J. Phys. Chem. 1994,98, 4283-4286
4283
Isomers of C ~ H M and C70H3s Lewis D. Book and Gustavo E. Scuseria' Department of Chemistry and Rice Quantum Institute, Rice University, Houston, Texas 77251- 1892 Received: November 24, 1993; In Final Form: February 17, 1994"
The molecular mechanics program MM3 and ab initio self-consistent-field (SCF) calculations are used to study the hydrogenated fullerenes C6oH36 and C70H36. Researchers have focused their search for the lowest energy structure of C60H36 on two isomers: one with T symmetry and the other with Th symmetry. We present Hartree-Fock S C F and gradient-corrected density functional theory calculations that predict that the Tisomer is lower in energy than the Th isomer by up to 97.4 kcal/mol. A class of C70H36 isomers, in which the hydrogens are concentrated in the caps of the c 7 0 structure and in 1 , 2 , 3 positions on the fullerene's 12 five-carbon rings, are studied with MM3 optimizations and SCF (STO-3G basis set) energy point calculations at the MM3 geometries. These isomers could be especially low energy structures of C70H36 because the equatorial region of the fullerene cage contains five linked, benzene-like rings that form a highly conjugated, graphite-like region.
Introduction
Since the isolation of fullerenes in macroscopic amounts,l these carbon-cagestructures have been shown to participate in several addition reactions.2-s In particular, the hydrogenation of the fullerenes Cm and C70 by the Birch reduction is of special interest. Mass spectra of the products of these hydrogenations indicate are the most abundant products that C&36 and but no unambiguous experimental evidence exists for their structures. The results of several theoretical studies of hydrogenated Cm have been rep~rted.~-lgHenderson, Rohlfing, and Cahi118.9used the semiempiricalPM3 and the ab initio Hartree-Fock methods to calculate the energies of several C d 2 and C70H2 isomers. They found that the two lowest energy ways of adding H2 to either fullerene were across a bond at the fusion of two six-atom rings or at 1,4 positions on six-atom rings. Dixon and co-workers have extensively studied addition patterns of hydrogen and other species to Cw using semiempiricalmethods.lb13 Yoshida et al.I4 examined CmHh (n = 1-30) with molecular mechanics (MM2/ P2) and the PM3 method. They reported that CmHw had the lowest strain energy of these 30 hydrogenated fullerenes. Bakowies and Thiel used MNDO, AM1, and PM3 to calculate equilibriumgeometries and vibrational spectra of various isomers of CaH2, C ~ H Mand , CmHm.ls Dunlap et al., employing the local density functional method and empirical hydrocarbon potentials, calculated the geometric and electronic structure of CaH36 and C d m . l 6 Guo and ScuseriaI7calculated energiesof C d l h (n = 1-5) isomers with Th symmetry. Using a double4 basis set at the Hartree-Fock level of theory, they found that of the exohydrogenated isomers, CmHx and C60H48were thermodynamically most stable. Taylor and co-workers18predicted that the structure of CmH36 has T symmetry and four unsaturated, benzene-like aromatic rings on the fullerene surface. Rathna and Chandrasekhar,lg in their MNDO and AM1 study of hydrogenated Cm, reported that the T isomer of CmH3.5 has a lower heat of formation than the Th isomer. To our knowledge, no theoretical studies have been published on C7OH36. In this paper, we use theoretical tools (molecular mechanics and HartreeFock SCF and density functional theory calculations) to gain further insight into CmH36 and to explore possible structures for C7d36. Molecular mechanics calculations were performed using the MM3-92 program with the MMP3 option in place.20 Heats of formation were converged to within 0.02 kcal/mol using the full*Abstract published in Advance ACS Absrracrs, April 1, 1994.
matrix optimization method. SCF energy points and geometry optimizations were done using the TURBOMOLE21 package. Calculations were performed at Rice University on a MIPS M-2000 computer and an IBM RS/6000-550 workstation.
