J. Phys. Chem. 1988, 92, 2141-2145 TABLE IV: Atomic Populations for ICq(CN),T' Cb(STO-3G) atom CdDZ+DJ 0.22
-0.10 -0.10 -0.1 1 -0.10 -0.09 -0.10
-0.09 -0.06 -0.1 1 -0.13 -0.1 1 -0.13
0.18 -0.26
0.07 -0.10 -0.08 -0.08 -0.07 -0.10 -0.07
-0.19 -0.19 -0.06 -0.06
C,( STO-3G)
0.09 -0.10 -0.10 0.08 0.07 0.06 0.07 0.06 -0.20 -0.25 -0.26 -0.25 -0.26
0.12
-0.19 0.00 0.07 0.05 0.05
0.09 0.08 -0.20 -0.32 -0.32 -0.20 -0.20
Mulliken charges in electrons. are excluding the C-N and C-C stretches) whereas the remaining b2 bands are weak. Hipps et al.15 do not give all the observed transitions as they remove various combination bands of a, and b2 from their listing of observed frequencies. From the frequencies listed we note that the 820-cm-' transition cannot be assigned as an a2 or bl fundamental; there are no frequencies of these symmetry types predicted to be that high. Besides the b2 band predicted at 495 cm-', we also predict an a2 band at 489 cm-l and a bl band at 500 cm-I. It is doubtful that the a, band would be as low as 456 cm-l, and we also cannot assign this transition. The transition at 345 cm-' is probably of bl symmetry although it would be very weak in the infrared, whereas the observed transition at 225 cm-l (if it is from the Raman) is probably of a2 symmetry. We predict a moderately intense band near 140 cm-' of bl symmetry, whereas the b2 band noted above would have no infrared intensity. We predict two very low energy out-of-plane transitions, a bl transition at 64 cm-l and an even lower a2transition at 22 cm-I. Thus, the molecule should be quite fluxional in these out-of-plane modes. The vibrational frequencies for the rotated C, structure are given in Table 111. The calculated force field shows that the C,structure is a transition state with one negative direction of curvature giving one imaginary frequency of a" symmetry. The imaginary fre-
2141
quency is for torsion about the C-C bond and is low, 87i cm-' (unscaled). For the rotated structure only two of the cyano bands are predicted to be very intense with the most intense band in the spectrum being the a" cyano stretch. The allylic C-C stretches become a C = C and C - C stretch. The scaled value for the C = C stretch is 1617 cm-l, and it is much less intense than the asymmetric allylic C-C stretch in the C,, structure. The a' C-C stretch at 1266 cm-' is also not very intense. Thus, many of the transitions in the C, structure are weaker than those in the C2, structure. The STO-3G frequencies and intensities are given for comparison purposes in Tables I1 and 111. The STO-3G intensities are qualitative at best. The STO-3G frequencies are usually higher than those determined with the larger basis set. This is most pronounced for the C N stretches where a scale factor of 0.82 is required. The C-C allyl stretches in the C,, structure and the C=C and C-C stretches in the C, structure are also too high. Below these stretches, quite good agreement is found for the two basis sets. Charge Distribution. The atomic charges are given in Table IV. The charge distribution for the C, structure shows that most of the negative charge is on the cyano groups attached to C2 and C3, confirming the importance of resonance structure IC. The charge of the C1(CN) group is 0.05 e while the two C(CN), groups each have a charge of -0.53 e. This charge distribution is that expected from a simple Huckel model which places 1.O e in the HOMO on C2 and C3,giving charges of -0.5 e on C2 and C3. For the C, structure, most of the negative charge is localized on the C(CN)2 group containing C2. The atom C2 is the nominal carbanion center, and the group charge is -0.80 e. The largest negative atomic charge is on C,, but -'I3 of the -0.80 e is delocalized to the cyano groups. The C(CN) group a t C I has essentially zero charge, and the remaining negative charge of -0.20 e is found on the C(CN), group a t C3. At C3, all of the excess negative charge is found on the cyano groups. The STO-3G charges for both structures exhibit the same trends as found with the D, + D, basis set. The only difference is that the STO-3G basis set gives a larger charge separation between C and N on the cyano groups, making N more negative and C more positive. Registry No. [C3(CN)s]*-,45078-37-3.
