J . Phys. Chem. 1990, 94, 3226-3221
3226 50
66
TABLE VI: d Spacings and Relative Growth Rates
27
s
-7
w
l9
c) 115
Figure 6. Fractional charges, X103.
In addition to the unit cell and symmetry information, this method requires atomic coordinates, partial charges, and van der Waals interaction parameters. Fractional charges on each atom in the molecule were calculated by using MNDO'O and are given in Figure 6. A 6-12 function was used to describe the van der Waals interactions, with parameters taken from Hopfinger." Calculations were carried out using the program P C L E M C . ' ~ All molecules within 40 A of the central molecule were included in the calculations; increasing this distance did not increase the lattice energy significantly. The total lattice energy was -39.14 kcal mol-', of which the electrostatic contribution was 8%. Attachment energies were calculated for the eight sets of faces with the largest d spacings. Relative growth rates were obtained by dividing the calculated attachment energy for each face by the attachment energy of the slowest growing (01 1) face. The results are given in Table VI, and Figure 5d shows the resulting predicted morphology prepared by using SHAPE.' Five of the forms are present.
Discussion This single-crystal structure determination, carried out on a crystal grown from racemic solution, shows unequivocally that 1 forms a racemic mixture. This suggests that an economic separation of isomers based on crystallization is possible. There are no strong intermolecular bonds in the structure. Two weak electrostatic bonding interactions have been highlighted: a (IO) Dewar, M. J . S.; Thiel, W. J . Am. Chem. SOC.1977, 99, 4899. ( 1 1 ) Hopfinger, A. J . Conformational Properties of Macromolecules; Academic Press: New York, 1973; p 47. (12) Docherty, R.; Roberts, K . J. Comput. Phys. Commun., in press.
face
d(hkl), 8,
(01 1)" (002)* (012) (020) (l0l)Q ( 1 10) (111)
11.157 9.827 7.956 6.776 5.562 5.331 5.145 5.145
(iii)
relative nrowth rate molecular mechanics Donnay-Harker 1 .OOOb 1.oooc 1.1356 1.121c I ,124' 1.402 1.647 1.298 1 .467e 2.006b 2.093b 1.623' 2.169 1.696 1.696 2.169
Face appears in experimental morphology (Figure 5b). Face appears in Donnay-Harker predicted morphology (Figure 5c). e Face appears in molecular mechanics predicted morphology (Figure 5d).
C-H-0 hydrogen bond and an edge-to-face aromatic interaction. Neither of these is allowed for explicitly in the molecular mechanics calculations. The theoretical morphology predicted by the Donnay-Harker method is in good agreement with experiment, except that the predicted { 110) faces do not appear. This is consistent with the absence of strong intermolecular interactions in this structure. The theoretical morphology predicted by the molecular mechanics methods is in broad agreement with the observed morphology, but the { 110) and (012)faces are not observed, and the predicted morphology is shorter in the a direction. This suggests that this method underestimates the strength of the accumulation of intermolecular interactions in the a direction, possibly because the weak edge-to-face electrostatic interactions are not calculated explicitly. The polar { 1 1 I ) and {TIT)faces, which are not related by symmetry, are predicted to have the same relative growth rates. This is a consequence of the prediction method used, which introduces a center of symmetry which is not present in this structure. Neither form is present in the observed morphology, so the chiral nature of the internal crystal structure is not apparent in the external crystal morphology. Thus, while a seeded crystallization separation process is feasible, it is not possible to separate these optical isomers by hand-sorting individual crystals. Acknowledgment. The authors thank J. B. Nelson, McCrone Research Ltd., London, for assistance with the optical goniometry, J. Kendrick, IC1 plc, for running MNDO, and K. J. Roberts, University of Strathclyde, for assistance with the computer programs. Registry No. I , 9033 1-90- I .
COMMENTS Comments on Cyclopentadlenyl Compound Thermochemistry Sir: Cyclopentadienyl ligands not only form interesting or-
ganometallic sandwich compounds, such as ferrocene, but also can give rise to partially unsaturated, reactive intermediates by virtue of strong polydentate bonding to the remaining sites. Thus, the thermochemistry involving this radical in neutral and ionic compounds and reactions is important in describing this chemistry. This Comment is an attempt to clarify this situation regarding the heat of formation of the cyclopentadienyl radical (Cp) and some of its implications. There are three fairly recent determinations of the cyclo0022-3654/90/2094-3226$02.50/0
pentadienyl heat of formation, aside from appearance potential derivations, which tend to be inaccurate. McMillen and Golden' in their review reanalyze the iodination study of Furuyama et al.* in light of Trenwith's observation3 to recommend a value of 58 f 1.5 kcal/mol. The ion cyclotron resonance (ICR)gas-phase basicity bracketing study of DeFrees et al! gives 63 2 kcal/mol.
