J. Phys. Chem. 1995,99, 9717-9723
9717
Theoretical Studies of Dihydroxybuckminsterfullerene, Cso(OH)z? Nobuyuki Matsuzawa" and Masafumi Ata SONY Corporation Research Center, 174 Fujitsuka-cho, Hodogaya-ku, Yokohama 240, Japan
David A. Dixon* DuPont Central Research and Development, Experimental Station, P. 0. Box 80328, Wilmington, Delaware 19880-0328 Received: November 30, 1994; In Final Form: February 17, 1995@
The relative energies of various conformers of 1,2- and 1,4-Cm(OH)2 have been calculated at the MNDO/ AM-1 semiempirical molecular orbital level based on geometries obtained at this level. There are three low-lying conformers of 1,2-Ca(OH)2 and six low-lying conformers of 1,4-C60(OH)2. The conformers of lr2-Cm(OH)2 all are lower in energy as compared to the energy of the most stable conformer of (OH)2. The energies were recalculated at the nonlocal density functional theory (NLDFT) level with a polarized double-g basis set. The relative energies at this ab initio level are similar to the values obtained at the MNDO/ AM-1 level. The energy difference between the lowest energy conformers of l,2-C6o(OH)2 and 1,4-c60(OH)* is 6.6 kcaYmol at the NLDFT level. An analysis of various conformations of ethylene glycol is also presented at the DFT and semiempirical molecular orbital levels as an aid to understanding the behavior of the dihydroxyfullerene derivatives.
1. Introduction Although the chemistry of fullerenes could be quite complex because of the large number of potential reaction sites on the carbon cage, the factors goveming the addition chemistry of fullerenes extemal to the cage have gradually been elucidated.'-'2 Hydrogenation' and halogenation of Cm and C70233have been studied, and only 1,2- and 1P-addition to a cyclohexatrienyl unit of C a have been observed (the numbering system of carbon atoms is shown in Figure 1). Complexes of c 6 0 with organometallics have been synthesized, yielding osmylated c 6 0 and C704and q2-metal complexes such as Ni-, Pd-, Pt-, Ir-, and Rh-Cm c ~ m p l e x e s . (Note ~ ~ ~ that y2-metal addition can be considered as a form of 1,2-addition.) Recently, formation of a Re-Cm complex was reported, and this addition was proposed to occur 1,4.7 The observed products of radical addition to Cm8 showed that the radicals added to double bonds radiating from a five-membered ring, which corresponds to 1,Caddition. Addition of diazomethane to C609has been reported to occur as a 1,Zaddition process, although the addition leads to rearrangements of the double bonds in the cyclohexatrienyl unit. This addition scheme as well as 1,3-dipolar cycloaddition to C a have been used to synthesize a wide variety of c 6 0 derivative^.^ Amino addition to Cm'O and epoxidation of Cml' have also been observed, both of which can be considered as 1,Zaddition. Formation of [2 21 photoadducts and DielsAlder adducts of Cm has recently been reported, yielding, again, 1,Zaddition derivatives.I2 Addition of hydroxy groups to Cm has also been perf~rmed.'~Chiang et al. have synthesized Cm(OH),, (n = 14-20) by electrophilic attack of the nitronium ion, or in nitric acid.'3b They also showed that formation of hemiketal moieties can occur as well as vicinal diol moieties in the presence of strong We have been performing theoreticalkomputational studies on the addition chemistry of Cm in order to clarify the factors that control the regi~chemistry.'~Semiempirical calculations
+
' DuPont contribution @
no. 6995. Abstract published in Advance ACS Absrracts, April 15, 1995
have been performed on all isomers of C60H2, which showed that only 1;2- and 1,Caddition should Calculations at the density functional level were performed on the addition of hydrogen and halogen molecules to c 6 0 in order to further examine the preference for 1,2- and 1,4-additi0n.'~~The calculations showed that 1,2-addition is preferred over 1,4addition for hydrogenation, fluorination, and chlorination, whereas 1,Caddition is preferred for bromination and iodination. These calculations showed that there are two factors which control the pattem of addition to Cm: (1) the steric interactions between the added groups and (2) the electronic effect due to migration of a double bond into a five-membered ring. In this report, we present our theoretical calculations on the addition of hydroxy groups to c60 to form C60(OH)2. Because of the potential existence of hydrogen bonds, hydroxy addition may be more complicated than addition processes such as hydrogenation and halogenation that only involve the addition of atoms.