Normal Vibrational Modes of Buckminsterfullerene Richard E. Stanton*+ Chemistry Department, Canisius College, Buffalo, New York 14208
and Marshall D. Newton* Chemistry Department, Brookhaven National Laboratory, Upton, New York 1 1 973 (Received: August 31, 1987) The MNDO approximation is employed to compute normal modes of vibration for the proposed c60 isomer known as buckminsterfullerene. Group theoretical invariance theorems are derived to aid in the interpretation of the normal modes. One particularly interesting mode (the sole A, vibration) consists entirely of a rotary oscillation of the pentagonal rings of c60, with all rings rotating in the same direction.
Introduction The proposed existence of buckminsterfullerene (BF), a soccer ball shaped Ca molecule, has been the subject of a spirited debate since its announced discovery 2 years ago in graphite vaporization experiments.' The bibliography to date includes numerous experimental'+ and papers and also articles from the astrophysical community.20-22 In our own MNDOZ3calculations7 we found BF to be significantly lower in energy per C than several possible competitors, 'Research Collaborator, Brookhaven National Laboratory.
0022-36541881,2092-2 141$01.50/0
namely, graphite fragments, straight chains, and an alternative spheroidal (26, structure known as graphitene.88 Another issue (1) Kroto, H. W.; Heath, J. R.; O'Brien, S.C.; Curl, R. F.; Smalley, R. E. Nature (London) 1985, 318, 162-163. For earlier speculation see: Stankevich, I. V.;Nikerov, M. V.; Bochvar, D. A. Russ. Chem. Rev. (Engl. Truml.) 1984, 53, 640-655. (2) (a) Rohlfing, E. A,; Cox, D. M.; Kaldor, A. J . Chem. Phys. 1984,81, 3322-3330. (b) Cox,D. M.; Trevor, D. J.; Reichmann, K. C.; Kaldor, A. J. Am. Chem. Soc. 1986, 108,2457-2458. (c) A recent claim to have observed a BF-like C6,, entity has been made on the basis of an electron microscopic study of graphitized carbon: Iijima, S. J . Phys. Chem. 1987, 91, 3466-3467.
0 1988 American Chemical Society
2142
The Journal of Physical Chemistry, Vol. 92, No. 8, 1988
we addressed was the intrinsic stability of BF against vibrational distortion or collapse. We found that it was indeed stable, Le., that its normal-mode frequencies were all real. Table I of the present paper contains a complete listing of these frequencies and a partial description of the motion in each mode. The validity of this description depends on a series of symmetry theorems which we prove below. Intensity information for the IR-active modes (only Flu is allowed) is provided in Table 11. Our calculations and those of others show the BF structure to be a likely candidate for the observed cluster. Clearly, experiments which go beyond the limitations of mass spectrometric observation will ultimately be necessary before any final structure identification can be accepted. We hope that the present IR predictions will be useful for this purpose. At the same time we believe that the motions in the various modes are sufficiently interesting to be worthy of analysis of their own right.
Invariance Theorems Let R be a symmetry operator for BF (or any other symmetric molecule), let V be a column of atomic displacement vectors
and let R be the 3n X 3n matrix which effects the action of R on V. We assume that v,, v2, etc., share a global coordinate system. Then R can be written as the direct product of a permutation matrix P and a 3 X 3 rotation matrix r.
R=P@r
Stanton and Newton
Figure 1. The A, rotary oscillation in BF. (Only the upper half of the molecule is shown.) Numerical labels correspond to those in Table I. All five-membered rings are rotating in the same "direction" (Le., counterclockwise with respect to their respective radial vectors).
where p i is the atom rotated into position i by P. Let this transformation be applied to VFa, a normal-mode eigenvector which transforms like the a t h member of a basis for the irreducible representation P.
