J . Phys. Chem. 1992,96, 6937-6941 (25) Tonkyn, R.; Ronan, M.; Weisshaar, J. C. J . Phys. Chem. 1988.92, 1992. (26) Stevenson, D. P. Discuss. Faraday Soc. 1951, 10, 35. (27) Armentrout, P. A. Personal communication, 1991. (28) Dao, P. D.; Peterson, K. I.; Castleman, A. W., Jr. J . Chem. Phys. 1984.80, 563. (29) Gipumousis, G.; Stevenson, D. P. J . Chem. Phys. 1958, 29, 294. (30) Handbook of Physics and Chemistry, 76th ed.; CRC Press: Boca Raton, FL, 1988. ‘ (31) Su,T.; Chesnavich, W. J. J . Chem. Phys. 1982, 76, 5183. (32) Schelling, F. J.; Castleman, A. W., Jr. Chem. Phys. Lett. 1984, 1 1 1 , 47. (33) (a) Zakin, M. R.; Brickman, R. 0.;Cox, D. M.; Kaldor, A. J . Chem.
6937
Phys. 1988, 88, 3555. (b) Zakin, M. R.; Brickman, R. 0.;Cox, D. M.; Kaldor, A. J. Chem. Phys. 1988, 88, 6605. (c) Upton, T. H.; Cox, D. M.; Kaldor, A. J . Phys. Chem. 1989, 93, 6823. (d) Irion, M.P.; Selinger, A.; Schnabel, P. Z . Phys. D. 1991, 19, 393. (e) Schnabel, P.; Irion, M. P.; Weil, K. G. J . Phys. Chem., submitted for publication. (f) Nakajima, A.; Kishi, T.; Sugioka, T.; Sone, Y.;Kaya, K., unpublished results. (34) Freas, R. B.; Dunlap, B. I.; Waite, B. A.; Campana, J. E. J . Chem. Phys. 1987, 86, 1276. (35) Begemann, W.; Dreihofer, S.; Meiwes-Broer, K. H.; Lutz, H. 0. Z . Phys. D. 1986, 3, 183. (36) Armentrout’s group has determined the bonding strength of Co,, + Co in an ion beam technique.” Their results indicate that the bonding energies for the bare cobalt cation clusters are either near or larger than 2.0 eV.
Application of Density Functional Theory to Infrared Absorption Intensity Calculations on Transition-Metal Carbonyls Liangyou Fan and Tom Ziegler* Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N I N4 (Received: February 13, 1992)
Approximate density functional theory has been evaluated as a practical tool for calculations on infrared vibrational frequencies and absorption intensitiesof transition-metal complexes. The density functional schemes included the local density approximation (LDA) by Gunnarson (Phys. Rev. 1974, BIO, 1319) as well as a self-consistent nonlocal density functional method (LDAINL) in which the gradient-corrected exchange term by Becke (Phys. Rev. 1988, A38, 3098) and the gradient-corrected correlation term by Perdew (Phys. Rev.1986,833,8822) have been added to LDA. The LDA and LDA/NL schemes have been applied to calculations on the infrared vibrational frequencies and absorption intensities of Ni(C0)4and Cr(C0)6. The calculations were carried out with a double-l plus polarization basis set for C and 0 and a triple-f plus polarization basis set for Cr and Ni. The simple theoretical LDA model has been found to reproduce vibrational spectra of metal carbonyls adequately. The more sophisticated, and also more expensive, nonlocal scheme does not introduce important improvements in the calculated vibrational frequencies for Cr(C0)6and Ni(CO).+ The calculated frequencies are in general in better agreementwith experiment than values obtained by ab initio Hartree-Fock calculations. Calculated atomic polar tensors and harmonic force fields are provided for both molecules.