2. Cakulations Semiempirical molecular orbital theory was used to optimize the various structures and conformers of C60(OH)2. The AM-1 parametrization of the MNDO Hamilt~nian'~ was used as implemented in the MOPAC p r ~ g r a m . ' ~ ~ . ' ~ Energy calculations on Cm(OH)2 were performed at the density functional theory (DFT)17 level at the MNDO/AM-1 final geometries. The DFT calculations described below were done with the program systems DMol'* and DGauss.I9 Detailed descriptions of how these calculations were performed have been given p r e v i o ~ s l y . 'The ~ ~ ~DMol ~ ~ calculations were done with the FINE mesh. A double numerical basis set augmented by polarization functions (DNP) was used for the calculations which were performed with gradient (nonlocal) corrections (NLDFT) as well as at the LDFT (local density functional theory) level. The form for the exchange-correlation energy of the uniform electron gas for the LDFT/DNP calculations is that derived by von Barth and Hedin (BH).2' The gradient correction to the correlation potential is that derived by Lee, Yang, and Parr (LYP),22and the correction to the exchange potential is that
0022-3654/95/2099-9717$09.00/0 0 1995 American Chemical Society
Matsuzawa et al.
9718 J. Phys. Chem., Vol. 99, No. 24, 1995
TABLE 1: Relative Energies of the Ethylene Glycol Conformers in kcahnola tTt tTe eTe gTg’ gTg tTg tGt tGg’ tGg gGg’, g Gg gGg eEe eEt tEt gEg tEg
BH/DNP
BLYPIDNP
BPIDZVP2
MNDO/AM-1
0.00
0.00 1.99 3.79 0.44 0.51 0.07 0.29 -2.21 0.82 -1.68 -1.18 0.75 1 1.22 4.07 8.19 2.46 7.27b
0.00
0.00 0.06 -0.63 -3.23 -2.97 - 1.40 0.30 -2.96 -0.24 -3.85 -3.95 -3.55 2.28 0.77 5.61 -3.95 -0.42
1.27 1.88 -0.64 -0.64 -0.35 0.34 -3.98 -0.26 -5.00 -3.53 -1.38 10.15 1.75 8.66 -0.27 5.30b
2.11 3.52 -0.37 0.12 0.14 1.59 -2.50 1.07 -2.21 -1.39 0.23 11.32 3.06 9.43 1.81b 6.59
a Calculated energies for the tTt conformer are -228.565 637 au (BWDNP), -230.268 677 au (BLYPIDNP), -230.352 243 au (BP/ DZVPZ), and -107.5 kcaYmol (MNDO/AM-I). Calculated with the optimized gEg geometry parameters and the ~ ( H I O I C I Cand ~) t(H602C2Cl) torsion angles from the MNDO/AM- 1 tEg structure.
3. Results and Discussions
Figure 1. Calculated conformers of ethylene glycol and the numbering system of the atoms.
derived by B e ~ k (BLYP). e~~ Geometries were optimized by using analytic gradient method^.'^^'^,^^ Because of convergence difficulties with DMol for the Cm derivatives, the final energies for C60(OH)2 were obtained with the DGauss program. The Gaussian basis sets used in DGauss were calculated with all electron basis sets25 of the form (41/1) for H and (721/51/1) for C and 0 (DZVP2 basis set). The fitting basis sets for the electron density and the exchange-correlation potential have the forms [4] for H and [7/3/3] for C and 0. The calculations were performed at the self-consistent gradient-corrected (nonlocal) level with the nonlocal exchange potential of B e ~ k together e~~ with the nonlocal correlation functional of PerdewZ6(BP). All of the calculations were done on Cray YMP and C90 computer systems in single and multiple processor modes.