Comparison of the ith blocks of (3) and (4) provides a relation between the amplitude vectors of symmetrically equivalent atoms:
(2)
Its action on V is
(3)
(3) Bloomfield, L. A.; Geusic, M. E.; Freeman, R. R.; Brown, W. L. Chem. Phys. Lett. 1985, 121, 33-37. (4) (a) Zhang, Q. L.; O'Brien, S. C.; Heath, J. R.; Liu, Y.; Curl, R. F.; Kroto, H. W.; Smalley, R. E. J . Phys. Chem. 1986,90,525-528. (b) Heath, J. R.; OBrien, S. C.; Zhang, Q. L.; Liu, Y.; Curl, R. F.; Kroto, H. W.; Tittel, F. K.; Smalley, R. E. J . Am. Chem. SOC.1985,107,7779-7780. (c) Liu, Y.; OBrien, S. C.; Zhang, Q. L.; Heath, J. R.; Tittel, F. K.; Curl, R. F.; Kroto, H. W.;Smalley, R. E. Chem. Phys. Letr. 1986, 126, 215-217. (d) OBrien, S. C.; Heath, J. R.; Kroto, H. W.; Curl, R. F.; Smalley, R. E. Chem. Phys. Lert. 1986, 132, 99-102. (5) OKeefe, A,; Ross, M. M.; Baronavski, A. P. Chem. Phys. Lert. 1986, 130, 17-19. (6) Hahn, M. Y.; Honea, A. J.; Paguia, A. J.; Schriver, K. E.; Camarena, A. M.; Whetton, R. L. Chem. Phys. Lerr. 1986, 130, 12-15. (7) Newton, M. D.; Stanton, R. E. J . Am. Chem. SOC.1986, 108, 2469-2470. (8) (a) Haymet, A. D. J. J . Am. Chem. SOC.1986, 108, 319-321. (b) Haymet, A. D. J. Chem. Phys. Lett. 1985, 122, 421-424. (9) Disch, R. L.; Schulman, J. M. Chem. Phys. Lett. 1986,125,465-466. (10) Haddon, R. C.; Brus, L. E.; Ragavachari, K. Chem. Phys. Leu. 1986, 125,459-464. (11) (a) Klein, D. J.; Schmalz, T. G.;Hite, G . E.; Seitz, W. A. J . Am. Chem. SOC.1986, 108, 1301-1302. (b) Klein, D. J.; Seitz, W. A,; Schmalz, T. J. Nafure (London) 1986, 323, 703-706. (12) Ozaki, 0.;Takahashi, A. Chem. Phys. Lett. 1986, 127, 242-244. (13) Satpathy, S. Chem. Phys. Left. 1986, 130, 545-550. (14) Hess, B. A,, Jr.; Schaad, L. J. J . Org. Chem. 1986, 51, 3902-3903. (15) Hale, P. D. J . Am. Chem. SOC.1986, 108, 6087-6088. (16) (a) Fowler, P. W.; Woolrich, J. Chem. Phys. Leu. 1986, 127, 78-83. (b) Fowler, P. H. Chem. Phys. Lett. 1986, 131,444-450. (17) Stone, A. J.; Wales, D. J. Chem. Phys. Lett. 1986, 128, 501-503. (18) Marynick, D. S.; Estreicher, S. Chem. Phys. Lerf. 1986,132,383-386. (19) Almlof, J. Chem. Phys. Lett. 1987, 135, 357-360. (20) Rabilizirov, R. Asrrophys. Space Sci. 1986, 125, 331-339. (21) Heymann, D. J . Geophys. Res. 1986, 91, E135-El38. (22) Lewis, R. S.; Ming, T.; Wacker, J. F.; Anders, E.; Steel, E. Narure (London) 1987, 326, 160-162. (23) (a) Dewar, M. J . S.; Thiel, W. J . Am. Chem. SOC.1977, 99, 4899-4907. (b) Ibid. 4907-4917. (c) Dewar, M. J . S.; Ford, G . P.; McKee, M. J.; Rzepa, H. S.; Thiel, W.; Yamaguchi, Y. J . Mol. Sruct. 1978, 43, 135-138. (d) Stewart, J. J. P. QCPE 1986, 18, 455.
Let the two sides of eq 5 be multiplied by their transposes and summed over degenerate modes. Because r and F F are orthogonal matrices, the resulting equality serves to prove that the rootmean-square displacement amplitudes of symmetrically equivalent atoms are equal when averaged over a set of degenerate modes:
In BF every atom can be permuted into the position of every other atom by some symmetry operation, so all have the same rms displacement (per unit change of the normal coordinate), and this clearly has the same value, (1/60)'/2, in all modes. Instead of forming the dot product of an atomic displacement vector with itself, one can multiply it by the displacement vector of some other atom. It then follows in exactly the same manner that this dot product is the same for all equivalent pairs when averaged over a degenerate set. (7)
Dot products between adjacent atoms can be used to determine whether the atoms are moving in phase with one another, as in long-wavelength vibrations over the spheroidal surface of the molecule, or out of phase as in a bond stretching vibration or when a bonded pair rotates about s a n e intermediate axis. Additional equivalence theorems can be derived if the global coordinate system used above is replaced by a local coordinate system at each atomic center. In BF these can be chosen so that one local axis is normal to the spheroidal surface. The corresponding radial coordinates ( p ) are rotaLed without change from atom to atom by the group operations R, and it is easy to prove that their averages over a degenerate set of vibrations are the same for all atoms.
