J. Phys. Chem. 1992,96, 10265-10268
An ab Initio Study of the Cl0 Fullerene Isomers John R. Colt and Gustavo E.Scuseria*f Department of Chemistry and Rice Quantum Institute, Rice University, Houston, Texas 77251-1892 (Received: June 22. 1992) The two possible isolated-pentagon fullerene isomers of (276, a chiralD2 structure with a closed-shell electronic structure and a Td isomer with an open-shell electronic configuration, are investigated by employing the Hartree-Fock self-consistent field method with minimal and double-f quality basis sets. The Td structure has a partially filled HOMO and is subject to first-order Jahn-Teller distortion. We found a closed-shell 'AI state in Du symmetry to be the lowest energy state for the Td isomer. Nevertheless, the 0 2 isomer is found to be 43 kcallmol more stable than the symmetry-lowered T p D u isomer at the SCF level of theory with the double-{ basis set. Equilibrium structures and ionization potentials for both isomers are also presented.
Introduction The synthesis and isolation of C, and c 7 0 in gram quantities' has stimulated interest in the macroscopic isolation of other molecular forms of carbon. In the original method devised by Kritschmer, Lamb, Fostiropoulos, and Huffman,' macroscopic quantities of C, and C70 are produced by the resistive heating of graphite under an inert atmosphere. Recently, evidence of fullerenes larger than C70 has been reported in relatively small amounts in the soot from the formation of macroscopic quantities of C, and C70.2.3Chromatographic separation of the toluenesoluble soot resulted in the isolation of several new fullerenes: c76, c78, c82, and c84. The properties of these new fullerenes are now being evaluated. For example, the electrochemical properties of c 7 6 were found to be different from those of C, and C70.4This higher fullerene was shown to have up to four reversible reduction steps and a single reversible oxidation step, unlike Cso and C70 that show only reversible reduction steps. Fullerene structures require a closed network of atoms following Euler's theorem. They consist of 12 fivemembered rings (5MR) and (n - 20)/2 six-membered ring (6MR), where n is the number of carbon atoms in the cluster. This type of structure is found to be most stable when the isolated-pentagon rule' (IPR) is satisfied. The IPR states that there are no abutting SMRs within the molecule, which destabilizes the conjugated system of relectrons.' Two topologically distinct fullerene, IPR structures fit this criteria for c76: one having Td symmetry and the other with D2 symmetry? On the basis of qualitative molecular orbital theory it was readily observed that the Td structure corresponds to an open-shell electronic configuration while the D2 structure corresponds to a closed-shell electronic configuration.6 For the Td isomer, the open-shell electronic configuration consists of a doubly-occupied, triply-degenerate (t:) highest occupied molecular orbital (HOMO). The possible electronic states arising from this configuration are 3T1,'E, IT2, and 'Al. Except for the 'Al state, these electronic states are subject to first-order Jahn-Teller (JT) distortion that will effectively lower the molecular symmetry. The spatial degeneracy may be partially removed by lowering the symmetry from Td to D u where the tl orbital transforms as a2 + e. The ti 'Al state becomes a: IA1, and one of the components of the t: 3TI becomes e2 3Az. Both the a: 'Al and e2 3A2electronic states in D u symmetry are JT stable. The other two states in Td symmetry ('E and IT2) remain spatially degenerate in Du symmetry. Lowering the molecular symmetry from D u to D2 makes the e orbital transform as b2 + b3 (also note that a2 becomes bl), and JT stable states may be formed by occupying these D2 molecular orbitals. In this work, we have examined in detail some of the Du and 4electronic states. In particular, we cam'ed out geometry o p timizations of the a: 'Al and e2 3A2states in D u symmetry, corresponding to the 'Al and states in Td symmetry. w e found Camille and Henry Dreyfus Teacher-Scholar.