As mentioned above, researchers have focused their study of isomers on two structures, the Th and Tsymmetry isomers (Figure 1). The Th structure, first proposed by Haufler et a1.,6 is formed by attaching three hydrogen atoms to adjacent positions on each of Cm's 12 five-membered rings so that the molecule's 12 remaining doublebonds are separated as far apart as possible. The T isomer, suggested initially by Taylor,22-23 is constructed by distributing the molecule's 12 double bonds among four sixmembered rings located at tetrahedral positions on the Cm cage. In both of these isomers, the hydrogens occupy 1, 2 , 3 positions on each of the fullerene's 12 five-atom rings, while a double bond exists between the fourth and fifth carbon atoms of the pentagonal rings. At this point in time, the highest level calculations that allow for the comparison of geometriesand energies of these two isomers have been done using the MNDO and AM1 semiempirical methods.lg The T isomer has been found to be lower in energy than the Th isomer by both methods. We studied the thermodynamic stability of these two isomers using ab initio HartreeFock self-consistent-field (SCF) calculations. Employing the STO-3G basis set24the geometries of these two structures were optimized. Energy point calculations were then performed at the SCF/STO-3G geometries using a double-Ps-26 (DZ) basis set (8s4p/4s2p). Exchange and correlation effects were determined with the nonlocal (gradient corrected)Be~ke2~-LeeYangParr28 hybrid of Hartree-Fockand density functional theories29-30 as implemented in our research group.31 This method is herein referred to as BLYP/DZ. The results of our Hartree-Fock SCF calculations, along with the previously reported semiempiricalcalculations, are shown in Table 1. All levels of theory indicate that the Tisomer of CmH3a is lower in energy than the Th isomer. However, the SCF calculations show a much greater difference in thermodynamic stability between the two isomers than do the semiempirical calculations. On the basis of MNDO and AM1 energies, the T isomer is more stable than the Th isomer by 3.9 and 15.6 kcal/ mol, respectively, while according to SCF/STO-3G, SCF/DZ, and BLYP/DZ calculations, the T isomer is lower in energy by 73.3,69.5, and 97.4 kcal/mol, respectively. Taylor et. a1.18after examining several suggested candidates for the structure of CmHs6,predicted that this Tisomer would be the experimentally
0022-3654/94/2098-4283%04.50/0 0 1994 American Chemical Society
4284 The Journal of Physical Chemistry, Vol. 98, No. 16, 1994
Book and Scuseria
Layer I
Figure 2. Nomenclature for Clo used in this paper.
T Figure 1. Th CsoHls formed by spacing the molecule’s 12 double bonds as far apart from each other as possible6 and T CmHls formed by distributing the molecule’s 12 double bonds among four six-membered rines at tetrahedral wsitions on CmZ3 The T isomer was calculated to be Tower is energy than the Th strkture at all levels of theory reported in this work. TABLE I: Relatibe Energies ( k c a l h o l ) of the T, and T C a w Isomers (See Figure I ) Determined at Various Levels of Theory level 01theory
TI isomer
T isomer
MVDOO AMIa
0.0 0.0
SCF/ST0-3G
0.0
SCF/DZ’
0.0 0.0
-3.9 -15.6 -73.3 49.5 -97.4
BLYP DZ’
A. Rathna and J. Chsndrssekhar. ref 19. Energy paint calculated at SCF STO.3C.optimiz.ed gwmctry.
determinedstructure because it had the most delocali7ationenergy and caused the fuilerene structure to be least disrupted from its unsaturated equilibrium geometry. Our theoretical predictions clearlyshow that the Tisomer ismorethermodynllmicallystablc than the Th isomer.