The remaining axes at each center (the tangential ones) can be chosen so that one lies in the plane formed by the radial axis and what we call the "double"-bond direction (i.e., the vector defined
Normal Vibrational Modes of Buckminsterfullerene
The Journal of Physical Chemistry, Vol. 92, No. 8, 1988 2143
TABLE I: Analysis of Normal Coordinates atomic motionb % ' tangential mode v," cm-l 7% radial C=C perp
rms dot products' (vltv2)
(vltv6)
internal coordinates" bond stretching angle bending C-C C=C C-C-C C-C=C
0 0
0.0 33.3
50.0 33.3
50.0 33.3
0.92
1.oo
0.92 1.oo
610 1667
100.0 0.0
0.0 100.0
0.0 0.0
0.91 0.40
0.94 -0.94
0.039 0.100
627 865 1410
90.6 4.9 4.5
4.0 7.0 39.0
5.4 88.1 56.5
0.34 0.32 -0.77
-0.61 -0.53 0.21
0.022 0.121
591 784 919 1483
0.1 0.3 98.7
99.1 12.3 0.5 88.0
0.31 0.04 -0.75 -0.61
0.67 0.65 -0.85 -0.47
0.016 0.016
0.8
0.7 87.4 0.7 11.2
49 1 579 856 1235 1404 1650
89.8 2.4 97.9 5.5 3.0 1.4
2.2 71.2 0.3 3.3 40.1 83.0
8.0 26.4 1.8 91.2 56.9 15.7
0.32 0.58 -0.48 -0.25 -0.64 -0.35
0.66 0.45 0.67 0.72 -0.25 -0.91
0.012 0.0 12 0.007 0.124 0.111 0.090
263 447 77 1 924 1261 1407 1596 1722
69.3 90.0 96.5 30.5 9.6 2.1 0.8 1.2
15.2 5.7 2.1 27.1 48.5 21.7 87.2 92.5
15.5 4.3 1.4 42.4 41.8 76.2 12.0 6.3
0.88 0.54 0.52 0.49 -0.16 -0.32 0.01 -0.41
0.88 0.27 0.19 0.67 0.09 -0.21 -0.92 -0.97
0.008 0.006 0.004 0.064 0.095 0.133 0.103 0.078
972
0.0
0.0
100.0
0.3 1
-1
577 719 1353 1628
93.5 66.6 6.0 0.5
3.2 15.3 48.7 99.5
3.3 18.1 45.3 0.0
0.46 0.73 0.72 0.34
-0.62 0.83 0.70 -0.91
0.001 0.048 0.122 0.098
348 776 1134 1314 1687
84.5 96.6 14.3 2.6 1.9
14.2 1.6 59.0 28.5 96.7
1.3 1.8 26.7 68.9 1.4
0.86 -0.51 0.22 -0.60 0.03
0.40 0.04 0.68 0.78 -0.90
0.007 0.006 0.096 0.136 0.068
362 750 914 1110 1436 1587
83.5 1.4 98.9 14.5 0.9 0.7
2.9 83.5 0.3 6.7 33.8 72.7
13.6 15.1 0.7 78.7 65.3 26.6
0.53 0.15 -0.70 0.09 -0.53 -0.35
0.88 0.61 -0.86 0.55 -0.26 4.93
0.010 0.015 0.004 0.081 0.130 0.110
403 546 706 822 1344 1467 1709
1 .o 89.1 8.3 92.8 5.9 1.9 1.o
46.1 8.3 14.7 1.1 22.3 19.1 88.2
52.8 2.5 77.1 6.1 71.8 78.9 10.7
0.75 0.18 0.27 -0.36 -0.14 -0.62 -0.58
0.72 0.55 0.21 -0.49 -0.71 -0.29 -0.98
0.01 1 0.006 0.018 0.007 0.100 0.135 0.084
0.0 0.0
0.0 0.0
0.0 0.0
0.1 0.0
0.0 1.5 7.8
6.1 12.0 9.0
0.9 12.0 3.7 8.3
7.6 6.0 7.7 10.0
0.001 0.032 0.148
3.1 6.8 4.9 4.4 11.1 8.2
4.7 5.1 6.3 5.6 9.6 9.0
0.010 0.01 1 0.025 0.151 0.167
2.4 3.3 5.7 3.5 7.1 4.9 4.6 11.6
2.5 4.3 4.5 2.9 6.8 6.2 6.5 8.5
0.0
14.6
0.008 0.002 0.173
0.1 1.1 76 2.0
5.6 0.7 4.7 2.3
0.003 0.008 0.171
4.3 5.3 3.9 9.3 8.9
2.7 4.7 2.9 3.9 6.2
1 .o 11.2 4.1 5.2 9.1 6.1
4.1 5.7 7.3 5.9 7.3 9.1
3.3 5.0 1.3 5.5 5.7 7.4 11.7
3.9 4.5 9.0 6.3 10.0 9.9 9.5
0.006 0.177
0.143 0.001
.oo
0.001 0.010 0.043 0.128
0.020 0.161