*
( I ) McMillen, D. F.; Golden, D. M. Annu. Rev. Phys. Chem. 1982, 33, 493. (2) Furuyama, S.; Golden, D. M.; Benson, S. W. Int. J . Chem. Kinet. 1971. 3, 237. (3) Trenwith, A. B. J . Chem. SOC., Faraday Trans. 1 1980, 76, 266. (4) DeFrees, D. J.; Mclver, R. T.; Hehre, W. J. J . Am. Chem. SOC.1980, 102. 3334.
0 1990 American Chemical Society
J . Phys. Chem. 1990, 94, 3227-3228 ICR equilibrium measurements of cyclopentadiene a ~ i d i t y , ~ coupled with an electron affinity determination6 for cyclopentadienyl radical, produce a radical heat of formation of 61 f 2 kcal/mol. Telnio and Rabinovich’ give a lower value of 50 kcal/mol. It is this latter value that is quoted and used by Connors in his review of organometallic thermochemistry and, subsequently, used and propagated in discussing related bond energetics and This Comment presents arguments for the higher value of lHf029s (Cp,g) and revises the related values given previously. From the rate constant for I + c-C5H, HI C5H5,2and a reverse activation energy of 3 kcal for the slightly exothermic reverse (see ref 3 as applied to pentadiene), one obtains the 58 kcal/mol heat of formation. This gives a resonance stabilization energy for cyclopentadienyl of 2 1 kcal/mol, slightly above the value of 19 kcal/mol for pentadienyl itself, as expected according to ref I . The low value of ref 7 would contend that the iodination reaction above is exothermic, contradicting the observations of ref 2. It also gives a resonance stabilization energy more than double that of the simple allyl system and unrealistically high given the cyclic alkene systems discussed in ref 1. One might also argue that the 3-5 kcal higher ICR values lead to a RSE of 16-18 kcal/mol, which seems too low, but this is less conclusive. The ICR techniques also possess some weaknesses: The difficulty to exactly discern between exo- and endothermic reactions and the uncertainty concerning the values of the proton affinities of the reference bases lower its degree of accuracy. In this connection, we remark that the “bracketing” ICR results for many radicals (allyl, cycloheptatrienyl) are a few kilocalories per mole larger than with other method^.^ The equilibrium results5 are probably more accurate. Thus we adopt, pending future measurements, a value of 58 f 2 kcal/mol for the 298 K cyclopentadienyl heat of formation. The adoption of this value will then raise the “average bond dissociation enthalpy” for cyclopentadienyl compounds given in ref 8 by 8 kcal/mol. The energy required to remove both ligands from the metallocene sandwich compounds is 16 kcal greater than previously stated as a result. Particularly, the dissociation threshold of ferrocene into two radicals and atomic iron occurs at 6.9 eV. This reduces the maximum available energy of translation during the multiphoton dissociation of ferrocene.” This higher threshold accounts for the paucity of two-photon dissociation to atoms at 351 nmIo (3.5 eV) and the lack of atom production at 193 nm I 2 (6.4 eV). In ref 9 we reported a first bond dissociation energy of 91.4 kcal/mol for ferrocene from a pyrolysis measurement. Using the above cyclopentadienyl heat of formation, the second bond dissociation energy, D(Fe-Cp), becomes 67 kcal/mol rather than the value of 51 kcal/mol originally reported9 via the thermochemistry given in ref 8. The use of a more recent determination of the gas-phase heat of formation of ferroceneI3 gives a 68 kcal/mol second bond energy. This also has implications for ion-molecule chemistry and thermodynamics. The absolute heats of formation of FeCp cation and anion, and thus the thermodynamics of their dissociations and ion-molecule reactions, will be similarly affected. One example of a chemical consequence is that the dissociative attachment reaction FeCp + e- Fe + Cp- considered in ref 9 is endothermic
-
+
-
(5) Bartmess, J. E.; Scott, J. A.; Mclver, R. T. J . Am. Chem. SOC.1979, 101, 6046. Cumming, J. B.: Kebarle, P. Can. J . Chem. 1978, 56, 1. (6) Engelking, P. C.; Lineberger, W. C. J . Chem. Phys. 1977, 67, 1412. (7) Telnoi, V. I.: Rabinovich, I. B. Tr. Khim. Khim. Tecknol. Corky 1972, 2, 12: Russ. Chem. Rec. 1977,46,689, translated from Usp. Khim. 1977,46,
3227
by 26 rather than IO kcal/mol if 1.78 eV for the Cp electron affinity6 is used, and need no longer be considered. Another example concerns the low Fe cation appearance potential measured by electron impact ionization, 14.1 eV,I4 and photoionization, 13.5 eV.I5 These do not agree with our calculated 14.8-eV threshold for Fe+ formation reactions, FeCp, + e- Fe+ + 2Cp + 2e-. Therefore, the difference between Fe and FeCp cation appearance potentials, reported as low as 0.3 eV,I5 cannot be used to calculate D(Fe+-Cp). It is evident that a larger value must exist to explain the stability and the abundance of the FeCp+ cation in the ferrocene mass spectrum as claimed by Flesch et a1.I6 Effectively, a lower limit for this dissociation energy has been assigned by using the ICR technique by Jacobson and Freiser.” It is 2.8 eV with the use of the adopted heat of Cp formation.”*’* This result indicated that, in the ferrocene cation, it would require about 5 eV to remove the first ligand and 3 eV the second. This is much more comparable with the situation in the neutral species where 4 eV is necessary to remove the first ligand and 3 eV the second.
