 4 and 5) confirmed that the relative MNDOC energies are not very sensitive to the choice of N, and NV.
Correspondence to: W. Thiel, Theoretische Chemie, Universitat GH Wuppertal, W-5600 Wuppertal1, Germany.
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1 I September 1992
CHEMICAL PHYSICS LETTERS
Volume 197, number 3
Single-point ab initio SCF calculations with the 321G basis [ 191 at the MNDO SCF optimized geometries were carried out using the TURBOMOLE program [ 201 to provide an ab initio prediction for the relative stabilities. Since these single-point SCF calculations with 702 contracted basis functions took between 11 and 43 h of CPU time (IBM RS/6000 32H), geometry optimizations were not attempted at the ab initio level.
3. Results and discussion Table 1 summarizes the most important structural data for the CT8fullerene isomers l-5 (see fig. 1 of ref. [ 111 for a definition of these structures). According to the MNDO SCF results listed, the average bond lengths R,, are almost identical for l-5 ( 1.4475 k 0.0003 A). The extent of bond alternation is indicated by the minimum and maximum bond lengths (R,, - R,in=0.115f0.011 A for 1-S). The curvature at a given atom i may be measured with the help of the n orbital axis vector (POAV [ 2 1 ] ) which is geometrically defined such that it has equal angles Pi with the three bonds of that atom. The corresponding POAV angle is then defined as @i=pix/2 (i.e. 8i=O in the planar case). The average POAV angle e,, are fairly uniform for 1-5, with a slight increase in the series 2 < 5 < 4 x 3 < 1. Similar trends are found for the spread 0,, - Bminof POAV angles and for the measure [ 8,9] of overall curvature I@, which indicates that isomer 2 has the “most spherical” shape followed by isomer 5. According to previous correlations (see fig. 7 of ref. [ 91) consideration of strain energies should favor isomers 2 and 5 over the others.
The optimized AM1 and PM3 geometries (not listed in table 1) are quite similar to those from MNDO. the average bond lengths are somewhat shorter (AM1 1.4352f0.0004 A, PM3 1.4313+ 0.0003 A), but the bond length alternations and the POAV angles are almost the same as in MNDO. For example, the average POAV angles in AM1 and PM3 differ by at most 0.01’ from those in MNDO, and the curvature measure C 0: by about 0.01 rad2 (consistently higher in AM 1 and PM3, no change in sequence for 1-5). Hence, the three methods predict essentially the same shape for a given cluster, with a slight overall “shrinkage” in AM1 and PM3 that leads to shorter average bond lengths. The carbon atoms in the fullerenes have been classified [ 35 ] as pyrene-like (shared by three hexagons), corannulene-like (shared by two hexagons and one pentagon, not connected to another pentagon), and pyracylene-like (shared by two hexagons and one pentagon, connected to another pentagon). In the optimized MNDO SCF structures of 1-5 (as well as of ChOand C,,,), these three types of carbon atoms are associated with POAV angles that lie in typical ranges: pyrene-like usually below 9”, corannulene-like usually 10 ’ - 11 O, and pyracylene-like usually 11o- 12’. Likewise, the net atomic charges in MNDO assume typical values: pyrene-like +0.025 +O.OlO, corannulene-like -0.015 + 0.010, and pyracylene-like + 0.005 f. 0.0 15. Analogous trends are found for the POAV angles and net-atomic charges in AM1 and PM3. It would seem tempting to correlate such regular behavior with the experimental 13CNMR shifts [ 3-61 but, in the absence of definite assignments for the C8 isomers, we have only noted a rough correspondence between the calcu-
Table 1 Structural data for the C,s isomers *) Isomer
R .Y
R&
R Inax
@a”
%in
%8X
xej
1 bh
1.4478 1.4473
1.367 1.367 1.385 1.374 1.370
1.480 1.492 1.489 1.484 1.491
10.36 10.22 10.32 10.30 10.26
6.90 8.87 6.81 6.77 7.56
12.12 11.66 12.01 12.25 12.26
2.636 2.500 2.593 2.580 2.535
2 DB 3D3 4 Cl” S CZ”
1.4475 1.4475 1.4473
‘) MNDO results, see text for comparison with AM 1 and PM3. Average, minimum, and maximum bond lengths (R,,, R,i., R,) (in A); average, minimum, and maximum POAV angles (e,,, 6&, 8,,,,) (in deg); sum of squares of all 78 POAV angles ei (in radz).