the a: 'Al state to be lower in energy than the e2 3A2state. We also investigated the b: 'Al and b: 'A, states in D2 symmetry that correapond to the 'E state in Td symmetry. However, these states are double excitations from the b: 'Al state in D2 symmetry (equivalent to the a: 'AI state in D2d symmetr ) and they were found to lie much higher in energy than the a!A 'I state in Du symmetry. Electronic states in D2 symmetry like b2b3 'B1corresponding to the IT2state in Td symmetry were not analyzed due to their open-shell singlet nature. Our preliminary results clearly indicated that the cla9ed-shell a: 'A, state in D u symmetry had the lowest energy of the states arising from the ti Td configuration. In the following, the a: 'Al state will be indicated as Td+DM Structural information of the experimentally isolated c 7 6 fullerene was obtained by Ettl, Chao, Diederich, and Whetten (ECDW).7 From the "C NMR spectra they reported a series of 19 distinct lines each with approximately the same intensity. These 19 resonance lines span the same region as the I3CNMR spectrum of C70 and were assigned to 19 distinct carbon environments,each set c o m e of four symmetry-equivalent carbon atoms. In the interpretation of the experimental data obtained by ECDW, the D2 symmetry structure was chosen over the Td symmetry structure since its point-group symmetry fit the data from the I3C NMR spectrum and it had a closed-shell electronic configuration. A limited number of theoretical studies have been completed so far for c76. The first study was done by Manolopoulos using qualitative molecular orbital theory? In this work the D2 isomer was predicted to be the ground-state structure since it had the largest HOMO-LUMO separation. It was also argued that the D2 structure had a closed-shell electronic configuration, similar to other known fullerenes such as C, and C70. More recently Zhang, Wang, and Ho (ZWH) completed a theoretical study of large fdlerenes using a tight-binding method! In their study they predicted the equilibrium structures of the closed-shell Dz and T p D u symmetry c 7 6 structures. These authors found the T,+--Du isomer to have a less favorable cohesive energy by 5.3 kcal/mol relative to the D2 isomer. %to, Sawada, and Hamada (SSH) calculated the equilibrium structure of D2 c 7 6 using a model potential for carbon.g They also predicted the one-electron energy levels using a tight-binding model and found there was good agreement between the dculated density of states and the experimental photoemission spectra, further supporting the D2 structure for the experimentally isolated c76.
In this work the equilibrium structures of the closed-shell D2 C76 and D u c 7 6 (corresponding to the ti Td state) are predicted at the ab initio HartretFcck self-consistent field level of theory employing minimal basis sets in conjunction with analytic energy gradient techniques. The energy separation between the two isomers is also obtained with a double-t basis set. The large HOMO-LUMO gaps found are indicative of closed-shell ground-state structures. The predicted bond lengths fall in the range of the calculated and experimental bond lengths of C, and c70.1*13
0022-365419212096-10265$03.00/0 Q 1992 American Chemical Society
10266 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992
Colt and Scuseria
Figure 1. D2 isomer of c76.
Figure 3. Connectivity pattern for the D2 isomer of c76. G
Figure 2. T p D u isomer of
H
c76.
Computational Details
For the geometry optimization of C76the STO-3G basis, the standard minimum basis consisting of (2s 1p) contracted functions,I4 was used in conjunction with the direct SCF15,16method as implemented in the TURBOMOLE package.17 Previous ab initio calculations of Csoand C70 have shown that SCF geometry optimizations using the STO-3G basis set have given qualitatively reliable nsults (-0.01-A difference8 in the optimized bond lengths of STO-3G/SCF and dz/SCF).'OJ1 At the optimized SCF/ STO-3G geometry, an SCF energy point was calculated by using a double-f (dz) basis set originating from a (4s2p) contraction of Van Duijneveldt's (7s3p) primitive set.18 All calculations were performed at Ria University on an IBM RS-6000/550 workstation.
R d t s aod Discmion The D2 and the T p D u structures consist of 28 6MRs and 12 5MRs. The D2 structure contains 19 symmetry distinct sets of four equivalent C atoms resulting in 57 internal degrees of freedom, 30 of those being symmetry-distinct, first-neighbor stretcha. The T p D u structure contains three symmetrydistinct sets of four equivalent C atoms and eight distinct sets of eight equivalent C atoms resulting in 30 internal degrees of freedom, 17 of which are symmetry-distinct, first-neighbor stretches. The 0 2 and T p D u C,6 structures are presented in Figures 1 and 2. To understand the difference between the two isomers, each C76 structure may be separated into caps consisting of 38
2--.- _.$L-. G
~
:__. ---d'
H
'
Figure 4. Connectivity pattern for the T p D u isomer of
(276.