3.1. Energies and Geometry Parameters of Ethylene Glycol. Before describing the results on C60(OH)2, we first discuss the relative energies and geometry parameters of conformers of ethylene glycol (CH2(OH)CH2(OH))as obtained from LDFT and NLDFT calculations. We chose this molecule as a model for the 1,a-addition site in Cm(0H)z. The different conformers that were studied are shown in Figure 1. The calculated relative energies are shown in Table 1. Except in special cases such as 1,2-difl~oroethane*~ and structures28 where hydrogen bonds can form between the substituents in the 1 and 2 position in 1,2-disubstituted ethanes, most 1,2-disubstituted ethanes have an all trans structure as the lowest energy form. The base structure that we chose for our model is thus trans about the C-C bond with two trans OH bonds (tTt). If the CCOH torsions are kept at 180” the trans structure is the minimum energy structure with the gauche (tGt) conformation 1.59 kcal/mol higher in energy at the BPDZVP2 level. The tGt structure is only 0.29 kcaVmo1 higher in energy at the BLYPDNP level. The barrier to rotation if the two groups pass by each other in the eclipsed conformation (tEt) is 9.43 kcaVmol at the BPDZVP2 level and 8.19 kcal/mol at the BLYPDNP level. Hydrogen bonding between the OH groups can change the potential for torsion about the CC bond. At the local B ” P level, there are five gauche conformers that are lower in energy than the tTt conformer. However, at the BLYPDNP or BP/ DZVP2 levels, only three conformers are lower in energy. The lower energy conformers at the nonlocal levels are tGg’, gGg’, and g’Gg’, all of which have the possibility of having hydrogen bonds. The global minimum at the BLYPDNP level is the tGg‘ conformer with one hydrogen bond, followed by the gGg’ conformer with the possible formation of two hydrogen bonds (see d(0-H) in Table 2). At the local DFT level, the gGg’ structure is the global minimum. Several microwave studies on the structure of ethylene glycol have been reported.29 Experimentally, two conformers of ethylene glycol have been observed, tGg’ and gGg’.29b,cIt has been reported that the tGg’ conformer is more stable than the gGg’ conformer by 0.33 kcaV The nonlocal results are in agreement with the experimental ones with an energy difference of 0.53 kcal/mol at the BLYPDNP level and 0.28 kcaVmol at the BPDZVP2
Theoretical Studies of C ~ O ( O H ) ~
. I . Phys. Chem., Vol. 99, No. 24, 1995 9719
TABLE 2: Calculated Geometry Parameters of the Ethylene Glycol Conformew BWDNP 0.985 1.428 1.495 1.111 1.112 1.106 1.113 1.412 0.989 108.5 105.0 110.5 109.5 111.3 108.0 110.5 104.9 173.0 -64.3 175.4 56.7 45.8 175.3 54.0 3.612 2.252 2.764 110.9 r(H1-O1) r(Ol-CI) r(Cl-C*) r(c1-H~) r(CI-H3) r(C2-Hd) r(C2-H5) r(C2-02) r(H6-02) ~(HIOICI)
0.996 1.410 1.502 1.107 1.119 1.111 1.107 1.427 0.988 103.7 e(olcIc2) 109.9 B(H2ClC2) 110.1 109.5 O(HjCiC2) e(H4C2C1) 110.9 110.5 O(HsC2Cl) e(02czc1) 109.6 107.0 e(C202H6) ~ ( C ~ C I O I H ~35.7 ) t(01ClC202) -51.0 t(OiCiC2H4) -174.8 ~ ( O I C I C ~ H S64.4 ) t(02C2ClH2) - 170.9 t(OzC2ClH3) 70.7 t(CiC202H6) -67.8 r(H1-02) 2.102 r(H6-01) 3.063 r(01-02) 2.717 e(OlH602) 118.0
BLYPDNP
MNDO
exptb
expt‘
tGg’ 0.985 1.462 1.522 1.104 1.104 1.098 1.106 1.448 0.987 107.5 107.4 110.5 109.5 110.1 109.9 112.1 105.6 171.4 -68.2 174.1 55.6 51.4 171.8 54.1 3.759 2.487 2.935 107.3
0.964 1.419 1.527 1.121 1.122 1.122 1.122 1.412 0.966 106.9 106.4 110.3 110.4 110.0 109.9 111.4 106.8 176.1 -67.4 176.4 54.9 57.3 173.2 52.0 3.697 2.466 2.860 104.1
0.956 1.423 1.526 1.09 1.09 1.09 1.09 1.423 0.956 108.0 109.5 109.0 109.0 109.0 109.0 109.5 108.0 -198.0 -60.0
--53.6
gGg’ 0.991 1.445 1.531 1.102 1.108 1.103 1.099 1.461 0.987 104.3 110.5 111.4 110.0 112.0 110.2 110.4 107.4 35.3 -51.7 -178.0 64.0 - 171.2 70.1 -64.8 2.213 3.121 2.811 117.5
