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, 1327. (8) Connor, J . A. Top. Curr. Chem. 1977, 71, 71. (9) Lewis, K. E.; Smith, G.P. J . Am. 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.
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. Am. 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
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
3228 The Journal of Physical Chemistry, Vol. 94, No. 7 , I990 varying quadratically with the number of electrons on the atom, subject to the constraint of a fixed total number of electrons. We wish to point out that eq 1 may similarly be derived from in an alternate the general expression for xepgiven earlier by form involving electronic chemical potentials 1.1 = -x for systems of arbitrary size n, stoichiometry {wi),and net charge Q . In lchikawa's notation our earlier result (eq 9 of ref 3) may be written
Comments where Qi = Q; is the difference between the charge Qi on atom i which minimizes the molecular energy for fixed total Q and the charge Q: which minimizes the atomic energy for variable atomic charge; the latter charge6 is simply - x / v = - l / ~ , so that the assumption of constant y i is equivalent to the assumption of constant Q?. If the total charge Q is not zero, but y is still taken as a constant, then xq is given by
(3)
Equation 3 was obtained3 by a generalization of that used2 by Wilson and lchikawa to obtain eq 2, namely, an energy minimization procedure in which p = -x is the Lagrange multiplierS associated with the constraint of a constant number of electrons N = -Q, where N is taken relative to the electron number No for a neutral species. Equation 1 now follows readily from the general expression eq 3 provided that two assumptions are made, namely, that Q = 0 and that y is constant for all atom types in the compound. Equation 3 may also be written3 as m
xeq
m
= [ E w i ( Q i- Q i O ) l / [ C ( w i / ~ i ) l i= I
I=
I
(4)
where x W ~ O is xWHfrom eq 1 for a neutral system ( Q = 0), so that the variation of xq with Q has an explicit dependence on the value taken for y. Otherwise, eq 5 is a simple extension of eq 1.
In conclusion, we have demonstrated how the weighted harmonic mean electronegativity xWHmay be obtained from the chemical potential 1.1 = -xq for a system of arbitrary charge and stoichiometry. Note. The addressed author is in agreement with this Comment. ~
(3) Lohr, L. L. Int. J . Quantum Chem. 1984, 25, 211. (4) For extensions to the protonic counterpart of electronegativity, see: (a) Lohr, L. L.J . Phys. Chem. 1984,88, 5569. (b) Lohr, L. L. Nobel Laureate Symposium on Applied Quantum Chemistry, PACCHEM84, Honolulu, HI; Smith, V . H., Ed.; D. Reidel: Dordrecht, 1986; pp 223-230. (c) Lohr, L. L. Int. J . Quanrum Chem., Quanrum Chem. Symp. 1986, 19, 731. (5) This association of fi with -x is based on the assumption that the energy is a quadratic function of the charge and hence that the electronegativity is a linear function of the charge.
~~
~
(6). A reference charge state, usually but not necessarily neutral, is assumed in defining x and 7 for each atom type.
Department of Chemistry Unicersity of Michigan Ann Arbor. Michigan 48109
Lawrence L. Lohr
Received: Nooember 21, 1989