carbon atoms each. The caps and connectivity pattern between them are depicted in Figures 3 and 4. The two caps for the T p D 2 isomer are symmetrically equivalent but rotated 90° relative to each other. The only difference between the two structures is the upper cap of the D2 structure. The two caps in the D2 structure are not symmetrically equivalent to each other ( F w 3). The lower cap in the figure is equivalent to the cap of the T p D w structure. The upper cap differs by the replacement of four C atoms (bold atoms in Figures 3 and 4). Starting from the T p D u structure (Figure 4), two of the four bolded atoms are moved to positions near a m D,E, F, and G completing a new hexagon (destroyins hexagon 1 and creating hexagon 1'), and similarly the other two bold atoms are equivalently shifted to the position to complete another hexagon (destroying hexagon 6 and creating hexagon 69. The upper cap is then rotated approximately 3 5 O counterclockwise
Study of the
1 1 2 2 3 3 4 4 5 5 6 7 7 8 9 9 10 10 11 11 12 12 13 14 14 15 16 17 18
c76
2 6 3 8 4 19 5 17 6 16 7 8 13 9 10 19 10 11 12 13 14 19 15 15 17 16 18 18 18
The Journal of Physical Chemistry, Vol. 96, No. 25, I992 10267
Fullerene Isomers
1.495 1.386 1.475 1.435 1.477 1.374 1.456 1.438 1.462 1.397 1.475 1.480 1.403 1.414 1.411 1.418 1.461 1.485 1.406 1.472 1.422 1.456 1.363 1.462 1.455 1.376 1.361 1.461 1.454 1.381
1 1 2 2
3 3 4 5 6 6 7 7 8 9 9 10 11
1 2 3 10 4 8 5 6 7 11 7 8 9 10 11 10 11
1.457 1.431 1.490 1.393 1.424 1.395 1.412 1.441 1.398 1.463 1.491 1.438 1.467 1.467 1.354 1.413 1.472
"See Figures 1 and 2 for corresponding bonding atoms.
and connected to the lower cap. The dashed lines indicate a connecting bond between caps corresponding to the letter of the atom. Connecting the two caps results in the formation of eight 6MRs and four 5MRs around the "waist" of each isomer (indicated as 5 and 6 below). The connectivity pattern is, however, differmt for the two isomers. Starting in both from the ABC pentagon (dashed lines) in Figures 3 and 4, the waist patterns for the D2 and the T p D 2 d structures are 565666565666 and 566566566566, respectively. The symmetry-distinct first-neighbor bond lengths, optimized at the STO-3G/SCF level of theory, for the D2 and T p D u isomers are presented in Table I. The D2 isomer bond lengths range from 1.36 to 1.49 A. The T p D w isomer bond lengths range from 1.35 to 1.49 A. These values fall within the expected range for fullerenes and are similar to SCF predictions for Cm and C70.10JIThe dimensions along the three s metry axes of the D2 structure are D, = 8.82 A, 4 = 7.71 r a n d D, = 6.83 A. The dimensions from SSH's optimized structure for the D2 h o d differ from OUR by -0.05, -0.2 1, and 4.29 & respectively. The dimensions along the three symmetry axes of the T p D u isomer are all the same, being D, = 4 = Dc = 7.76 A. The closed-shell electronic configuration (lAl) for the experimentally isolated D2 isomer is 59a2 57bf 56b: 56b:. As noted earlier, the Td isomer is subject to firstsrder Jahn-Teller distortion, which effectively reduces the spnmetry. The Tdopen-shell electronic configuration is 15af 6a2 19e4 23tf 33tl 24tf. The possible electronic states resulting from this electronic configuration are 'Al, 'E,3T1, and IT2. The closed-shell electronic configuration of the 'Al T p D u component is 34a: 24a: 25b: 33b: 56e4. The total energies at the equilibrium structures of the D2 and T p D u (276 isomers are presented in Table 11. At the STO3G/SCF level of theory the D2 isomer is predicted to be the lowest energy isomer by 45.4 kcal/mol over the T p D u isomer. With the dz basis set, the 4structure is favored by 42.7 kcal/mol. This energy separation between isomers is over eight timea larger than
(hW)Of tk D1 rad T c D u TABLE U T ~ t d ISOEIHS Of Cm As Redktd by the SCF h d Of Tkory basis: STO-3G double-s no. of bfs 380 760 -2842.821 99 -2874.391 91 0 2 E per C atom -37.405 55 -37.820 95 -2842.749 67 -2874.323 80 TPDU E per C atom -37.40460 -37.82005 AE,kcal/mol 45.4 42.7 TABLE Ilk heq#era (io hrbees) of the Hiphest Oaupied (HOMO) lad Lowest U D O C C (LUMO) U ~ ~ ~ orbihb for t h Dl rad TPDM IBO Of C, IAs D Predicted Wby S the SCF h e l Of Tbcory D, TPDW STO-3G (HOMO
a
bi b2 b3
(HOMO
-0.213 -0.170 -0.184 -0.21 1
81
a2
bl b2 e
-0.241 4.138 -0.154 -0.226 -0.219
~LUMO
CLUMO
a
0.086 0.200 0.104 0.099
bl
b2 b3
81
a2
bl b2 e
0.124 0.245 0.099 0.187 0.052
Double-( (HOMO
a
bl b3
-0.309 -0.272 -0,284 -0.310
(LUMO
a
bl
bz b3
-0.040 0.057 -0.028 -0.032
(HOMO a1 a2
bl
b2 e
CLUMO 81
a2
bl b2 e
-0.337 -0.243 -0,257 -0.323 -0,321 -0.009 0.105 -0.030 0.046 -0.07 1
"Theionization potentials may be readily obtained by using Koop man's theorem as I, = -(HOMO. the results achieved by ZWH using a tight-binding method.* It is unlikely that inclusion of polarization functions and electron correlation will reduce the energy separation between the isomers by such a factor. In Table 111, the molecular orbital energies of the HOMO and LUMO of each irreducible representation are presented for the D2 and the T p D u isomers. Negative LUMOs are not common for closed-shell SCF wavefunctions, but similar characteristics have been observed in Cm and C7010J1and may be typical of the fullerene clusters. The ionization potentials may be obtained by using Koopmans' theorem as 1, = -€HOMO.