"These frequencies have been employed elsewhere in an attempt to define a simple force field for BF.'O See also ref 31. bThe local Cartesian coordinate system for this decomposition is defined by (1) the radial direction outward from the center of the molecule, (2) the direction perpendicular to the radius and in the plane formed by the radius and the double bond (see Figure l ) , and (3) the tangential direction perpendicular to the first two. Rms dot products, based on the normalized vi vectors defined by eq 1. Rms variation in internal coordinte per unit variation of normal coordinate (deg/A for the bending modes). The maximum possible value is 1/3O1I2 = 0.183 for the double bond. For the single bond a universal maximum is not possible because the single bonds are not orthogonal to one another (cf. the value of 1/6O1I2 = 0.129 for the case of 60 orthogonal bonds). For the bond stretch modes, values of 20.001 have been listed. 'The pure rotations and translations have been included for purposes of comparison.
"
by the two atoms involved in a double bond; see Figure 1 for the definition of these bonds and our atomic numbering system). Like the rms radial displacements, the rms values of these tangential coordinates are invariant to the choice of atom. The same is true, of course, for the third local coordinate, a tangential displacement
perpendicular to the plane defined by the radial direction and the double-bond direction. The orthogonality of the radial and tangential directions allows one to characterize each vibrational mode as being divided into percentage contributions from each of the three directions. The results are shown in Table I.
2144
The Journal of Physical Chemistry, Vol. 92, No. 8, 1988
TABLE II: Intensity Data for IR-Active Modes mode u, cm-’ dipole derivative,’.b D/A 1F,,, 571 1.48 .. 2Fl“ 719 0.85 1353 3F1, 2.03 1628 3.12 ‘The rms value, based on the three components of the dipole vector. bBecause all the atoms have the same mass, the dipole derivatives with respect to normal coordinates can be expressed in units of D/A.
The rms amplitudes of internal coordinates like the double- and single-bond stretching modes and bond angles are also invariant to the particular choice of coordinate made from a symmetrically equivalent set. When these coordinates are orthogonal to one another, as are the doublebond stretches, their squared amplitudes can be summed to give a percentage corresponding to the entire set. However, the single-bond stretches and the bond angle bonds are orthogonal neither to each other nor to the double bonds. Since these nonorthogonalities make percentage breakdowns problematical, we have chosen to characterize the normal modes by listing the rms variation in each internal coordinate of interest per unit variation of the normal mode. Calculation of Force Constants and Dipole Derivatives
The Cartesian force constant matrix F is invariant to all symmetry operations.
F = RtFR
(9)
If F is decomposed into 3 X 3 atomic blocks F,, then it follows from (2) and (9) that these can be rotated into one another.
