J. Phys. Chem. 1994,98, 1756-1757
1756
Symmetric Isomers of CaHx B. I. Dunlap' and D. W. Brenner Theoretical Chemistry Section, Code 6179, Naval Research Laboratory, Washington, D.C. 20375-5342
G. W. Schriver Exxon Chemical Company, P. 0. Box 536, Linden, New Jersey 07036
Received: Nwember 15, 1993'
Local density functional electronic structures of four isomers of CmH36, which have been proposed in the literature, are studied at geometries given by an empirical potential. The conjugation of the unsaturated bonds is quite different in each structure, yet the ionization potentials of each are the same within 0.12 eV. There is even greater agreement among the electron affinities, which are negative. The tetrahedral isomer with four six-membered rings of unsaturated carbon atoms is energetically the most stable.
CmH36 was the first chemical synthesized from C60.l Since then, CmH36 has been made in other laboratories2 and by other means.3 There are roughly 1013possible isomers of CmH36.4 It is unlikely that all will be synthesized. The most stable isomers probably have the strain due to curvature distributed over the entire surface, possibly leading to fairly high symmetryfor isomers that can be made experimentally. In this Letter we report the relative energies and geometric and electronic structures of four rather symmetric isomers of the CmH36 molecule using the empirical potential I of ref 5 and all-electron, self-consistent, local density functional (LDF) ~alculations.6.~ The LDF used is the Perdew-Zungere (PZ) fit that interpolates between the essentially exact Ceperley-Alderg free-electron gas calculations in the completely ferromagnetic and completely paramagnetic limits. The four isomers are sufficiently different that one might expect large differences in their electronic structures. Icosahedral Cm has two distinct types of bonds. The 6-6 bonds form an edge that is shared between two hexagonal rings of carbon atoms. The 6-5 bonds connect pentagonal and hexagonal rings. To a degree the molecule is aromatic,1° but the conjugation weakens as a function of surface curvature" to the point that the shorter 6-6 bond can be viewed as a double bond and the longer 6-5 bond as a single bond. The most symmetric isomer of has 12 double bonds (pairs of nearest-neighbor carbon aioms lacking hydrogen atoms) as far apart as possible on its surface.' This isomer has a double bond on each pentagon and Th symmetry.12J3 This bond was a "single" bond in the starting material. It is possible that this is not the only isomer of CmH36 that can be made or even that it is the most stable isomer energetically. Incorporating the double bonds in "aromatic" sixmembered rings yields a slightly less symmetric T structure that has four six-membered rings of carbon atoms lacking hydrogen atoms, located at the corners of a tetrahedron.l+17 In such a structure conjugated 6-6 double bonds are possible resonant form. Intermediate between these two extremes are particular, still less symmetric D3d and S6 isomers.'*J9 These last two isomers have two six-membered rings of carbon atoms lacking hydrogen atoms, located at the poles along the 3-fold axis. The other six double bonds are isolated, 6-5 bonds that point roughly east-west and north-south for the D3d and Sg isomers, respectively. These four isomers are drawn in Figure 1, where the unsaturated carbon atoms are connected by boldface lines. To the extent that there is a penalty to forming 6-5 double bonds relative to 6-6 double bonds the T isomer might be expected to be more stable than the others. Self-consistent-field calculations have been performed
* To whom correspondence should be addressed. 0
Abstract published in Aduance ACS Abstracts. February 1, 1994.
0022-3654/94/2098- 1756$04.50/0
T
Th
'6
D3d
Figure 1. Carbon atoms of four isomers of C d 3 6 considered in this work are depicted as verticcs in this drawing. The unsaturated carbon atoms ae connected by dark lines. Each isomers is labeled by its point-
group symmetry.