Conclusion Ab initio self-consistent field HartretFock calculations employing minimal and double-f basis sets have been carried out on the possible isolated-pentagon fullerene isomers of c 7 6 . Two topologically different structures of c 7 6 within the isolated-pentagon ruleS are possible: one having D2 symmetry and a closedshell electronic configuration and the other having Td sy!nmeF and an open-shed electronic configuration. Jahn-Teller cfistortmg the Td isomer to D u and D2 symmetry we found a 'Al ground state for this isomer in D u symmetry. Our beat theoretical prediction gives an energy separation of 42.7 kcal/mol in favor of the D2 structure over the T p D 2 d isomer. Acknowledgment. This work was supported by the National Science Foundation (Grant CHE9017706). We thank Dr.Roger Grev for helpful discussions. References 8nd Notes (1) KrHtschmer, W.;Lamb, L. D.;Fostiropoulos, K.;Huffman, D. R. Nature 1990, 347. 354.
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J. Phys. Chem. 1992,96, 10268-10275
(2) Diederich, F.; Whetten, R. L. Acc. Chem. Res. 1992, 25, 119 and references therein. (3) Kikuchi, K.;Nakahara, N.; Wakabayashi. T.; Suzuki, S.;ShuOmaN, H.; Miyake, Y.; Saito, K.; Ikemoto, I.; Kainosho, M.; Achibe, Y. Nature 1992, 357. 142. (4)Li, Q,; Wudl, F.; Thilgen, C.; Whetten, R. L.; Diederich, F. J . Am. Chem. SOC.1992,114,3994. (5) Schmalz, T. G.;Seitz, W. A.; Klein, D. J.;Hite, G.E. Chem. Phys. Lett. 1986,130, 203. Kroto, H.W. Nature 1987, 329, 529. (6) Manolopoulos, D. E. J. Chem. Soc., Faraday Trans. 1991,87,2861. (7) Ettl, R.;Chao, I.; Diederich, F.; Whetten, R.L. Nature 1991,353,149. ( 8 ) Zhang, B. L.; Wang, C. 2.;Ho, K. M. Chem. Phys. Lett. 1992,193,
(10)Scuseria, G.E. Chem. Phys. Lett. 1991. 176. 423. (11) Scuseria, G.E. Chem. Phys. Lett. 1991; 180; 451. (12) Hrdberg, K.;Hedberg, L.; Bcthune, D. S.;Brown, C. A.; Dorn, H. C.; Johnson, R. D.; de Vries, M. Scfence 1991,254,410. (1 3) McKenzie, D. R.;Davis, C. A.; Cockayne. D. J. H.; Muller, D. A.; Vassallo, A. M. Nature 1992, 355, 622. (14) Hehre, W. J.; Radom, L.; von R.Schleyer, P.; Pople, J. A. Ab Idtfo Molecular Orbital Theory; Wiley: New York, 1985. (IS) Almlaf, J.; Fa@, K.,Jr.;Korsell, K.1. Compur. Chem. 1982,3,385. (16) Him,M.; Ahlrichs, R. J . Compur. Chem. 1989, 10, 104. (17)Ahlrichs, R.;Bir, M.; Haser, M.; Horn, H.; Kalmel, C. Chem. Phys. Lett. 1989. 162. 165. (18)van Duijneveldt, F. B. IBM Research Report RJ 945, 1971.
22s.
(9)Saito, S.;Sawada, S.; Hamada, N. Phys. Rev. B, in press.
