J. Phys. Chem. 199498, 2555-2563
2555
Dimerization of Ca: The Formation of Dumbbell-Shaped Clmf Nobuyuki Matsuzawa' and Masafumi Ata SONY Corporation Research Center, 174 Fujitsuka-cho, Hodogaya- ku, Yokohama 240, Japan
David A. Dixod DuPont Central Research and Development, Experimental Station, P.O. Box 80328, Wilmington, Delaware 19880-0328
George Fitzgerald Cray Research, Inc., 655E Lone Oak Drive, Eagan, Minnesota 551 21 Received: September 2, 19938
The structures of three possible Cmdimers with intact cages have been calculated at the semiempirical (MNDO/ AM-1, PM-3) and a b initio density functional theory (DFT) levels. At the DFT level, both local (LDFT) and nonlocal (NLDFT) calculations have been performed. The dimers are formed by the 1,2-, 1,4-, and 1,2+1,4cycloadditions of a cyclohexatrienyl unit of each Cm. The energies of the dimers relative to that of the most stable 1,2-C@ dimer are 74.0 kcal/mol (AM-l), 75.2 kcal/mol (PM-3), 69.7 kcal/mol (LDFT), and 76.2 kcal/mol (NLDFT) for the 1,4-Cm dimer and 93.0 kcal/mol (AM-l), 87.0 kcal/mol (PM-3), 69.8 kcal/mol (LDFT), and 69.5 kcal/mol (NLDFT) for the 1,2+1,CCm dimer. The dimerization reaction to form the Cm dimers from Cm is calculated to be weakly endothermic only for the formation of 1,2-(Cm)z, and for the others, the reaction is predicted to be strongly endothermic. This result suggests that 1,2-cycloaddition is the most plausible scheme for the dimerization and polymerization of Cm molecules, if the cages remain intact.
1. Introduction
Although the chemistry of fullerenes can be quite complex because of the large number of reaction sites, the addition chemistry of fullerenes has gradually been revealed.l-" Hydrogenation' and halogenation of C&3 have been intensely studied, and only 1,2- and 1,4-additionto a cyclohexatrienylunit of Cm have been observed (the numbering system of carbon atoms is shown in Figure 1). Complexes of Cm with metals have been synthesized, yielding +metal complexes such as osymylated Cm,4 Ni-, Pd-, and Pt-Cm complexes,5 and an Ir-Ca complex.6 q2Metal addition can be considered as a form of 1,Zaddition. The observed products of radical addition to Cm showed radicals added to double bonds radiating from a five-membered ring, which corraponds to 1,4-addition.7 Furthermore,dimerization of R-Cm radicals has been observed with the two Cm's connected by a C-C single bond.* Addition of diazomethane to Cm has been repsrted to occur as a 1,Zaddition process, although the addition leads to rearrangementsofthedouble bonds in thecyclohexatrienyl unit.9 Aminoaddition to CmlOandepoxidation of C,ll have also been observed, both of which can be considered as 1,Zsddition. Most recently, addition of H2 to Cm has been reported.12 As an aid to understanding the addition chemistry of Cm, we have been performing theoretical calculations13 which are in accord with the experimental results described above. Semiempirical molecular orbital calculations showed that 1,2- and 1,4additions to C a are energetically more favorable than other dditi0ns.1~~ Density functional theory (DFT)calculations at the local level (LDFT) have shown that the preference for 1.2versus 1,4-additionis controlled by a balance between the steric destabilization due to addition at two adjacent carbons (1,2addition) and the electronic destabilization due to the rearrangement of double bonds necessary to maintain a Kekul6 structure for the a framework of Cm (l,r)-addition).'3* There have been several experimental efforts to synthesize polymers containing Cm9bJ4 as the electric conductivity of Cm DuPont contribution no. 6630.
Abstract published in Advance ACS Abstracts, January 1, 1994.