Introduction IR spectroscopy can supply important information about the structure of transition-metal complexes. The force constants representing bond stretches and angular bendings afford in addition valuable clues to the nature and strength of the bond between transition-metal centers and coordinating ligands. The absolute IR absorption intensities finally provide information about charge delocalizations associated with ligand coordination to a metal center The experimental determination of general quadratic force fields in transition-metalcomplexes is usually hampered by insufficient experimental data. That is, the number of independent force constants in a molecule is usually much larger than the number of observable frequencies due to the same system. Thus,additional information must be obtained by observing frequencies due to an often large number of isotope-substituted species. Isotope substitutions in organometallics are laborious, and it is often not possible to generate the required number of species. Furthermore, the absolute IR intensities of metal carbonyls are measurable only for C-O stretching modes. The other bands are too weak in comparison with the dominating CO band to be accurately measured by experiment. Theoretical calculations are therefore expected to play an important part in supplementing experimental information. Unfortunately, theoretical studies on vibrational spectra are rather scarce for transition-metal complexes in contrast to the situation among classical main group molecules. There are few theoretical calculations on vibrational spectra and IR intensities of transition metals. The paucity of ab initio calculations in this field stems primarily from the fact that ex-
pensive high-level methods with extensive treatment of electron correlation are required. This makes ab initio studies on transition-metal systems less attractive than similar studies on organic molecules where the more economical Hartree-Fock method can be used. Vibrational studies should in principle be attractive for methods based on DFT. However, the required computer programs for such studies have only emerged over the past few years. Among the limited calculations based on density functional theory, Baerends and Rozendaa12calculated the frequencies of C-O and Cr-C stretches in Cr(CO), by the X, method. Rosch and Jbrg have used a similar method to calculate the frequencies of Ni-C and C-O stretches in Ni(C0)438as well as the symmetrical Fe-Cp stretch in ferrocene.3b Papai et al. r e p r o d u ~ e dthe ~ ~vibrational frequencies of Ni(C0)4, NiC2H4,and PdC2H4. Dunlap et al. calculated the dipole strengths of NiCO for Ni-C and C-O stretches.4b The frequencies calculated by DFT in these cases agree reasonably well with experiment. However, a complete set of IR intensities and a full general quadratic force field of transition-metal complexes calculated by DFT have not previously been published. We present here a full analysis of the vibrational spectra for Ni(C0)4 and Cr(CO), based on DFT. We have made some efforts to reproduce vibrational frequencies by the HartreeFock-Slater (HFS) method in a previous studyas The satisfactory agreement between experimentally observed frequencies and HFS calculations encourages us to extend our investigations to IR absorption intensities. We shall further make use of the more sophisticated density functional methods introduced over the past 10 years. These methods include the local
0022-3654/92/2096-6937$03.00/0 0 1992 American Chemical Society
6938 The Journal of Physical Chemistry, Vol. 96, No. 17, 1992 TABLE I: Metal420 Bond Distances and Bond Dissociation Energies in Ni(CO)4 and Cr(CO), molecule property HF HFS LDA' LDA/NL/ Ni(CO), R(Ni-CO) 1.884' 1.794d 1.795 1.841 R(C-0) 1.139 1.141 1.144 1.148 D(Ni-CO)b 194 192 106 Cr(C0)6 R(Cr-CO) -2.0' 1.868' 1.872 1.909 1.153 1.143 1.141 W-O) 278 276 147 D(Cr-CO)b
exptf 1.825 1.122 104 1.914 1.140 162
Bond distances in A from ref 23. First metal-CO bond dissociation energies in kJ/mol are as cited in ref 1 la. Rosch et al. reported a higher Ni-CO bond energy of 207 kJ/mol by HFS method in ref 26. 'Reference 24. dReferences log and 10m. e Reference 2. 'Reference 9b. #Experimental bond lengths (A) for Ni(C0)4 and Cr(C0)6 are from refs 20 and 25, respectively.
Fan and Ziegler TABLE II: Vibrational Frequencies of mode LCGTW A, C - 0 s-stretch 2167 Ni-C s-stretch 44 1 E Ni-C-0 bend 504 81 C-Ni-C bend F, C-O a-stretch 2096 Ni-C-O bend 512 Ni-C a-stretch 458 56 C-Ni-C bend 285 F, Ni-C-O bend Reference 4a. quency.
Reference 17.