Ab Initio Molecular Orbital Study of Nitrogen-Containing Polyenes with Donor-Acceptor Substituents: Dipole Moment and Statlc First Hyperpolarizability Tetsuya Tsunekawa* Polymer Research Laboratories, Toray Industries, Inc., 3-2- I Sonoyama Otsu, Shiga 520, Japan
and Kizasbi Yamaguchi Department of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan (Received: June 26, 1992; In Final Form: September 14, 1992)
Ab initio CPHF calculations have been carried out in order to clarify the relationship between dipole moment ( p ) and first hyperpolarizability (8)of nitrogen-containing *-conjugated polyenes with donoracceptor substituents attached on the end. The systematic calculations on the polyene-like model compounds indicate that nitrogen-atom substitutionsin *-conjugated systems (N substitutions) fluctuate p-values and gradually decrease &values with increasing the number of substituted nitrogen atoms. From the calculated results, several tendencies are recognized for the changes of p- and &values induced by the N substitution. The molecules with nitrogen atom at the even-numbered position counted from an electron-accepting nitro group have larger &value but smaller p-values than those with nitrogen atom at the odd-numbered position, which is the other position of the same double bond. Especially, an introduction of a single nitrogen atom into the even-numbered position of hexatriene analogs decreases the p-value as controlling the reduction of &value. These ab initio mults support our previous conclusions based on semiempirical CNDO/S calculations of stilbene and benzylideneaniline molecules. The analyses of molecular orbitals and full SCI calculations of the electronic transitions for the model compounds have revealed the intrinsic effects of N substitutions; the decrease of 8-value is mainly attributed to the blue shift of the absorption maxima, and the N substitution at the even-numbed position counted from nitro p u p enhances the indued polarization through the effective variations of the energy levels and shapes of the frontier *-orbitals. It is umcluded that N substitutionsat the specifc positions provide us an effective approach in designing molecules with relatively small p-values but large @-values,which are desirable from the view point of crystal engineering of the nonlinear optical materials.
Iatroduction Recently, some organic crystals' comprising donor (D)-dcceptor (A) molecules (DA molecule)2 have been intensively studied due to their demonstrated large second-order nonlinear optical susceptibilities which may enable us to realizc optical devioes in future photonic technology such as optical telecommunication and information processing. This characteristic property of organic crystals is attributable to a large intramolecular nonlinearity ( f i t hyperpolarizability, 8) of the DA molecule and a favorable noncentrosymmetric molecular orientation in its crystalline state.' The large @-value originates from strong chargetransfer interaction in the DA molecule which enhances the electronic polarization induced by incident laser light. Therefore, we accomplish large &value through designing an adequate DA molecule. On the other hand, the problem in obtaining a new organic nonlinear optical crystal is a rather difficult task. In light of the present scientific level, molecular orientations and crystal structures are hardly controllable because they are generally determined by the delicate balance among several intermolecular forces such as van der Waals,d i p ~ l d i @ ~and , hydrogen-bondingintetactionS. A Useful working hypothesis for controlling molecular orientation is that smaller p is rather favorable since it suppresses the strong dipoledipole interaction among DA molecule which generally leads to an unfavorable centrosymmetric molecular packing. Therefore, Oo22-3654/92/2096-10268$03.Oo/O
a promising approach for a new molecular crystal with improved nonlinearity is designing a DA molecule with large but small pvalues as has been already demonstrated e~perimentally.~.~ For the last two decades, detailed studies on B- and 1-values of unsaturated hydrooerbon DA molecules have been camed out both theoretically and experimentally.' It has been already pointed out that &values increase together with the increase of p-values by extending ranjugatad systems and by introducing a strong D and A pair. Moreover, it is well-known that 8-values compensate for transition energies which limit the wavelength of available laser light for second harmonic generation (SHG).' Concerning DA molecules with heteroatoms involved in *-conjugated systems, systematic investigations on both the 8- and pvalues have not been carried out theoretically even though interesting molecular properties have been found out experimentally.'*5*6For example, DA pyridine molecules skilLfully designed were reported to be effective for improved molecular properties such as smaller ~-valuesS and shorter cutoff wavelengths6 as compared with corresponding hydrocarbon DA molecules. It may be considered that heteroatom substitutions at r-conjugated networb have capabilitiee of providing us a useful guiding principle for new sophisticated organic nonlinear optical crystals. In a previousworl~,~.~ for the purpose of investigating the effects of nitrogen-atom substitutions in *-conjugated systems (N substitutions), we calculated the 1- and &values of DA diphenyl (8
1992 American Chemical Society