Since all atoms of BF are equivalent, eq 10 allows one to compute the entire force constant matrix of BF from just three columns, those containing the diagonal and off-diagonal elements of a single atom. These in turn can be calculated from just three gradient calculations. In practice, we used numerical differentiation based on the gradient in the “equilibrium” geometry and six additional configurations, two for each coordinate of the arbitrarily chosen atom. The same methods can be used to calculate dipole moment derivatives. Let a be the 3 X 180 matrix of derivatives of the dipole moment with respect to Cartesian coordinates. One can show that its atomic blocks rotate into one another in the following manner. ap,= Itair
(11)
The effect once again is to allow complete calculation of cy from the calculation of a single atomic block. We are aware that the concept behind eq 10 and 11 is not new and has in fact frequently been used.24 We have included it here since we are not aware of any published work in which the procedure denoted by eq 10 and 11 appears explicitly. It should be noted that its practical consequence is very great indeed. In its absence the calculations reported here would have been more costly by a factor of -60. Discussion
We note that only four frequencies are infrared-active (Flu). This is a consequence of the rich symmetry of the icosahedral group. Carbon clusters of comparable size, but lower symmetry, have many more IR-active frequencies. The graphitene isomer of c60, for example, which has Dsh symmetry, has 20 IR frequencies. Other examples include Cs4,a planar graphite fragment with Dsh symmetry, 22 active frequencies; and cso, a spheroidal cluster with DShsymmetry, again 22 active frequencies. Dewar et al.23chave published an extensive summary of comparisons of MNDO frequencies with experimental data. The least (24) Takada, T.; Dupuis, M.; King, H. F. J. Chem. Phys. 1981, 75, 333-336.
Stanton and Newton TABLE 111: Comparison of A,. Stretching Freauencies A,, frequency, cm-l molecule mode type‘ MNDOb C2H4 c=c 1782 trans-C4H, c-c I298 c=c 1841 C6H6 c-c 1197 C60 C-c* 610 c=c 1667
expte 1623 1196 1630 990
“Dominant valence bond character of the bonds involved in the A,, mode. bPresent work. ‘Reference 25. dRadial breathing.
accurate M N D O predictions occur for the grossly anharmonic torsions about C-C single bonds: mean observed value equal to 240 cm-’ vs a mean computed value of 142 cm-’. More typically, computed frequencies are high by about lo%, just as is the case for large basis, a b initio S C F calculation^.^^ Taking benzene as an example, we find the rms deviation of the MNDO frequencies from the experimental valuesz5to be 171 cm-’. With the exception of the lowest frequency A,, mode (where the MNDO value (1 197 cm-’) is 205 cm-’ larger than the experimental value (992 cm-I)), the M N D O values are within 10% or 100 cm-’ of the experimental values. It seems reasonable to expect similar errors for the frequencies in BF. The dipole moment derivatives listed in Table I1 are probably less reliable. In comparing calculated M N D O derivatives for ethylene with accepted experimental values,26 we obtained a least-squares fit of Idji/dQlexpt= 0.1 0.51d,Z/dQIMND0i 0.2 (D/(A amu’/2)), with a correlation coefficient of 0.88. In spite of uncertainties, the calculated results for BF are expected to provide useful estimates of the vibrational intensities (see also ref 27). The finding that all the frequencies are real and finite demonstrates the stability of BF. In order to assess the reliability of the lowest calculated frequency, we carried out M N D O calculations for the normal-mode vibrations in the series benzene, naphthalene, and anthracene. The lowest benzene value, 368 cm-’, corresponds to the E,, mode, which is also found to be the lowest frequency mode e ~ p e r i m e n t a l l y with , ~ ~ a frequency (404 cm-’) in reasonable agreement with the calculated value. For both naphthalene and anthracene the lowest energy out-of-plane M N D O frequencies belong to nearly degenerate A,, and B3” modes: respectively 153 and 164 cm-’ (naphthalene) and 99 and 88 cm-’ (anthracene). These calculated frequencies are in good agreement with the available experimental data assigned to the low-frequency B3,, modes: 166 cm-’ for naphthalene2* and 106 cm-l for a n t h r a ~ e n e .These ~ ~ results give some basis for assuming the validity of the corresponding calculations for the low-frequency BF modes. We note that the lowest frequency mode in BF (1HJ is not completely analogous to the out-of-plane modes of the planar aromatics, since it includes about 3 I % tangential motion. The dot product entries in Table I, (vltv2) = ( v l t v 6 ) = 0.88, clearly
-
-
+