Cmk The nomenclature used in this paper to refer to carbon atoms was previously defined by Henderson and Cahill (Figure
2): In this representation, a Clo molecule Viewed vertically is considered to consist of nine layers of atoms, A-I. Layers C-G contain 10 atoms each while layers A, B, H, and I contain five each. We examined a group of C70H16 isomers characterized by hydrogenation patterns that followed two rules. First, all hydrogens were placed in 1,2, 3 positions on the 12 five-carbon rings of the CT0fullerene. Because both the T and Th isomers of CmHI6are hydrogenated in this manner, we hypothesized that low-energy isomers of CloH16 might follow the same pattern. This observation could be related to the fact that 36 hydrogens are the most common number attached Cm and Clo following Birch reduction;perhaps hydrogenationbecomes unfavorableafter threepositionsoneachoftbe 12five-membered ringsina fullerene are saturated. Secondly, we examined isomers whose hydrogen atoms were concentrated in the A 4 and G-I layers of Clo, with few or no hydrogens in the D-F layers. These structures may be low in energy because unsaturated carbon atoms in the middle layers (D-F) form a series of five r-conjugated, benzene-like rings. Hydrogenation of this region of Clo may be tbermcdynamicallyunfavorablebecauseit breaks upthis”graphite” region. High-level Hartree-Fock SCF calculations (double4 plus pclarization basis set) on Clo support this interpretation.” This study predicts that the bond lengths between the six-membered rings around the Clo waist, D-D and D-E bonds, are 1.415 and 1.407A. respectively. Thenear equality ofthesetwobond lengths indicates significant aromatic character in this region of the molecule. The shortest bonds in Clo (by more than 0.03 A) are the ones connecting carbon atoms in the A level to atoms in the B level (and 1atoms to H atoms) and between atoms within the C level (and G level). A-B bonds were calculated to be 1.375 AandC-Cbondswerecalculated tobe 1.369.k Becauseshorter bonds have more double-bond character, they may be more susceptible to hydrogenation and other addition reactions. Because of the large size and low symmetry of the CloH* isomers we studied, ab initio geometry optimizations were not practical. We chose the molecular mechanics program” MM3 to optimize the geometries of structures we studied. HartreeFock SCF energy point calculations with the STO-3G basis set were then performed at the MM3 geometries. MM3 optimizations followed by SCF/STO-3G energy points have been shown to be an inexpensive and reliable method for determining the relative energies of fullerenes.’] A Cl0HI6 isomer that satisfies the hydrogenation pattern we established can be formed by attaching hydrogen atoms to all carbon atoms in the B, C, G, and H layers of C ~ and O to three adjacent carbon atoms in both the A and I layers. When Viewed down the Cs axis of the Clostructure, the hydrogen atoms in the A and H layers eclipse each other. This isomer (1, see Figure 3) has C, symmetry, an MM3 heat of formation of 492.8 kcal/ mol, and an SCF/STO-3G energy (at the MM3-optimized
The Journal of Physical Chemistry, Vol. 98, No. 16,1994 4285
TABLE 2: Symmetry Point Groups and MM3 and SCF/ STO-3C Relative Energies (kcal/mol) of C 7 a y Isomers (See Figure 3) isomer wint MM3 SCF/STO-3@ . K-~ O U.D 1 2 3 4 h b
5bb 5eb l"er
cz
c 2
C,
m c C, C,
0.0 4.4 4.1 -2.1 -2.8 -1.9
0.0 4.8 4.3 9.8 7.5 8.4
4.3
EnergypintscalculatedatMM3-optimizedgeometries. Structurcs not shown in Figure 3; see text.
t
t
Ism" 3
Ch
t
?
lromer 4
Figure 3. Some CIOHM isomers explored in this study. Isomer 1has C1, symmetry and is formed by distributing the hydrogens evenly between the top and bottom three rows of carbon atoms in C~O.The hydrogen atoms in the fivemembered rings at the poles of the C,Oeclipse each other. Isomer 2 has C2 symmetry and is formed by shifting the groups of three hydrogens in the five-membered rings at the poles of isomer I one carbon over relative to each other. This is the lowest energy CtoH16 isomer found in thisstudy by at least 0.5 kcal/mol (STO-3/SCFenergies at MM3 geometries). Isomer 3 can be formed from isomer 1by shifting the groups of three hydrogens in the five-membered rings at the poles of the molecule twocarbonsover relative to each other. It has Czsymmetry and is the second lowest energy isomer of CtoH,s found in this study. Isomer 4 differs from isomer 1 by a shift of a pair of hydrogen atoms from the third highest (or lowest) level to the fourth highest (or lowest) level of carbon atoms in '270. Although MM3 suggested it was one of the lowest enerevisomersofC~nH~~.STO-3G/SCFcalculationsatthe MM3._ .. optimized &metry found it to be 10.6 k&l/mol above the lowest energy isomer found in this study.