0.967 1.413 1.525 1.122 1.124 1.121 1.123 1.415 0.965 107.1 111.8 110.7 110.0 110.3 110.6 110.6 107.3 44.5 -59.6 177.4 55.6 -176.6 62.2 -66.3 2.394 3.214 2.865 102.2
28.0
2.236 2.771 105.6
-53.9
2.457 2.885 105.1
Units in angstroms for the bond lengths and distances, and degrees for the angles. Experimental values from ref 29b. In this reference, each 0-H, C-H, and C - 0 bond lengths were assumed to be the same. Experimental values from ref 29c.
level. The local DFT results as noted above favor a structure with two possible hydrogen bonds and a larger energy difference of 1.02 kcaVmo1 between the two gauche structures. This difference in the local and nonlocal results is not surprising as it is well-established that LDFT leads to overstimation of the strength of nonbonded interactions including hydrogen bonds.30 The potential presence of hydrogen bonds in the transition state for rotation about the C-C bond can lead to significant
reductions in the barrier height (for example, compare the relative energies of the eEt and tEt structures). We examined five structures for the gauche-gauche barrier height. At the MNDO/AM-1 level, frequency analysis showed that the tEt and tEg conformers are true transition states with one imaginary frequency. The eEt and eEe structures have two and three imaginary frequencies, respectively. The eEt structure can relax to the tEg structure, which has only one imaginary frequency, whereas the eEe can relax to the gEg structure. At the MNDO/ AM-1 level, the gEg structure is of very low energy, the same as the g’Gg’ conformer, and is a minimum on the potential energy surface. Calculations at the DFT level were performed on the various structures, and the geometries were optimized except for the tEg structure where a transition state structure could not be optimized with DMol. For this latter structure, the torsion angles ~ ( H I O I C I C and Z ) r(H602C~C1)were taken from the MNDO/AM-1 structures and the remaining geometry parameters were taken from the optimized gEg conformer. Frequency calculations at the BPDZVP2 level. were generally in line with the MNDOIAM-1 results except that, at the DFT level, gEg is not a minimum but is a transition state for rotation. However, the tEg structure is higher in energy than the eEt structure. At the BPDZVP2 level the barrier height is reduced by 6.4 kcdmol (AE(tEt-eEt)) with one hydrogen bonding interaction and by 7.6 kcaVmol (AE(tEt-gEg)) to give a minimum gauche-gauche rotation barrier of 4.3 kcal/mol. At the BLYPDNP level the barrier height is reduced by 4.1 kcaV mol (AE(tEt-eEt)) with one hydrogen bonding interaction and by 5.7 kcaVmo1 (AE(tEt-gEg)) to give a minimum gauchegauche rotation barrier of 4.7 kcaVmo1. We note that the actual barrier may be higher than this as the hydroxyl hydrogens still must reorient to pass by each other. The actual barrier may be more like the value for the eEt structure which gives barriers of 5.6 and 6.3 kcaVmol at the BP and BLYP levels, respectively. Both sets of calculations of the barrier height are larger than the range of 2-3.5 kcaVmol obtained for the gauche-gauche barrier height from infrared spectral measurements in an argon matrix.31 The errors in overestimating the hydrogen bond strengths approximately cancel at the BWDNP level so that the rotation barriers at the local level are comparable to the barriers at the nonlocal level. Although the energies for the two most stable structures are similar, there are differences in some of the AE values as calculated at the two nonlocal levels. For example, tGt is only 0.29 kcaVmo1 above tTt at the BLYPDNP level whereas this energy difference is 1.59 kcaVmo1 at the BPDZVP2 level. There are a number of other theoretical studies32 of the conformations of ethylene glycol, and