Ni(CO)4 (in c LDA N L 2142 2112 403 363 488 447 43 27i 2073 2039 483 445 476 419 78 35 292 251
'Reference
d ) HF* exDtc 2351 2154d 217 371 493 380? 43 62 2262 2092d 493 459 377 423 93 79 326 300
20. dHarmonic fre-
available in the HFS program developed by Baerends et al.13 We have implemented an algorithm to evalaute the derivatives by numerical differentiation
density approximation (LDA) due to Gunnarson et a1.6aas well as the nonlocal corrections proposed by Becke7for exchange and Perdews for correlation. We have recently implementedga a (4) self-consistent version of the nonlocal theories due to Becke6and Perdew.' The self-consistent version has been applied extensively to molecular properties? including molecular geometriesgband where pelis evaluated in the standard way by eq 5 . vibrational frequencies of main group molecules.9c The introduction of nonlocal methods has led to a substantial improvement pel = - ($olrl$o) + CWa (5) a in DFT calculations on metal-ligand bond energies and bond distances as indicated in Table I. Thus the two local methods, The high symmetry of Ni(C0)4 and Cr(CO), permits a simHFS and LDA, afford metal-ligand bonds that are both too plification in the evaluation of force constants and dipole moment shortgband too shrong.lla Nonlocal corrections afford a better derivatives. We calculate force constants by numerical differdescription of the metal-ligand bond by making it weakerlla and entiation of analytical first-order energy derivatives somewhat longergb (Table I). We shall in the present study investigate whether nonlocal corrections have a substantial inF,,= Ag,/b, (6) fluence on the metal-ligand stretching frequencies as well by where g, = aE/axi is the energy derivative with respect to nuclear presenting a full analysis of the vibrational spectra of Ni(C0)4 coordinate x,. We choose Cartesian displacement coordinates and and Cr(CO),+ evaluate F,,for only one atom of each element. The dipole moment The successful implementationloof analytical energy gradients derivatives with respect to displacements on these atoms were within the DFT formalism has led to many DFT studies on molecular structures' lasbvd and vibrational f r e q ~ e n c i e s .IC~The , ~ ~ ~ ~ ~ calculated in a similar way by numerical differentiation of the analytical dipole moments. The Cartesian displacement used in present investigation affords the first systematic study among the calculation is Ax = h0.05 a,. The force constants and dipole transition-metal complexes on the calculation of vibrational fremoment derivatives with respect to the remaining atoms can be quencies by nonlocal density functional theory as well as the first derived from symmetry relations. extensive study on the calculation of infrared absorption intensities The calculations are carried out at two levels of density by DFT based methods. functional theory. The fmt level is the local density approximation Program Implementations and Details of Calculation (LDA)6ain the parametrization by Vosko et a1.6band the second level is a more sophisticated approach in which we have included The absolute IR absorption intensity A, dependsI2 on the dethe nonlocal correlation correction by Perdews and the nonlocal rivatives of the electric dipole moment, pel, with respect to the exchange correction due to B e ~ k e .The ~ inner shell orbitals are normal coordinates, Q,,as kept frozent3in the calculations, and the valence electrons are described by a set of Slater-type orbitalsI4of either double-{plus polarization for C and 0 or triple-{ plus polarization for Ni and Cr. The numerical integrations involved in our calculation are where A, has the unit of km/mol and n, is the degeneracy of carried out by the scheme proposed by Boerrigter et al.I5 vibration i . However, it is inconvenient to evaluate the electric dipole Vibrational Spectra of Ni(CO)., moment derivatives with respect to normal coordinates directly Nickel tetracarbonyl is one of the few transition compounds since the normal coordinate Q,is a linear combination of Cartesian for which vibrational frequencies have been determined by excoordinates. Instead, the derivatives of pelwith respect to a set periment as well as ab initio calculations. Calculations based on of working coordinates (Cartesian, internal, or symmetry coordensity functional theory have appeared4a recently as well for dinates) S are evaluated first and then transformed back to the Ni(C0)4. The frequencies obtained in the present study are corresponding derivatives in terms of normal coordinates. The compared with the experimental values in Table I1 along with transformation is straightforward previous theoretical results. Our calculations are labeled LDA for the local density approximation6and NL for the approach in which we have included the nonlocal correlation correction by Perdews and the nonlocal exchange correction due to B e ~ k e The .~ where L is the matrix consisting of the eigenvectors of the force experimental harmonic frequencies are available only for the two constant matrix evaluated in coordinate S. The normal coordinate C-O stretching modes v 1 and u5. However, the anharmonic Q and S are related by eq 3. In the expression of eq 2 pelshould corrections for the other modes are believed to be very small, Le., within experimental resolution.16 Thus, the comparison with S = LQ (3) experiment should provide a valuable evaluation of the theoretical models. be considered as a 1 X 3 vector and apel/aQ has the dimension The LDA C-O stretching frequencies for v1 and v5 agree reof (3N - 6 ) X 3, where N is the number of nuclei in the molecule. markably well with the experimental harmonic frequencies. The The analytical algorithm for evaluating apeI/8!3is currently un-
The Journal of Physical Chemistry, Vol. 96, No. 17, 1992 6939
Transition-Metal Carbonyls TABLE III: Infrared Absorption Intensities of Ni(CO)4 (km/mol) HF" mode LDA NL 4145 2246 F2 C - O a-stretch v5 2757 N i - C - O bend ~6 0.07217 1.398 49.97 158.9 N i - C a-stretch v7 207.1 296.6 5.717 2.187 C-Ni-C bend v8 0.7693 a Reference
17.