geometry) of -2639.841 82 hartrees. The 36 hydrogen atoms of isomer 1 are divided evenly between the two caps of the C7,, structure. Fifteen of the 17 total double bonds are located in the waist region of the C7o structure, while a double bond is located in each of the five-membered rings at the poles (the A and I layers) of the C70structure. Several modified versions of the low-energy C,. isomer were calculated to have energies competitive with isomer 1. A modification of 1 that lowers the energy of the resulting isomer involves changing the positions of the groups of three hydrogen atoms in the A and I levels in relation to each other. Shifting the groups of hydrogens one and two carbons relative to each otherformsinequivalent isomers Zand3,respectively (Figure 3). Isomer 2 was calculated to be lower in energy than 1 by 0.4 kcal/mol (MM3) and 0.8 kcal/mol (SCF/STO-3G),whileisomer 3 was lower in energy than 1 by 0.1 kcal/mol (MM3) and 0.3 kcal/mol (SCF/STO-3G). These were the two lowest energy
(Sa-), formed by changing the relative positionsofthe hydrogen atoms in layers A and I of isomer 4, all had energies similar to that of 4 (see Table 2). Isomers with more than one pair of hydrogens moved from layers Band C (or G and H) to layer D (or F) have MM3 energies significantly higher than theisomers presented in this study. Using MM3, wetriedseveralother arrangementsof 36 hydrogenatoms around the C70structure (such as putting many hydrogen atoms in layers D-F). We found that all thesecombinations have much higher energies than theisomers formed by placing the hydrogens primarily in layers A-C and G-I.
Conclusions Theoretical studies of C60H36have focused on the T and Tk isomers. In this paper we present the highest level calculations yet reported of the relative thermodynamic stabilities of the two isomers. Using BLYP/DZ energy points at the SCF/STO-3Goptimized geometries, our results indicate that the T isomer is lower in energy than the Tk isomer by 97.4 kcal/mol. These predictions support Taylor and mworkers'sl8 claim that the T isomer is the true structure of CaH36. Using MM3 optimizations and SCF/STO-3G energy calculations, we studied a class of C7&6 isomers we believe could be especially low in energy. The hydrogenation patterns of these isomers are determined by two rules. First, all hydrogens are placed in 1.2, 3 positions on the 12 five-carbon rings of the C70, following the hydrogenation pattern found in both the T and Tk isomers of CaHa. Second, the hydrogens are concentrated in the caps of the Cl0 structure, leaving the equatorial region extensively conjugated. We determined the relative energies of several isomers in this class of C70H36structures. The lowest energy structure we found (Figure 3, isomer 2) is formed by hydrogenating all carbon atoms in the E D and F-H levels of C70,three carbons in 1,2,3 positions of the five-membered ring inlayerhand threecarbonsin2,3,4positionsinlayerI.However, some of the other isomers studied in this paper are within a few kcal/mol of each other, and (at the level of theory used in this study) we cannot completelyrule them out as possiblecandidates for thelowest energy isomer ofC70H36.Our theoreticalpredictions await experimental confirmation. Acknowledgment. G.E.S.is a Camille and Henry Dreyfus Teacher-Scholar. This work was partially supported by the National Science Foundation (CHE-9321297) and the Welch Foundation.
isomersofC70H36wefoundonthehasisofSCF/STO-3Genergies. References and Notes
Another modification of isomer 1, that results in isomers energeticallycompetitivewithit,involvesmovinga pair ofadjacent hydrogen atoms on the same five-memher ring from layers B and C to the two positions on that fivemembered ring in layer D. Thisisomer,4 (Figure3), which has C, symmetry, wascalculated with MM3 to belower inenergy than 1by2.1 kcal/mol. However, the SCF/STO-3G calculation determined that isomer 4 was higher in energy than 1 by 9.8 kcal/mol. Three other isomers
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