the most relevant one to this study is the recent work of Oie et al.32awho used DFT to look at the conformations. These authors showed that the BP/ DZVP2 level calculations as well as those at the BP/TZVP level are in very good agreement with 6-311G**/MP4(SDTQ) calculations. They note a slightly different ordering for tGg’ and gGg’, but this number is very small and it is clear that slight changes in the geometries can affect this result. Their relative energies for the structures are i n good agreement with our values. The only other reported value for the gauche-gauche barrier height is the HFDZ calculation of Almlof and S t ~ m n who e~~~ report a value of about 4.5 kcal/mol in reasonable agreement with our NLDFT results. At the MNDO level, the relative energies are in, at best, qualitative agreement with our NLDFT values for the trans and gauche structures. The tGg’ structure is not predicted to be the global minimum, rather the g’Gg’ structure is predicted to be the lowest energy conformer. However, the MNDO/AM-1
9720 J. Phys. Chem., Vol. 99, No. 24, 1995 results are consistent with the higher level NLDFT calculations as there are a significant number of low energy conformers. As expected following previous work,2o1the rotation barrier is too low at the semiempirical molecular orbital level. The geometry parameters for the two lowest energy gauche conformers are given in Table 2 where they are compared to the available experimental data and the geometry parameters for the other conformers are given as Supplementary Material. The BH/DNP and BLYPDNP results are in qualitative agreement for the structures of the gauche conformers. The difference is less than 0.005 8, for the 0 - H bond lengths. For the C - 0 and C-C bond lengths, the BLYPDNP values are longer by -0.035 and -0.028 A than the B " P values, respectively, whereas the BLYPDNP C-H bond lengths are shorter by 0.005-0.011 8,. The differences in the bond and dihedral angles are slightly larger with maximum differences of 2.1" and 5.6", respectively. These differences are due to the BLYPDNP 0 a . H hydrogen bond distances HI - 0 2 ) and r(H2-01) being longer than the B " P values. The difference is most pronounced for the nonbonded distances less than 2.5 8, and is typical of what has been observed in other hydrogen-bonded systems which show that at the LDFT level hydrogen-bonding interactions are overestimated. Indeed, a general feature of LDFT calculations is that nonbonded interactions are usually not repulsive enough. The MNDO/AM-1 geometries are in good agreement with the other theoretical results. Experimental geometries are available from microwave measurement^^^^,^ for the tGg' conformer (Table 2). The calculated values are in reasonable agreement with the bond lengths determined by Caminati et al.29b with the largest difference being 0.029 8, for r(0l-Cl). For the bond angles, the difference between the theoretical and the experimental values is only 2.6". Larger differences (23.4") are predicted for the torsion angle Z(C1C202H6). The calculated values are in reasonable agreement with the experimental values of Walder et al.,29c although they only reported the hydrogen bond parameters, r(H2-01), r(01-02), and 6(01H602)and the torsion angle z(01CI C202). 3.2. MNDO/AM-1 Calculated Rotational Potentials of C60(OH)2. There are several possible conformers for 1,2- and 1,4-C60(OH)2. Torsional potentials for 1,2- and 1,4-C60(OH)2 were calculated in order to find all possible conformers of the compound. The MNDO/AM-1 method was used for calculating the potential, as ab initio molecular orbital or DFT methods are computationally too expensive for the large number of conformations whose geometries must be optimized, although we do note that the rotational barriers will be too low at the semiempirical level. The goal here is to find low energy conformers and then perform DFT calculations at these conformers to obtain relative energies. The local structure of the 1,2- and 1,4-C60(OH)2 conformers together with the numbering system of the atoms and the definition of the torsion angles is given in Figure 2. For the calculations of the potential, we first fully optimized the structures of 1,2- and 1,4-C60(0H)2.