TABLE 1: Coordinatm and Number of Equivalent Atoms for Each Symmetry-Inequivalent Type of Atom in the Tb Symmetric CsaHj~Isomer type atom no. x,A Y,A z, A C C C
24 24 12 24 12
2.510 3.267 3.886 4.070 4.943
0.664 1.528 0.789 2.020 1.012
2.246 1.262
0.000
H 1.770 H O.Oo0 on C6& , isomers.12.13,16,*23The semiempirical calculations21 showed that shifting one or two of the double bonds around to other 6-6 and 6-5 bonds on the surface of the Th isoqer gave less stable structures;however, another semiempiricalcalculation16 showed that the T isomer is more stable than the Th structure. The geometry of each isomer was optimized using the empirical potential.24 The results are given in Tables 1-4. Table 1 gives the optimized coordinates of a representative of each set of symmetry-inequivalent atoms in the Th O H 3 6 isomer. Table 2 gives the optimized coordinates of the symmetry-inequivalent atoms of the T isomer. These coordinates require that the 3-fold axes of the tetrahedral group point in the (l,l,l), (1,-1,-1), etc., directions. Table 3 gives the optimized coordinates of the 0 1994 American Chemical Society
Letters
The Journal of Physical Chemistry, Vol. 98, No. 7, 1994 1757
TABLE 2: Coordinates and Number of Equivalent Atoms for Each Symmetry-InequivalentType of Atom in the T Symmetric C&~S Isomer atom no. 12 12 12 12 12 12 12 12
tYPc C C C C C H H H
x,A 2.334 2.758 3.855 -2.873 -3.440 4.854 -3.714 -4.358
z, A
y,A 0.491 1.205 0.783 -0,842 -1.663 1.086 -0.756 -2.097
2.041 0.927 -0.026 -2.524 -1.330 0.213 -3.188 -1.690
TABLE 3: Coordinates and Number of Equivalent Atoms for Each Symmetry-Inequivalent Type of Atom in the Symmetric C&~S Isomer type atom no. x, A Y,A Z,A C C C C C C H H
12 12 6 12 6 12 12 6 6 12
H H
1.216 2.533 3.367 2.061 3.937 2.947 3.117 4.258 5.003 3.752
-0,705 -1.271
3.077 2.548 2.113 1.460 0.656 0.265 3.268 2.722 0.839 0.520
O.Oo0 2.224 0.000 2.540 -1.800 0.000 0.000 3.207
TABLE 4 Coordinates and Number of Equivalent Atoms for Each Symmetry-InequivalentType of Atom in the S, Symmetric C&~S Isomer type atom no. x,A Y,A Z,A C C C C C C C C C C H H
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
H H H H
TABLE 5
1.218 1.209 2.585 2.544 3.378 2.084 2.376 3.836 2.544 2.929 3.137 3.100 4.291 2.880 4.896 3.860
-0.710 0.700 -1.291 1.281 0.005 2.236 -2.549 -0.018 2.206 -2.519 -1.658 1.801 0.029 -3.333 -0.184 -3.053
2.987 2.993 2.625 2.560 2.138 1.47 1 1.727 0.654 0.216 0.253 3.471 3.307 2.710 2.261 0.732 0.225
Energetics of the C d x Isomers
relative enerxy, eVa
svm
empirical
LDF
IP,eV
EA.eV
HOMO
LUMO
~
Th T
Djd s6 a
o.OO(1) 0.75(3) 1.24(4) 0.32(2)
2.10(3) O.OO(1) 2.35(4) 0.43(2)
6.49 6.52 6.48 6.40
-0.27 -0.21 -0.23 -0.23
27tu 17e 33% 33%
~
7a, 5ot 34eg 34%
The numbers in parentheses order the isomers energetically.
symmetry-inequivalent atoms of the D3d isomer. Table 4 gives the optimized coordinates of the symmetry-inequivalentatoms of the& isomer. Thecoordinatesof theselast two isomers require that the 3-fold axes lie along the Z axis. Additionally, for the D3d isomer a 2-fold axis must lie along the Y axis. The relative empirical potential and LDF energies computed at these geometries are given in Table 5. Despite the fact that the empirical potential incorrectly orders the isomers energetically, studies of fullerene isomers suggest that the LDF ordering will be correct.2s Thus, we expect the Tisomer to be theenergetically most stable of the isomers studied. A semiempirical AM1 calculation16 also gives the T isomer more stable than the Th isomer by0.7 eV. Table 5 alsoincludes theLDFvertical ionization potential (IP), electron affinity (EA), highest occupied molecular orbital (HOMO), and lowest unoccupied molecular orbital (LUMO) of these isomers. Table 6 gives the full electronic
TABLE 6
Electronic Structure of the C d x Isomers
sym
electrons of each svmmetry
HOMO-LUMO xaD. eV
Th T
162t, 132t, 22a, 44eg 24e, 12a, 68e 294t 34a 132% 132e, 44a1,42azu 24a1,22a2~ 132% 66a, 132e, 66a,
3.91 3.90 3.90 3.84
D3d s6
structure of these isomers, i.e., the total number of electrons of each orbital symmetry. Each one-electron symmetry is ordered by the relative energy of its HOMO. Furthermore, the first four HOMOs of the Th isomer belong to different irreducible representations. Similarly, the first two HOMOs of the T and &isomers belong todifferent representations,and the first three HOMOS of the S.5 isomer belong to different representations. These four isomersof CboH36arevery different. The remaining unsaturated bonds are 6-5 in the Th isomer and 6-6 in the T isomer. The unsaturated bonds are isolated and conjugated in hexagonal rings, respectively, in these same two isomers. The D3d and s 6 isomers share features of these two extreme isomers. Nevertheless, the ionization potentials of these isomers are 6.47 f 0.05 eV (where this uncertainty is the standard deviation for the four isomers), and the electron affinities of these isomers are -0.24 f 0.03 eV. (The negative sign indicates that the anion is unstable.) It is possible that one does not need to iylate CmHk isomers, for x in the region where the number of possible isomers is astronomical, to have a very good idea of their ionization potentials.