TABLE IV Dipole Moment Derivatives of Ni(CO), and Cr(C0)6 (debye/A)"
(b) Cr(C0)6
(a) Ni(CO),
Figure 1. Cartesian coordinate system for (a) Ni(C0)4 and (b) Cr(CO)@
Ni(COh
pxx pzz
Ni
LDA Cl
0 1
Ni
-6.5928 -6.5928
1.6336 11.6656
-0.4488 -9.0906
-7.4010 -7.4010
NL Cl
0 1
1.2163 -0.8124 11.565 1 -6.8 184
Cr(C0)6
E
LDA Cr pxx pzz
-13.1980 -13.1980
CI
TABLE V Harmonic Force Fields of Ni(CO)," LDA NL HFb 17.7565 21.78 Ai F1, 18.0845
NL 0 1
-0.5376 2.4632 13.7318 -10.9840
Cr -12.5325 -12.5325
C1 2.1590 13.7128
0 1
F2
-0.3599 -1 1.0448
-
F=5, F56
F57 F58 F66
"The coordinate systems are defined in Figure 1. Atomic polar tensors of the other atoms can be derived by symmetry.
LDA frequencies are slightly (within 20 cm-l) lower than the experimental values. The frequencies of the two Ni-C stretching modes v2 and v7 are on the other hand predicted by LDA to be 30-50 cm-l higher than the observed numbers. The high values here reflect that M-L bond distances are underestimated by LDA (Table I). Not surprisingly, nonlocal corrections reduce the frequencies for the Ni-C stretches, and the agreement between NL and experiment is now within 10 cm-l as shown in Table 11. Meanwhile, the C-O stretching frequencies are lowered as well by NL due to the slightly longer C-O bonds (Table I). The deviation with experiment has now increased to 40-50 cm-l. The frequencies for the five bending modes calculated by LDA are also seen to be very close to experiment with discrepancies of the order of 50 cm-l or less, except for the v3 Ni-C-O bending mode. However, the experimental frequency for v3 is questionable as discussed by Carsky and Dedieu.17 The experimental frequency at 380 cm-l due to Jones (Table 11) was derived from substituted nickel tetracarbonyls18and conflicts with an earlier experimental value19 of 461 cm-l. Hartree-Fock17 calculations place the frequency at 493 cm-l, and a similar value was found by local spin density calculations due to Papai et al.4a Our calculated frequencies at 488 and 447 cm-' by LDA and NL, respectively, also favor the earlier experimentallg estimate for this mode. Nonlocal corrections do not seem to improve LDA frequencies consistently as indicated in Table 11. As a matter of fact, the frequency for v4 calculated by NL is even imaginary which is obviously inconsistent with Ni(C0)4 being a stable molecule. It is certain that NL underestimates the strength of C-Ni-C bending, but the small imaginary value of 27i cm-l most likely originates from numerical errors. The sources of the errors are twofold: the first is related to the numerical differentiationused to obtain force constants, and the second, which is probably more important, involves the numerical evaluation of nonlocal potentials. The appearance of p-3/4in the nonlocal potentials may bring in errors 0 at large distances from the nuclei. when p Experimental IR absorption intensities for Ni(C0)4 are available for the C-O stretching band. The intensities of this band have been measured in solutionsla and vary from 2395 to 4459 km/mol depending on the solvent. Table I11 affords a comparison of our results with Hartree-Fock calculation^.^^ It is noticeable that the intensity for the C-O band obtained by HF is much stronger than the corresponding intensities calculated by LDA and NL. Also, the relative intensities of v6 and vg are reversed in the HF case. We feel it is hard to judge which theoretical model yields the more accurate intensities without accurate experimental evidence. In Table IV we report the atomic polar tensors (dipole
Fl2 F22 F33 F34 FM
Fh,
Fi8 F77 F78