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lated POAV angles and the measured [22,23] r3C NMR shifts for CTO. Table 2 contains theoretical data on the relative stabilities of the CT8isomers 1-5. According to simple Htlckel theory [ 111 the D3,, structure 1 should be favored because it has the highest n: delocalization energy and the largest HOMO-LUMO gap of the live isomers, and because it is the only one with a closedshell electronic configuration (positive LUMO energy ). In contrast to this “unambiguous” prediction [ 111 from qualitative MO theory, 1 has not yet been observed experimentally [ 5,6] and is calculated to be the least stable isomer by all methods applied presently (see table 2). This failure of the simple Htlckel approach can be overcome by introduction of a curvature correction [ 9 ] for the resonance integral, i.e. &= (Sc/So)& where Sc is the average MNDO xrc overlap integral in the cluster, So the MNDO ICXoverlap integral in a graphite sheet, and & the resonance integral for graphite [ 9 1. This correction accounts for the reduced rtrr interactions due to the curvature of the cluster, in the spirit of the POAV/ 3D HMO model [ 24 1. Upon introduction of this correction, 1 becomes the least stable isomer also at the Htickel level (see last column of table 2). This example emphasizes our previous conclusion [ 9 ] that a suitable curvature correction is essential for realistic stability estimates at the Htlckel level. All methods listed in table 2 predict the CZvstructure 5 to be the most stable isomer, and they agree in the energy ordering 5x4~ 3 < 1 whereas the po-
11 September 1992
sition of 2 differs for different methods (between 51 4, 413, or 3/l). Some of the calculated energy differences are so small that they cannot be regarded as conclusive. It is reassuring, however, that the theoretically most stable isomer 5 has been observed experimentally [ 61, as well as the isomers 3 and 4 [ 5,6] which are calculated to lie only a few kilocalories per mole above 5. A comparison of the MNDOC SCF and BWEN results in table 2 indicates that electron correlation has only a minor influence on the relative stabilities of l-5, at least at the semi-empirical level. The ab initio 3-2 1G SCF results in table 2 yield and energy ordering 5 < 4 < 3 < 2 < 1, and differ from the semiempirical results mainly in predicting a relatively low energy of 4 and a relatively high energy of 2. The present ab initio results refer to optimized MNDO SCF geometries, of course, but a reoptimization at the ab initio SCF level should not lead to drastic changes in the relative stabilities. This expectation is based on preliminary results from a Cs4 study [ 25 ] and on the very small changes in relative stabilities for l-5 when using MNDO SCF geometries instead of the corresponding optimized geometries with AM 1 or PM3 (see columns 3 and 4, and 8 and 9 in table 2 ). In view of the small energy difference between 4 and 5 at the 3-21G//MNDO level, however, additional ab initio calculations with geometry optimization and with the use of larger basis sets would seem desirable to check more reliably whether 5 is indeed the most stable CT8isomer.
Table 2 Relative heats of formation and relative energies for the CT8isomers ‘) Isomer
1 Da 2 Dx, JD, 4 Clv S Cl”
MNDO b,
23.4 1.6 10.5 7.1 0.0
AM1 b’
21.3 5.1 7.1 5.3 0.0
PM3 b,
17.5 5.6 6.3 3.8 0.0
MNDOC ‘) SCF
BWEN
20.5 3.8 9.2 5.4 0.0
23.4 3.7 9.5 6.5 0.0
3-2lG*’
AM1 d’
PM3 d’
MM3 =’
HMO” corr.
13.9 11.1 4.7 0.5 0.0
21.1 5.2 7.1 5.1 0.0
17.5 5.4 6.4 3.8 0.0
8.0 3.5 3.5 1.4 0.0
9.9 2.5 8.0 2.7 0.0
a) In kcal/mol, SCF values unless noted otherwise. b, At the corresponding optimized geometries. c, At the optimized MNDOC SCF geometries, N, = N, = 40 (see text ). d, At the optimized MNDO SCF geometries. =) MM3 force-field results from ref. [ 5 1. see ref. [ 9 ] for definitions. f, Curvature-corrected HMO results from AE.= nDCREPE,
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&h (2)
c,,15)
! I,
03
I
1500
I
1000
I
I
I
I
I
so0
II
t
I
[cm-l]
Fig. 1. Calculated infrared spectra for C,, fullerene isomers 1-5 (MNDO SCF, no scaling).
Force constant analysis confirms that the CT8isomers l-5 are local minima on the MNDO SCF potential surface. Figs. 1 and 2 show the complete calculated infrared spectra for l-5 and an expanded view of the region below 1200 cm-‘, respectively. Fig. 2 is included for convenience since MNDO is known to exaggerate the relative intensities of the
hip-f~quency bands in the fullerenes [ 26,271 so that details in the low-frequency region may be obscured in fig. I. Figs. 1 and 2 are intended to provide a qualitative picture of the expected infrared spectra, especially with regard to the overall distribution of the allowed transitions and the distinction between strong and weak bands. The calculated MNDO 327
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03 (3)
v ‘I
CZ”(51 800
400
Fig. 2. Calculated infrared spectra for the CT8ftilerene isomers l-5 in the region below 1200 cm-’ (MNDO SCF, no scaling).