0022-3654f 94f 2098-2555$04.50f 0
Figure 1. Numbering system for the carbon atoms present in the cyclohexatrienyl unit in Ca. might be modified by polymerization'5 and so that the high bulk modulusl6of Cmcould be incorporated into a polymer to enhance its mechanical properties. We have calculated the structures of dimers of Cm as well as the energetics of dimerization as an aid fordesigningpolymerscontainingCm. TheClm's that we describe below have a dumbbell shape because we studied dimers formed by 1,2- or 1,4-addition as these should be the lowest energy additions if the nature of the Cm cage is not disrupted. These additionschemesare the only ones found in the additionchemistry of Cm if the cage is not disrupted, and thus, these dimers should be the easiest to form. Recently, an IR peak attributable to a cyclobutaneunit was found in a Cm/C70 mixture film prepared by a plasma polymerization technique,I5*which suggests a C120 formed from the 1,2-additionof the two Cm's. This structure is denoted as 1,2-(Cm)2. Photoinduced polymerization of solid Cm films has also been carried out, and the existence of 1,2cycloaddition was indicated as a possible result of the polymerization process.1sb The four structures that we investigated are shown in Figure 2. For 1,2-(C,&, there is only one isomer with D2h symmetry, whereas for 1,4-(Cm)2, there are two possible isomers having C b or Czh symmetry. We also calculated the isomer formed by 1,2+1,4-addition (1,2+1,4-(C&) having C, symmetry. (0
1994 American Chemical Society
2556 The Journal of Physical Chemistry, Vol. 98, No. 10, 1994
Matsuzawa et al.
(9)
Figure 3. Model molecules and numbering system: (a) ethylene, (b) benzene, (c) cyclobutane,(d) unfi-l,2-(benzene)z,(e)syn- 1,2-(bmzene)z, (f) I,4-(benzene)z, (8) 1,2+1,4-(benzene)~.
mesh with the DN basis set for most of the calculations unless noted. The density was converged to 1W. For all calculations, a CRAY YMP computer in single processor mode or an Alliant FX-2800 computer was used.
3. ReuIts and Mscussiorrcl
Figure 2. Cm dimers: (a, top) 1,2-(C&, (b, upper middle) Ca-1,4(C&, (c, lower middle) CZ~-l,b(C.&, (d, bottom) 1,2+1,4-(C&. 2. Calculations
Because of the size of the systems, we used semiempirical molecular orbital theory to optimize the geometries. The calculations were carried out with the MNDO Hamiltonian1' with the AM- 1'8 and PM-3'9 parametrizations as implemented in the program system MOPACa20 No symmetry constraints were specified for the geometry optimizations, and the SCF convergence criteria were 1 V kcal/mol. Final energies were obtained at the density functional theory2* level by using the program DMoLZ2The exchange-correlation potential of von Barth and Hedid' was used. A double numerical basis set (DN basis set) or that augmented by polarization functions (DNP basis set) was used for these calculations with one of two grids (MEDIUM or FINE).24 The number of radial points N R for integration is given as
N~ = AR,J.~(Z
+ 2)lI3
(1)
where Z is the atomic n ~ m b e r . 2R ,~ is the maximum distance for any function from its atomic center. The angular integration points NOare generated at the NR radial points to form shells around each nucleus, and the value of Ne ranges from 14 to Nmx, depending on the behavior of the density and the maximum I value for the spherical harmonics, Lx. We used the MEDIUM