Fa8
F1
F99
0.4047 2.7513 0.3538 0.2007 0.2292 17.2795 0.6521 -0.0342 4.0631 2.4805 0.2350 0.1851 0.3195 0.1733 0.4437 0.2294
0.4041 2.2133 0.2325 0.241 5 0.1898 16.9068 0.665 1 -0.0376 -0.0191 1.9649 0.22 15 0.1977 0.2064 0.2291 0.3543 0.1730
-0.109 1.295 0.439 0.159 0.156 20.94 0.697 0.002 0.082 1.601 0.154 0.270 0.398 0.126 0.462 0.285
exptC 18.233 0.235 2.355 0.342
[OI 0.151 17.867 0.740
PI [OI
2.013 0.126 0.223 0.486 [O] 0.221 0.238
"Symmetry coordinates are defined in ref 20. Units are mdyn/A for stretching, mdyn for stretching-bending, and m d y d for bendingbending. Reference 17. E Reference 20.
moment derivatives with respect to Cartesian coordinates) of Ni(C0)4 and Cr(C0)6. The components that are not given in Table IV can be derived easily by symmetry considerations. The coordinate systems for the two molecules are illustrated in Figure 1. The force fields for Ni(C0)4calculated by LDA and NL are summarized in Table V along with those from Hartree-Fock calculationsand experiment. The numbering of the force constants refers to the symmetry coordinates defined by Hedberg.20 For the Al block both LDA and NL yield numbers very close to experiment. Flland F22refer to C-0 and Ni-C stretches, respectively. It is clear from Table V that the diagonal force constants calculated by NL are consistently lower than those by LDA. As a consequence, F22of NL is in better agreement with experiment while Fll of LDA is more close to reality. This accounts for the trends in calculated frequencies by the two methods discussed earlier. The F34element of the E block was set to zero in the experimental refinement.20 According to our LDA calculations as well as HF, the magnitude of F34is comparable to F44.The E block is where NL generates a negative frequency for one C-Ni-C bending. Comparison of NL force constants with experiment as well as LDA indicates that NL introduces an artifically high coupling constant, F34,and low diagonal forces F3, and F4 corresponding to N i x 4 and C-Ni-C bending, respectively. Test revealed that the imaginary frequency can be rectified by increasing F3, and F34but decreasing F34by 0.004 hartree/ao2. This is one of the reasons that we believe the negative frequency introduced by NL is more likely a numerical error than an inherent feature of the NL potential energy surface. This point should hopefully be resolved with the introduction of analytical second derivatives. The force constants for the F1 and F2 blocks evaluated by LDA and NL are similar; in both cases the agreement with experiment is remarkable.
Vibrational Spectra of Cr(C0)6 The vibrational frequencies of Cr(C0)6 obtained by LDA, NL, and experiment21 are given in Table VI. The experimental
6940 The Journal of Physical Chemistry, Vol. 96, No. 17, I992 TABLE M: Vibrational Frequencies (cm-I) and Absorption Intensities (km/mol) of Cr(CO)2 LDA NL exptb A,, C-O stretch uI 2212 2113 2139.2 Cr-C stretch v2 434.7 401.5 379.2 E C-O stretch u3 2119 2018 2045.2 Cr-C stretch u4 443.6 408.0 390.6 FI, Cr-C-0 bend u5 374.0 381.2 364.1 Flu c-0 stretch Y6 2101 (5911) 2001 (5899) 2043.7 (ws) Cr-C-0 bend v7 753.1 (669.3) 717.6 (559.9) 668.1 (vs) Cr-C stretch Yg 493.4 (4.591) 464.5 (28.62) 440.5 (s) C-Cr-C bend vg 72.16 (2.176) 95.35 (3.307) 97.2 (m) F,, Cr-C-O bend v I o 557.7 554.2 532.1 C-Cr-C bend v I I 17.60 26.01 89.7 Fzu Cr-C-O bend u I 2 526.5 529.5 510.9 C-Cr-C bend uI3 8.565 16.411' 67.9 ~
Fan and Ziegler TABLE VII: Harmonic Force Ficlds of Cr(CO)." LDA NL AI, Fll 19.1414 17.5422 F,2
E, FI, Flu
"Intensities are given in parentheses. bReference 21.