wavenumbers are subject to the usual uncertainties [ 26-29 ] and should be scaled by a factor of about 0.9 [26,27 ] when comparing with experiment. The normal modes for the five CT8isomers transform as follows: 1 2 1a; + I 7a; + 38e’+ 18a;’+ 2Oa;’ +3gefl, 2 2la;+18a;+39e’+18a;+19al+37e”, 3 39a, +37a2+76e, 4 59a, + 56a,+ 56b, +57b2, 5 60a, 328
+55a2f56b,+57bt. Hence, there are 58, 58, 113, 172, and 173 infrared-allowed bands for 1-5, respectively [ 111. Inspection of figs. 1 and 2 indicates that it will be hard to distinguish between the fairly congested infrared spectra of the two CzVisomers 4 and 5. To some extent, this also applies to the D3 isomer 3 whereas the computed spectra of the two Dsh
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isomers 1 and 2 have a simpler appearance. It is hoped that the predicted infrared spectra in figs. 1 and 2 will be helpful in the further characterization of the experimentally accessible CT8isomers [ 5,6].
Acknowledgement This work was supported by the Fonds der Chemischen Industrie and the Alfred-Krupp-Fiirderpreis. The semi-empirical calculations were carried out using the NEC SX-3 computer at RRZK Cologne.
References [ 1] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl and R.E. Smalley, Nature 3 18 ( 1985) 162. [2] W. Kr&chmer, L.D. Lamb, K. Fostiropoulos and D.R. Huffman, Nature 347 (1990) 354. [ 31 F. Diedetich and R.L. Whetten, Accounts Chem. Res. 25 ( 1992) 119, and references therein. [4] E. Ettl, I. Chao, F. Diederich and R.L. Whetten, Nature 353 (1991) 149. [ 51F. Diederich, R.L. Whetten, C. Thilgen, R. Ettl, I. Chao and MM. Alvarez, Science 254 (1991) 1768. [6] K. Kikuchi, N. Nakahara, T. Wakabayashi, S. Suzuki, H. Shiromaru, Y. Miyake, K. Saito, I. Ikemoto, M. Kainosho and Y. Achiba, Nature 357 (1992) 142. [ 71 H.W. Kroto, Nature 329 (1987) 529. [S] T.G. Schmalz, W.A. Seitz, D.J. Klein and G.E. Hite, J. Am. Chem.Soc. 110(1988) 1113. [ 91 D. Bakowies and W. Thiel, J. Am. Chem. Sot. 113 ( I99 1) 3704.
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[lo] D.E. Manolopoulos, J. Chem. Sot. Faraday Trans. 87 (1991) 2861. [ 111 P. W. Fowler, R.C. Batten and D.E. Manolopoulos, J. Chem. Soc.FaradayTrans. 87 (1991) 3103. [ 121 M.J.S. Dewar and W. Thiel, J. Am. Chem. Sot. 99 (1977) 4899. [ 13 ] M.J.S. Dewar, E.G. Zoebisch, E. Healy and J.J.P. Stewart, J. Am. Chem. Sot. 107 (1985) 3902. [ 141 J.J.P. Stewart, J. Comput. Chem. 10 (1989) 209,221. [ 15 ] W. Thiel, program MND09 1, version 3.2. 161 E.B. Wilson Jr., D.C. DEcius and P.C. Cross, Molecular vibrations (MC Graw-Hill, New York, 1955). 17 ] D. Bakowies and W. Thiel, to be published. 181 W. Thiel, J.Am. Chem.Soc. 103 (1981) 1413,142O. 19 ] J.S. Binkley, J.A. Pople and W.J. Hehre, J. Am. Chem. Sot. 102 (1980) 939. 201 R. Ahlrichs, M. B&r, M. H&r, H. Horn and C. Kolmel, Chem. Phys. Letters 162 ( 1989) 165. [ 2 I] R.C. Haddon and L.T. Scott, Pure Appl. Chem. 58 ( 1986) 137. [22 ] R. Taylor, J.P. Hare, A.K. Abdul-Sada and H.W. Kroto, J. Chem. Sot. Chem. Commun. ( 1990) 1423. [23] R.D. Johnson, G. Meijer, J.R. Salem and D.S. Bethune, J. Am.Chem.Soc. 113 (1991)3619. [24] R.C. Haddon, J. Am. Chem. Sot. 108 (1986) 2837. [ 25 ] R. Ahhichs, S. Richard, D. Bakowies, M. Kolb and W. Thiel, to be published. [ 26 ] D. Bakowies and W. Thiel, Chem. Phys. 151 ( 199 1) 309. [27] 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. [28] R.E. Stanton and M.D. Newton, J. Phys. Chem. 92 (1988) 2141,5314. [29]D.S. Bethune, G. Meijer, W.C. Tang, H.J. Rosen, W.G. Golden, H. Seki, C.A. Brown and M.S. de V&s, Chem. Phys. Letters 179 (1991) 181.
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