3.1. Geometries. We show in Table 1 the MNDO/AM-1, PM-3, and LDFT calculated geometry parameters for ethylene, benzene, cyclobutane, and tricyclododecatetraenes (benzene dimers), which are models for the addition sites in the Cmdimers, together with experimental geometries available.25 The numbering system of the atoms in the model molecules are shown in Figure 3. The calculated geometry parameters obtained by the MNDO methods agree well with the LDFT results, showing that no significant differences between the LDFT and MNDO calculated geometries are expected for the systems under consideration. We note that the MNDO frequency calculations for the model molecules yielded no negative frequencies, thus showing that the reported structures are indeed minima. The experimental geometry parameters for ethyleneand benzene agree well with the calculated geometries. For cyclobutane, the MNDO/AM-1 and PM-3 methods predict the D4h conformer to be stable with all positive frequencies,whereas the LDFT method predicts the D u conformer to be stable with all positive frequen~ies,2~*~' in agreement with the experimental geometry shown in Table 1. The geometry parameters calculated at the AM-1 and PM-3 levels for the (Cm)2)sare also shown in Table 2 with the numbering system of the carbon atoms given in Figure 4. Second derivative calculations at the MNDO/AM-1 level were carried out for 1,2(C&, 1,4-(C& (Cd,and 1,2+1,4-(C&and showedall three structures to be minima. If the bond lengths differ by less than 0.03 A from those in Cm, they are only given as supplementary material together with the molecular coordinates. The AM-1 and PM-3 calculated geometries agree for 1,2- and 1,4-(cm)2. The largest difference in bond lengths and angles is for r(C1-Cg) in C b - l , 4 - ( C ~ )and ~ B(C+21-C6) for 1,2-(Cm)2, and the magnitude of the difference is 50.01 A and 1 l 0 , respectively. For l,2+l,4-(C60)2, the agreement is still good but is worse than
The Journal of Physical Chemistry, Vol. 98, No. 10, 1994 2557
Dimerization of C a
TABLE 1: Ceometw Parameters for the Model Molecules' A M -1
PM-3
LDFT
exptb
1.331 1.094 121.8
1.339 1.086 121.1
Ethylene 1.326 1.098 122.7
1.322 1.086 123.1
Benzene 1.395 1.100
1.391 1.095
1.390 1.091
1.399 1.084
1.543 1.110 1.110 90.0 114.1 114.1 109.5 0.0 0.0
Cyclobutane 1.542 1.100 1.100 90.0 114.8 114.8 107.1 0.0 0.0
1.544 1.101 1.099 88.2 111.9 118.1 109.1 28.4 5.8
1.552 1.093 1.093
106.4 27.9 6.2
1,2-(Benzene)l(anti) 1.560 1.476 1.557 1.343 1.450 1.117 1.101 1.101 116.0 122.4 121.6 90.0 112.1 110.1 111.4 115.9 122.7 121.4 117.0
1.557 1.483 1.556 1.339 1.452 1.111 1.095 1.095 116.0 122.3 121.7 90.0 1 13.0 109.0 113.3 116.3 121.5 121.1 117.2
1.562 1.481 1.561 1.343 1.453 1.102 1.096 1.094 116.1 122.1 121.7 90.0 112.6 109.9 110.6 117.6 120.3 120.8 118.2
1,2-(Benzene)z(syn) 1.561 1.476 1.558 1.343 1.450 1.118 1.110 1.101 116.0 122.5 121.5 90.0 112.1 109.7 111.6 116.8 121.7 121.5 117.0 0
1.556 1.483 1.559 1.339 1.452 1.111 1.096 1.095 116.0 122.3 121.6 90.0 112.9 108.4 112.6 116.2 121.4 121.2 117.8
PM-3
LDFT