frequencies for the (2-0 stretches, vl, v3, and v6, are harmonic. Anharmonic corrections for the other frequencies are very small (less than 3 cm-l in most casesz1).The agreement between theory and experiment is in general good. As for the spectra of Ni(C0)4, NL predicts consistently lower frequencies for C-0 and Cr-C stretches. Baerends2 noticed that the Cr-C frequency of v2 calculated by the X, method is higher than the experimental value. Our LDA result for v2, 435 cm-I, is also 55 cm-l higher than the experimental value of 379 cm-I. NL improves the correspondence to experiment by affording 401 cm-l for this mode as shown in Table VI. Unfortunately, NL affords also for Cr(CO), a single imaginary frequency for a C-M-C bending mode (Table VI). The C-0 stretching frequencies calculated by NL are about 100 cm-l lower than those calculated by LDA. This reduction constitutes an improvement over the LDA results since the latter method affords harmonic frequencies that are somewhat too high compared with experiment. Both LDA and NL, however, represent experimental C-O frequencies very well as can be seen in Table VI. There are only four IR-active modes of Flu symmetry. The intensities of these modes predicted by LDA and NL are presented in Table VI. The experimental estimates are also given there. The relative intensities obtained by LDA and NL are both in accordance with experimental observations. The difference between LDA and NL for the C-0 stretch is however significant. Experimental measured intensitiesIa for this band in liquid phase vary from 6360 to 7070 km/mol. The intensities generated by LDA and NL are 591 1 and 5899 km/mol, respectively, which are close to the experimental assignments. The unique components of the atomic polar tensors for Cr(CO), are listed in Table V. The remaining components can be derived easily by symmetry. The atomic dipole tensors in conjunction with the force field given in Table VI1 make it possible to derive chemically meaningful bond dipole moment derivatives.' The calculated Cartesian force fields have been transformed to the corresponding symmetry force fields. The symmetry coordinates are as definedz2 by Jones et aLz' The results of our calculations are compared with experiment in Table VII. F68, F69rand FT9were fixed during the experimental refinement" in the ranges indicated in Table VII. As can be seen, both sets of theoretical force fields agree with experiment fairly well. The signs of cross terms yielded by LDA and NL are all consistent with experiment. Thus, our calculations bring a definite support to the experiment refinement.
Concluding Remarks We have studied the vibrational spectra of Ni(CO), and Cr(CO), by density functional theory. Two theoretical models, i.e., local density approximation (LDA) and LDA plus nonlocal corrections (NL), have been adopted in the calculations. The harmonic force fields and frequencies generated by theoretical calculations are in very good agreement with experimental derived values and may be considered as a support to experimental refinements. We have also provided the absolute IR absorption
0.3922 3.2278 F 3 3 17.8849 F34 0.7472 F44 3.3224 0.3854 F 5 5 17.9887 F66 0.8289 F61 F68 0.0103 F69 0.0427 F 77 2.3897 F78 -0.1487 F79 -0.2341 F88 0.4589 F89 -0.4395 F99 0.8829 FIO,IO 0.3411 -0.3190 F,,,11 F11,Il 0.3199 0.4569 F12.12 Fiz,,, -0.3113 F13,13 0.2188 F22
Fz~ F2u
0.3683 2.7413 16.3246 0.7047 2.7959 0.4108 16.4265 0.7863 0.0054 0.0576 1.9611 -0.1586 -0.1961 0.5152 -0.3577 0.9465 0.3508 -0.3322 0.2955 0.4776 -0.3130 0.2692
exptb 18.1 1 0.38 2.44 16.84 0.69 2.55 0.375 17.22 0.78 0 f 0.2 0 f 0.5 1.64 -0.18 -0.3 0.1 0.55 -0.21 0.79 0.39 -0.17 0.54 0.59 -0.11 0.35
*
"Symmetry coordinates are defined in ref 21. Units are mdyn/A for stretching-stretching, mdyn for stretching-bending, and m d y d for bending-bending. Reference 21.