~~ Based on these initial geometries, we then performed constrained optimizations by varying the torsion angles 81 and 02. For the constrained optimizations, only the positions of C I , C2, C3, C4, CS, c6, 01, 0 2 , H I , and H2 were optimized for 1,2-addition, whereas for 1P-addition, the positions of CI, C2, C3, C4, CS, c6, C7, CS, 01, 0 2 , H I , and H2 were optimized.34 The calculated torsion potentials are given in Figures 3 and 4 for 1,2- and 1,4-C60(OH)2 respectively. For l,2-C60(OH)2,the potential shows that there are three stable conformers ((a) 81 = -180" and O2 = -180°, (a) O1 =
Matsuzawa et al.
W
1,2-addition
1 .Caddition
Figure 2. Numbering system of the carbon atoms present in Cm(OH)2 and the definitions of the torsion angles.
856' -180
I
-90
I
I
I
0
90
180
Angles 0,
Figure 3. MNDO/AM- 1 calculated rotational potentials for 1,2-C60(OH)*.The plots for different 02 are shown in the figure. -180" and 02 = -60", and (c) 81 = -60" and 02 = -60"). These conformers are schematically shown in Figure 5. It should be noted that the conformer with I31 = -60" and I32 = --60" was not calculated to be a minimum. Except for 02 = 0" and 30°, the relative potential energies fall within a range of 5 kcaYmo1, whereas for 82 = 0", the range is -11 kcaYmol with I31 = 02 = 0" corresponding to the least stable structure. As noted above for the case of the model ethylene glycol, the MNDOIAM-1 barriers are likely to be too low, so the values shown in the figures should represent lower bounds. In contrast to 1,2-Cm(OH)2,the rotational potential for the 1,4-C60(OH)2 is much flatter, with energies falling within a range of 3-4 kcaY mol, consistent with the increased distance between the added groups. For 1,4-Cm(OH)2, MNDO/AM-1 calculations predicted six stable conformers as shown in Figure 6. All of them have 81 and I32 values which are either -0" or -&120" ((a) 0 , = -120" and I32 = -120", (b) 8, = -120" and e2 = --120°, (c) 81 = --120" and 132 = -120", (d) = -120" and = -O", (e) O1 = --120" and = -O", and (0 el = -0" and e2 = -0")). We note that for this case, the conformer with 01 = -0" and 8 2 = -0" was calculated to be a stable minimum. In order to further confirm that these conformers are actually minima, we fully optimized their structures at the MNDO/AM-1 level starting from the partially optimized geometries. The calculated energies and 81 and 132 angles are shown in Table 3. Frequency calculations (see the Supplementary Material) yielded all positive frequencies showing these structures to be true minima. Based on the above results for ethylene glycol, 1, the energies of the various conformers of Cm(OH)2 were calculated at the BPDZVP2 level (see Table 3). The MNDO and DFT values for the relative energies of the 1,2-C60(OH)2conformers are in
J. Phys. Chem., Vol. 99, No. 24, 1995 9721
Theoretical Studies of Cw(OH)2
TABLE 3: Calculated Relative Energies and Dihedral Angles of Ca(OH)z relative energy"
torsion angle (MNDO/AM- 1)
8, (deg)
1 3 (deg) ~
4.3 0.9 0.0
180.0 175.7 67.4
180.0 55.3 65.2
7.2 7.7 7.1 6.7 6.2 8.4
117.0 120.7 -117.9 126.4 -123.6 -3.2
116.7 -117.7 117.9 -0.7 -4.4 -5.2
MNDO/AM-1
BPIDZVP2
4.1 1.1 0.0
a
8.0
b
8.5
C
8.0 8.0
1,2-Cm(OH)z a
b C
1,4-Cm(OH)z
d
-180
-90
0
90
180
Angle 8,
e f
7.7 9.3
a Total energies for the most stable conformer are 857.6 kcal/mol (MNDO/AM-1) and -2438.594 147 au (BPIDZVP2).