Acknowledgment. Discussions with Bob Compton stimulated much of this work. These calculations were made using a grant of computer resources from the Naval Research Laboratory. This work was supported in part by the Office of Naval Research (ONR) through the Naval Research Laboratory. References and Notes (1) Haufler, R. E.; Conceicao, J.; Chibante, L. P. F.; Chai, Y.;Byrne, N. E.; Flanagan, S.;Haley, M. M.; O'Brien, S.C.; Pan, C.; Xiao, Z.; Billup, W. E.; Ciufolini, M. A.; Hauge, R. H.; Margrave, J. L.; Wilson, L. J.; Curl, R. F.; Smalley, R. E. J. Phys. Chem. 1990, 94, 8634. (2) Banks, M. R.; Dale, M. J.; Gosney, I.; Hodgson, P. K. G.; Jennings, R. C. K.; Jones, A. C.; Lecoultre, J.; Langridge-Smith, P. R. R.; Maier, J. P.; Scrivens, J. H.; Smith, M. J. C.; Smyth, C. J.; Taylor, A. T.; Thorburn, P.; Webster, A. S.J. Chem. Soc., Chem. Commun. 1993, 1149. (3) Rtichardt, C.; Gerst, M.; Ebenhoch, J.; Beckhaus, H.-D.; Campbell, E. E. B.; Tellgmann, R.; Schwarz, H.; Weiske, T.; Pitter, S.Angew. Chem., In?. Ed. Engl. 1993, 32, 584. (4) Balasubramanian, K. Chem. Phys. Lett. 1991, 182, 257. (5) Brenner, D. W. Phys. Reu. B 1990,42,9458. (6) Dunlap, B. I.; Connolly, J. W. D.; Sabin, J. R. J. Chem. Phys. 1979, 71, 3396, 4993. (7) Dunlap, B. I.; Rbsch, N. Adu. Quantum Chem. 1990, 21, 317. (8) Perdew, J. P.; Zunger, A. Phys. Reu. B 1981, 23, 5048. (9) Ceperley, D. M.; Alder, B. J. Phys. Rev. Lett. 1980, 45, 566. (10) Kroto, H. W.; Heath, J. R.; OBrien, S.C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (11) Haddon, R. C. Science 1993, 261, 1545. (12) Dunlap, B. I.; Brenner, D. W.; Mowrey, R. C.; Mintmire, J. W.; Robertson, D. H.; White, C. T. Mater. Res. Soc. Symp. Proc. 1991,206,687. (13) Dunlap, B. I.; Brenner, D. W.; Mintmire, J. W.; Mowrey, R. C.; White, C. T. J. Phys. Chem. 1991, 95, 5763. (14) Taylor, R. J. Chem. Soc., Perkin Trans. 2 1992, 1667. (15) Taylor, R. Philos. Trans. R . Soc. London, Ser. A 1993, 343, 87. (16) Rathna, A,; Chandrasekhar, J. Chem. Phys. Lett. 1993, 206, 217. (17) Austin, S.J.; Batten, R. C.; Fowler, P. W.;Redmond, D. B.;Taylor, R. J. Chem. SOC.,Perkin Trans. 2 1993, 1383. (18) Hall, L. E.; McKenzie, D. R.; Attalla, M. I.; Vassallo, A. M.; Davis, R. L.; Dunlop, J. B.; Cockayne, D. J. H. J. Phys. Chem. 1993, 97, 5741. (19) Attalla, M. I.; Vassallo, A. M.; Tattam, B. N.; Hanna, J. V. J. Phys. Chem. 1993, 97,6329. (20) Guo, T.; Scuseria, G. E. Chem. Phys. Lett. 1992, 191, 527. (21) Bakowies, D.; Thiel, W. Chem. Phys. Lett. 1992, 193, 236. (22) Matsuzawa, N.; Fukunaga. T.; Dixon, D. J. Phys. Chem. 1992,96, 10747. (23) Yoshida, Z.; Dogane, I.; Ikehira, H.; Endo, T. Chem. Phys. Lett. 1993, 201, 481. (24) The coordinates for the Th isomer differ from those reported in ref 12. The potential function used to determine the coordinates in that reference included dihedral terms given in: Brenner, D. W.; Harrison, J. A.; White, C. T.; Colton, R. J. Thin Solid Films 1991, 206, 220. (25) Dunlap, B. I. Phys. Reu. B 1993, 47, 4018.