1.507 1.568 1.338 1.114 1.093 106.6 111.2 118.4 109.7 108.4 118.5 123.1
1.510 1.618 1.332 1.100 1.093 107.4 111.1 118.0 110.3 106.7 119.7 122.2
l,2 + 1,4-(Benzene)2 1.510 1.510 1.509 1.508 1.558 1.561 1.345 1.340 1.345 1.340 1.546 1.551 1.485 1.489 1.342 1.338 1.447 1.449 1.115 1.110 1.092 1.090 1.092 1.090 1.129 1.118 1.101 1.097 1.100 1.095 106.9 106.8 113.9 113.8 113.9 113.8 105.7 106.8 106.9 106.4 109.1 108.8 110.5 110.4 123.6 123.3 120.9 121.1 112.9 112.7 1 13.0 112.5 1 1 1.1 111.3 119.7 120.5 119.8 120.5 126.4 125.8 126.4 125.7 108.0 107.7 107.5 108.2 106.9 105.9 115.1 115.7 121.4 121.0 121.7 121.3 117.4 117.6
1.500 1.503 1.584 1.336 1.334 1.548 1.491 1.340 1.447 1.097 1.093 1.091 1.104 1.096 1.093 109.7 113.8 113.8 105.6 105.8 108.4 108.9 123.3 121.2 113.4 113.1 109.7 121.5 121.5 124.6 124.5 105.7 109.4 108.4 116.4 120.3 120.2 118.6
AM-1 1,44 benzene)^ 1.505 1.558 1.342 1.122 1.096 107.0 110.8 118.5 111.0 108.2 117.6 123.9
1.560 1.483 1.568 1.340 1.453 1.102 1.095 1.093 116.1 122.0 121.8 90.0 112.6 109.5 111.1 117.7 120.2 119.9 1 18.4
Bond lengths in angstroms and bond angles in degrees. b Reference 25. See Figure 3c.
that for 1,2- and 1,4-(c&. The largest difference is found for r(Cp-CI0) with the PM-3 value 0.072 A longer than the AM-1 value. Both bond distances are long, >1.70 A, however, so this difference is not surprising as the parametrizations could yield quite different results in this weak bond regime. The largest differences in the angles are, not surprisingly, more than l o but are still less than 2O. For the other bond lengths and angles, the difference between the AM-I and PM-3 geometries is within 0.012 A and 0 . 6 O , respectively. We note that the structures determinedat thetwosemiempirical levels for 1,2+1 ,4-(benzene)z do not differ significantly with respect to each other.
For 1,2-(C&, the two CW subunits are connected by a cyclobutane moiety. The C-C bonds connecting the two C a fragments are like the C-C bonds in cyclobutane or in the 1,2dimer of benzene. The C-C bonds (r(C&z)) in thecyclobutane portion of Cm are elongated by 0.06 A as compared to r(C-C) of cyclobutane. This suggests that the rigidity of the Ca framework increases strain in this bond. The C I - Cbond ~ is also longer than the same bond in 1,2-C~H2 showing that it is not just substitution lengthening the C I - Cbond. ~ The c1-C~bond also lengthens from the C-C single bond length in Cm2*and is now very similar to a normal C-C single bond.29 The r(CI-C3),r(C3-
2558 The Journal of Physical Chemistry, Vol. 98, No. 10, 1994
Matsuzawa et al.
TABLE 2 Selected Ceometrv Parameters of the Dumbbell CI~O’S Obtained from MNDO Calculations’ ~~
1,2-(Benzene)f cyclobutaneb r(C1-C2) r(CIx3) r(Ca-C4) r(C4-G) r(C1-C7) e(crcI-c7) B(C3xl-C6) e(c3-cI-c2) e(c3-cI-c7)
1.603 1.515 1.371 1.477 1.546 90.0 102.1 114.8 118.0
1.508 1.378 1.556 1S44 1.368 1.604 105.5 106.2 104.2 99.1 133.5 105.0 124.0 124.9 109.3 123.4 111.9 120.8
AM-1 1.543
1.598 1.516 1.371 1.475 1.550 90.0 101.5 114.9 118.2
1,2 + 1,4-(cso)z AM-1 PM-3 r(C1-C2) r(C2-C3) r(C1-Cs) r(cl-c6) r(c6-c7) r(C1-C9) r(C9-Clo) r(C9-C11) r(C412) ~(c2-c1-c9) ~(c~-c~-c~) w 2 - C I-CS) ~(c5-cI~6) e(c5-cl-c9) e(c6-cl-c9) e(cl-crc4) e(c3-crc4) e(cl-c6