-
Acknowledgment. We thank one of the reviewers for bringing additional ICR results to our attention. Part of this work at SRI was supported by the U S . Department of Energy, Office of Basic Energy Sciences. Registry No. Cp, 2143-53-5; ferrocene, 102-54-5. (14) Puttemans, J. P.; Hanson, A. Ing. Chim. (Brussels) 1971, 53, 17. (15) Bar, R.; Heinis, Th.; Nager, Ch.; Junger, M. Chem. Phys. Lett. 1982, 91, 440. (16) Flesch, G . D.; Junk, G.A.; Svec, H. J. J . Chem. Soc., Dalton Trans. 1971, 1102. (17) Jacobson, D.B.; Freiser, B. S. J. A m . Chem. SOC.1984, 106, 3900.
(18) Hettich, R. L.; Jackson, T. C.; Stanko, E. M.; Freiser, B. S. J . Am. Chem. SOC.1986, 108, 5086.
CERIA-IIF-IMC Avenue Eniile Gryzon. I B- I070 Brussels, Belgium
J. P. Puttemans
Department of Chemical Kinetics, Chemistry Laboratory SRI International Menlo Park, California 94025
G. P. Smith* D. M. Golden
Received: August I O , 1989; In Final Form: January 19, I990
Electronegativity: The Relationship of Its Equalization and Its Weighted Harmonic Mean Sir: The usefulness of the weighted harmonic mean electronegativity xwbl in describing high-T, superconductors has recently been discussed.l This mean is given’ by m
xWH
= n[E(wi/~i)l-’ i= 1
(1)
where n is the total number of atoms in the formula unit, wi is the number of these atoms of type i with electronegativity xieach, and the summation is over the m types of atoms ( n = CzIwi). As noted earlier,2 the harmonic mean (not weighted harmonic mean) electronegativity that leads to eq 1 may be obtained, in the case of a diatomic system AB, from the expression for the equilibrium electronegativity xeq, namely
1327. (8) Connor, J . A. Top. Curr. Chem. 1977, 71, 71. (9) Lewis, K. E.; Smith, G.P. J . A m . Chem. SOC.1984, 106, 4650. (IO) Liou, H. T.; Ono,Y.; Engelking, P. C.; Moseley, J. T. J . Phys. Chem. 1986, 90, 2888. ( I I ) Liou, H. T.; Engelking, P. C.; Ono,Y.; Moseley, J. T. J. Chem. Phys. 1989, 90, 2892. (12) Ray, U.; Hon, H. Q.;Zhang, Z.; Schwarz, W.; Vernon, M. J . Chem. Phys. 1989, 90, 4248. (13) Chipperfield, J. R.; Sned, J. C. R.; Webster, D. E. J. Orgunomef. Chem. 1979, 178, 171. See also: Puttemans, J. P. Ing. Chim.(Brussels) 1983, 65. 95.
by assuming that the ratio y of the hardness 7 to the electronegativity x is constant, that is, by assuming that y = ( q r ) / x A ) = ( v B / x B ) . Equation 2 itself follows2 from the minimization of the molecular energy, taken as a sum of atomic energies each ( I ) Ichikawa, S. J. Phys. Chem. 1989, 93, 7302. (2) Wilson, M. S.;Ichikawa, S. J. Phys. Chem. 1989, 93, 3087.
0022-3654/90/2094-3227$02.50/0 0 1990 American Chemical Society