( 2 5 ) Shimanouchi, T. Tables of Molecular Vibrational Frequencies; Consolidated Volume I; NSRDS-NBS 39; US.Government Printing Office: Washinnton. DC. 1972. (26) See the values cited by: Komornicki, A,;McIver, J. W., Jr. J . Chem. Phys. 1979, 70, 2014-2016. (27) Michl, J.; Radziszewski; Downing, J. W.; Wiberg, K. B.; Miller, R. D.; Kovacic, P. C.; Jawdosiuk, M.; Bonacic-Koutecky, V. Pure Appl. Chem. .. 1983, 55, 315-321. (28) Sellers, H.; Pulay, P.; Boggs, J. E. J. Am. Chem. Soc. 1985, 107, 6487-6494. (29) Neerland, G.; Cyvin, B. N.; Brunvoll, J.; Cyvin, S. J.; Klaeboe, P. Z . Naturforsch. A : Phys., Phys. Chem., Kosmophys. 1980, 35A, 1390-1394. (30) Wu, 2.C.; Jelski, W. A,; George, T. F. Chem. Phys. Lett. 1987,137, 291. (31) The 2A, and 1H frequencies are greater than the values we reported earlier’ by a factor of 2’/! The error in the earlier results arose from a defect in the MOPAC23dimplementation of MNDO. This yields gradients which are too small by a factor of 2. If MOPAC is used directly for the calculation of frequencies, one obtains correct results because another portion of the code compensates for the error. Since we relied on a minimal set of gradients in an external construction of the force constant matrix, the error persisted in our original frequency calculations. -
~
-
-
j
~
-
r
-
~
J . Phys. Chem. 1988, 92, 2145-2149 show this mode to be a long-wavelength skeletal vibration, and its frequency (263 cm-I) seems safely removed from any indication of instability. To help place the BF vibrational frequencies in perspective, we compare the totally symmetric (Alg) frequencies with those of ethylene, trans-butadiene, and benzene in Table 111. The 2A!, frequency of BF, involving primarily double-bond stretching, is seen to be intermediate between the essentially pure double-bond stretching frequencies for ethylene and butadiene and the CC stretching frequency for benzene. The other BF AI, mode, with a frequency (610 cm-I) well below that for the "single-bond stretch" in tram-butadiene, is a pure radial breathing mode, having some double- as well as single-bond stretching character. The lA, mode at 972 cm-I is of particular interest. Note that the atomic motion is wholly tangential and perpendicular to the great circle planes containing the C=C bonds. Note also that the value of 0.31 for (vItvz) is just cos 2n/5. These results imply a rigid rotary oscillation of each pentagonal ring about its local fivefold axis, an interpretation that is confirmed by the O.O"/A entry for the C-C-C angle distortion. The -1.00 entry for (vltv6) indicates that all pentagonal rings rotate in the same direction, as illustrated in Figure 1. This maximizes the distortion of the
2145
angles (all C-C=C) in the hexagonal rings. Identical rotation of linked pentagonal rings is a necessary feature of the A, symmetry species but is not characteristic of other modes dominated by pentagonal ring rotation. In order of increasing frequency and angle distortion these are the 1F2g,3H,, and increasing C-C=C 2F,, modes at 591, 706, and 865 cm-I, respectively. The ring oscillation described above is not unique to BF. Independent ring oscillation coordinates can be defined for graphite and for many hypothetical spheroidal carbon clusters. We do not know how important these coordinates are, however, in describing the actual vibrational modes of these molecules. Acknowledgment. We are grateful to Prof. Harry F. King and James McIver of the Chemistry Department at SUNY-Buffalo for several helpful comments concerning this paper. The research at Brookhaven National Laboratory was carried out under Contract DE-AC02-76CH00016 with the U S . Department of Energy and supported by its Division of Chemical Sciences, Office of Basic Energy Sciences. Part of the work was performed at Canisius College, with the aid of a Cottrell College Science Research Grant provided by the Research Corporation. Registry No. Buckminsterfullerene, 99685-96-8.
Infrared Spectra of HNF,, NF,, PF,, and PCI3 and Complexes with HF in Solid Argon Robert Lascola, Robert Withnall, and Lester Andrews* Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901 (Received: August 10, 1987)
Infrared spectra of HNF2, NF,, PF3, and PCl, and their complexes with H F were observed in solid argon matrices. An asymmetric structure was deduced for (HNF2), based on comparison with HNF, spectra. Complexation of these bases with H F produced the following bands: HNF,, 3681 cm-' ( u s ) and 516 and 498 cm-I (vc); NF3, 3913 cm-' (v,) and 246 cm-' ( v p ) ; PF3, 3890 cm-' (v,) and 258 cm-' (vt); PCl,, 3868 cm-I (vs). The spectra suggested the formation of a hydrogen bond between HF and the N or P lone pair for all four complexes. A direct correlation between proton affinity and vs was found for fluoro-substituted amines, allowing prediction of the HNF2 proton affinity as 163 A 5 kcal/mol and that of NHzF as 181 f 5 kcal/mol. Basicity trends in nitrogen and phosphorus compounds are discussed.