-180
0
-90
90
180
Angles O1
Figure 4. MNDO/AM- 1 calculated rotational potentials for 1,4-Cm(OH)2 (a, top) for 0" 5 O2 5 180" and (b, bottom) for - 180" 5 B2 5 0".
A
n
r/
C60(OH)2 b conformer which corresponds to the gEt structure of 1 is 0.9 kcdmol higher in energy at the BP level. The energy difference between the gEg and tEg conformers for 1 is 4.8 kcdmol at the BP level, although a more appropriate comparsion is AE(gEg-eEt) which is only 1.2 kcaVmo1. The 1 , 2 G 0 (OH)2 a conformer is the least stable conformer and is 4.3 kcaV mol above the lowest energy structure at the NLDFT level. The energy difference of 3.4 kcaUmol between the 1,2-C@(OH)2a and b conformers is comparable to the value of 2.8 kcaVmo1 found for AE(tEg-tEt) in 1 at the BP level. The similarity in the relative energies of 1 and those in 1,2-Ca(OH)2 is somewhat surprising considering the differences in the geometries in the region of the OH groups. Although there are essentially no differences in the C-0 bond lengths for 1 or 1,2-Cw(OH)2, the C I - C ~bond lengths in the 1,2-C60(OH)2 conformers are 1.584-1.597 A, which are significantly longer than the corresponding lengths in the eclipsed conformers of 1 (1.526-1.530
A). (b) -1
Figure 5. Schematic drawings of the six stable structures for 1,2-Cm(OH12.
Figure 6. Schematic drawings of the six stable structures for 1,4-C60(OH12.
excellent agreement. The most stable conformer is the 1,2C@(OH)2c structure which corresponds to the gEg conformer of 1 which is the lowest energy eclipsed structure. The 1,2-
The conformers for 1,4-Cm(OH)2 are all less stable than the 1,2-C60(OH)2conformers. The DFT relative energies are somewhat smaller than the MNDO relative energies, but the overall agreement and ordering of stability is quite good between the DFT and MNDO values. There is some variation in the energies of the 1,4-C&H)2 conformers with the least stable being 1,4-C60(OH)2 f, which has the two OH protons pointing directly at each other. The most stable conformer is the 1,4e structure, which has one proton over the sixC,~OO(OH)~ membered ring with a torsion of 0" and one over a fivemembered ring with a torsion of 120". Comparable calculations for the relative energies of the 1,2 and 1,4 isomers of C60H2 and CaF2 are 6.8 and 6.6 kcdmol, respectively, at the BWDNP level and 4.4 and 4.2 kcdmol, respectively, at the MNDO/AM-1 level with the 1,2 isomer being favored over the 1,4 isomer.'4a The values for C60(OH)2, are 6.2 kcaVmo1 at the DFT level and 7.7 kcaVmol at the MNDO/AM- 1 level. These energy differences are remarkably similar for the three types of substituents. As noted previously,14a the difference in the energies of the 1,2 and 1,4 additions can be traced to a balance between the electronic destabilization of placing a C=C in a five-membered ring and the steric effects due to two groups substituted 1,2 which are approximately eclipsed. The results for the three substituents suggest that the electronic effect is dominating the steric effect. The results also suggest that the steric effects for the three substituents in the 1,Zaddition pattern are similar. This comparison suggests that the effect of hydrogen bonding, if present in the 1,2 isomer of
9722 J. Phys. Chem., Vol. 99, No. 24, 1995
Matsuzawa et al.
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