intensities for the two metal carbonyls which may be useful in futrue experimental studies. The simple theoretical LDA model has been found to reproduce vibrational spectra of metal carbonyls adequately. The more sophisticated, and also more expensive, nonlocal scheme does not introduce important improvements in the calculated vibrational frequencies of Cr(CO), and Ni(C0k. However, the present study is only the first investigation in this field and definitive conclusions must await further investigations. The success of LDA in reproducing vibrational spectra for Ni(CO)., and Cr(CO), is encouraging. This method should be an efficient alternativeto more costly post Hartree-Fock methods in the study of vibrational spectra of transition-metal complexes.
Acknowledgment. This investigation was supported by the National Science and Engineering Research Council of Canada (NSERC). We thank the University of Calgary for access to their IBM RISC-6000 facilities.
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J. Phys. Chem. 1992,96,6941-6944 New York, 1991. (c) Sim, F.; Salahub, D. R.; Chin, S.;Depuis, M. J. Chem. Phys. 1991,95,6050. (d) Fitzgerald. G.; Andzelm, J. J . Phys. Chem. 1991, 95, 10531. (12) (a) Person, W. B., Zerbi, G., Eds. Vibrational Intensities in Infrared and Raman Spectroscopy; Elsevier: Amsterdam, 1982. (b) Overend, A. J. In Infrared Spectroscopy and Molecular Structures; Davies, M. M., Ed.; Elsevier: Amsterdam, 1963. (c) Herzberg, G. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand: New York, 1945. (13) Baerends, E. J.; Ellis, D. E.; Ros, P. Chem. Phys. 1973, 2, 41. (14) (a) Snijders, G. J.; Baerends, E. J.; Vernwijs, P. At. Nucl. Data Tables 1982,26,483. (b) Vernwijs, P.; Snijders, G. J.; Baerends, E. J. Slarer Type Basis Functions for the Whole Periodic System; Internal Report; Free University: Amsterdam, The Netherlands, 198 I . (15) Boerrigter, P. M.; te Velde, G.; Baerends, E. J. Int. J . Quantum Chem. 1988,33, 87. (16) Jones, L. H.; McDowell, R. S.;Goldblatt, M. J . Chem. Phys. 1968, 48, 2663.
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(17) Carsky, P.; Dedieu, A. Chem. Phys. 1986, 103, 265. (18) Bigogne, M. Proceedings of the 9th International Conference on Coordination Chemistry; Schneider, W., Ed.; Helv Chim. Acta 1966, 140. (19) Crowford, Jr., B. L.; Horwitz, W. J . Chem. Phys. 1948, 16, 147. (20) Hedberg, L.; Iijima, T.; Hedbcrg, K. J. Chem. Phys. 1979,70, 3224. (21) Jones, L. H.; McDowell, R. S.;Goldblatt, M. Inorg. Chem. 1969, 8, 2349. (22) There is an obvious misprint in ref 21 for S’;$ The correct definition should be S‘k = 1/2(821+ - Bsl - 8 d . (23) Spangler, D.; Wendoloski, J. J.; Dupuis, M.; Chen, M. M. L.; Schaefer 111, H. F. J . Am. Chem. SOC.1981, 103, 3985. (24) Liithi, H. P.; Siegbahn, P. E. M.; Almlof, J. J . Phys. Chem. 1985,89, 2156. (25) Jost, A.; Rees, B.; Yelon, W. B. Acta Crystallogr. 1975, 831, 2649. (26) Riisch, N.; Jorg, H.; Kotzian, M. J . Chem. Phys. 1987, 86, 4038.
Formation of Carbon Nanofibers M. Endo**+and H.W.Kroto*J Department of Engineering, Shinshu University, Nagano, Japan, and School of Chemistry and Molecular Sciences, University of Sussex, Brighton BNl 9QJ, U.K. (Received: March 16, 1992)
Recently 3-1 50-nm-diameter carbon fibers have been discovered which appear to grow spontaneously by deposition from carbon vapor. It is proposed that these structures may be giant fullerenes which have grown by direct insertion into the graphitic network of smaller carbon species (atoms, ‘linear” chains, monocyclic rings, or even smaller fullerenes) accreted from the vapor phase.