Introduction The study of HNF, (difluoramine) and N F 3 and their hydrogen-bonded complexes with HF is interesting both in its own right and in view of recent studies in this laboratory. There is very little spectral information on HNF,, an explosive c o m p o ~ n d . ' Also, ~ investigation of the complexes continues an ongoing study of complexes between HF and substituted amines, including NH3,5 NHZF$ N H 2 0 H , ' NHx(CH3)3-x,8and NHzNH2.9 This study completes the series of increasing fluorination starting with NH, and ending with NF, and creates the possibility of studying the effects of fluorine substitution on a central atom. The HNF, dimer spectrum is also interesting, as HNF2 is related to NH3, and the ammonia dimer has received considerable attention.'OJl Finally, the phosphine-hydrogen fluoride complex has been characterized and found to be weaker than the ammonia-hydrogen fluoride complex based on the base interaction with the HF acid.', (1) Comeford, J. J.; Mann, D. E.; Schoen, L. J.; Lide, Jr., D. R. J . Chem. Phys. 1963, 38, 461. (2) Christe, K. 0.;Wilson, R. D. Inorg. Chem. 1987, 26, 920. (3) Christe, K. 0. J Fluor. Chem., in press and personal communication. (4) Craig, A. D. Inorg. Chem. 1964, 3, 1628. (5) Johnson, G. L.; Andrews, L. J. Am. Chem. SOC.1982, 104, 3043. (6) Andrews, L.; Lascola, R. J . Am. Chem. SOC.1987, 109, 6243. (7) Lascola, R.; Andrews, L. J. Am. Chem. SOC.1987, 109, 4765. (8) Andrews, L.; Davis, S . R.; Johnson, G. L. J . Phys. Chem. 1986, 90, 4273. (9) Lascola, R.; Withnall, R.; Andrews, L. Inorg. Chem., submitted for publication. (10) Nelson, Jr., D. D.; Fraser, G. T.; Klemperer, W. J Chem. Phys. 1985, 83, 6201. (11) Suzer, S.; Andrews, L. J . Chem. Phys. 1987, 87, 5131.
0022-3654/88/2092-2145$01.50/0
Proton affinitiesI3 and size effects suggest that this trend will reverse for N F 3 and PF3, and it is of chemical interest to make this comparison.
Experimental Section The vacuum and cryogenic techniques for matrix isolation experiments have been described previo~sly.'~,'~ HNF, synthesis was based on the methods of Parker and FreemanI6 and Christe and Wilson." The first step was to convert urea to difluorourea. Three grams of urea (Aldrich, reagent grade) was dissolved in 35 mL of H 2 0 in a 100-mL three-neck round-bottom flask. A Teflon sparge tube was introduced through one port, a thermometer was introduced through another, and the third held a Tygon exit tube. The flask was immersed in an ice-water bath, and the exit tube led to an acidic, aqueous KI solution. An Ar/F2 gas mixture (approximate ratio 211) was passed through the sparge tube at approximately 3 mmol/min until 100 mmol of F, was used; during this step the KI solution turned dark red. The difluorourea solution was then acidified and heated to liberate H N F 2 and C 0 2 in the same three-neck flask. One port admitted Ar carrier gas, one held a Pyrex dropping funnel containing 6 mL of concentrated H,SO,, and the third led to a series (12) Arlinghaus, R. T.; Andrews, L. J . Chem. Phys.1984, 81, 4341. (13) Dorion, C. E.; McMahon, T. B. Inorg. Chem. 1980, 19, 3037. (14) Andrews, L.; Johnson, G. L. J . Chem. Phys. 1982, 76,2875. ( 15) Andrews, L.; Johnson, G.L.; Kelsall, B. J. J . Chem. Phys. 1982, 76, 5767. (16) Parker, C. 0.; Freeman, J. P. Inorg. Synth. 1970, 12(55), 307. (17) Christe, K. 0.;Wilson, R. D., private communication.
0 1988 American Chemical Society