Introduction Carbon fibers have major industrial applications, and their growth mechanism and the factors which control their structure are of major strategic importance. Some fibers, as discussed by Endo,l are known to grow by catalytic intervention of small metal particles which leave hollow cylindrical graphite tubes in their wake. Recently a new type of microscopic carbon fiber has been detected which appears to consist of very small diameter graphite tubes from 3-150 nm in diameter. Iijima2 has published transmission electron microscope (TEM) images of such fibers which appear to grow on the cathode of a fullerene areprocessor similar to that developed by Kratschmer et al.3 Similar structures have also been observed by Endo4 in a carbon fiber generator. The cylinder walls may consist of only a few layers of graphite, 2-5, or as many as 50 or more. Such fibers are an exciting development in submicro/nanometer scale engineering as they may well be the strongest structures so far fabricated. Interestingly these tubes appear to grow spontaneously by accretion of carbon units from carbon vapor at high temperature without the intervention of a catalytic metal p a r t i ~ l e . ~This , ~ suggests that pure carbon structures grow spontaneously by some autocatalytic process. Recently there has been a breakthrough in our understanding the range of structures which can be fabricated solely from an array of sp2carbon atoms. This new perspective is based on the discovery of the f~llerenes,~ their isolation and structural characterization,’v6 and the development of likely mechanisms for their Since the discovery, there have been many studies of the fullerenes,10-’2and, in particular, it has been realized that hollow carbon cage structures may be small with 20-70 atomsI3 or very large with several hundreds to thousands of atoms, as in the case of the giant f ~ l l e r e n e s , ~and J ~ they appear to form spontaneously. F ~ l l e r e n e - 7 0 ~is~an J ~interesting -~ species in this context as it consists of two C30 fullerene-60 hemi-“spheres” connected by a ring of ten extra carbon atoms in the waist. It is clearly possible to add more such rings to produce elongated
’Shinshu University.
*University of Sussex.
0022-3654/92/2096-6941.$03.00/0
tubular fullerenes, and FowlerI6 has discussed various theoretical aspects of these structures. Indeed it is noteworthy that Buckminster Fuller patented related “elongated geodesic dome” structures.17 The fact that carbon can spontaneously nucleate to form fullerenes is fascinating, and possible intermediates in the formation process were discussed soon after they were f o ~ n d . ~ItJ was suggested that an extended sp2 carbon network, involving hexagons and pentagons must form in some way from smaller carbon species (Cn, atoms, chains, and rings), which may close-driven by the energetics involved in dangling bond elimination. If closure occurs, then fullerenes form; if not, then a spiraling graphite sheet7is expected to epitaxially self-wraps itself up to form an onionlike polyhedral graphite microparticle. The quasipolyhedral shapes which the giant fullerenes were found to have8 provided the key to an understanding of the detailed infrastructures of the spheroidal graphite microparticles observed by Iijima in 1980.18J9 The original refined nucleation scheme8recognized that multiple shell closure by (delayed) annealing-resulting in shell entrapment-could be important under certain conditions. However as perfect closure did not appear to be particularly effective in the formation of the spheroidal particles seen originally by Iijima,I8J9the ~ c h e m efocused ~ , ~ mainly on conditions where annealing was not important and explained the interconnected shell infrastructure observed in these particles. Carbon nucleation is complicated, and it is clear that the range of species produced depends critically on the temperature, pressure, nucleation time, and, in particular, the homogeneity of the physico/chemical environment as well as the intrinsic equilibrium of the nucleating system. (Note: In the case of carbon fiber growth, especially if attached to a surface, inhomogeneities will give rise to anisotropic growth. Under some gas-phase conditions, only small radicals form;20under others, microparticles form;l8J9and under yet other conditions, closure to form fullerenes may be the dominant process?1 Nanoscale fiber formation2y4appears to be yet another facet of carbon’s apparently limitless synthetic engineering capability, and the purpose of this paper is to draw attention to the fact that 0 1992 American Chemical Society
