J . Phys. Chem. 1984,88, 1047-1048
as well as Ti-0 bonds, thus explaining both the “wetting” and spread of a near monolayer and indeed the formation of a reduced titanium oxide phase in the presence of a few ppm of water. Two ways of forming this surface layer of a reduced titanium oxide under HTR have been proposed. Hydrogen spillover from the Pt leads to a partial reduction of adjacent TiOz, followed by the “wetting” and spread of a reduced Ti oxide film across the surface of the Pt Alternatively, as Tauster et al.’ pointed out, the formation of bimetallic &/Ti crystallites is possible under HTR and this provides” a route for the transport of Ti from the support to the surface of the Pt crystallite. Although simple criteria suggest that surface segregation of Ti should occur on &/Ti crystallites in vacuo, segregation calc~lations’~ indicate that this is improbable. However, similar calc~lations’~ also show that the presence of a few ppm of water in conventional HTR is sufficient to cause oxidation of any Ti atom in the Pt surface and the adsorbed oxygen then causes extensive segregation of Ti, giving a surface layer of reduced titanium oxide. From equilibrium and diffusion calculation^'^ the same processes are possible under LTR but are too slow to give any detectable SMSI effects. The presence of a mobile “flux” of K2Ti03under LTR would promote the formation of a similar Ti oxide layer to that produced under HTR. Only low concentrations of potassium would be needed for this mechanism and once a steady-state reduced titanium oxide layer had been formed on all Pt crystallites, no further change in chemisorption properties would be seen on further K addition. This is also in agreement with Chen and White’s results. As Cairns et al.I3 have shown, oxygen attacks the surface layer of reduced titanium oxide to re-form crystallites of Ti02, which do not “wet” the platinum surface, so allowing the SMSI inhibition to be reversed. However, several recycles through the SMSI state lead to gross deposition of Ti02on the platinum surface and give permanent deactivation.15 The high activityI6 of Ti02-supported metals after HTR for hydrocarbon formation from CO/Hz is probably due to similar oxidation of the Ti-0 surface layer by water produced in the initial stages of reactions and consequent reversal of SMSI. Registry No. H2.1333-74-0; Pt, 7440-06-4; TiO,, 13463-67-7; K, 7440-09-7. (14) M. S. Spencer, unpublished. (1 5) J. A. Cairns, personal communication. (16) M. A. Vannice and C. C. Turu, J . Cutal., 82, 213 (1983).
M. S. Spencer Imperial Chemical Industries PLC Agricultural Division Billingham. Cleveland TS23 1 LB, England
1047
I, where they report to demonstrate this, is very misleading. In making comparison with experiment, they list the predictions of the algebraic Hamiltonian, where the parameters were optimized to fit the data. They also list, under the heading spectroscopic fit, the predictions of an anharmonic expansion with DarlingDennison coupling. They did not fit the parameters for this Hamiltonian, but chose parameters that had been fit to a different data set! These parameters4 were obtained by fitting (to an accuracy of better than 1 cm-I) transitions to vibrational levels of ozone less than 4027 cm-l. In their table, however, Benjamin et al. only list the predictions of levels above 3200 cm-I, therefore, the excellent agreement for the lower energy levels could not be appreciated. In addition, two closely fit levels above 3200 cm-’ were not listed. The poor agreement found when these parameters were extrapolated to higher energy is not surprising. In order to fairly compare the two Hamiltonians, we have done a least-squares fit of the reported experimental transitions (listed accuracy 10 cm-l) to an anharmonic expansion with both Darling-Dennison and the algebraic coupling. The fits were almost identical, with rms deviations of 7.69 and 7.77 cm-I, respectively. The predicted energy levels were within 1 cm-l of each other. This is not surprising, for the off-diagonal, coupling matrix elements differ by only a few percent for the given energy levels. In contrast, the coupling constants are only determined to approximately 10%. We note that there is a error in the energy listed for the (3,0,4) level in Table I of Benjamin et al. Their listed value is 6987 cm-’ but the correct value, according to ref 3, is 6897 cm-I. We also note that our fitted parameters differ from those listed by Benjamin et al.; their’s gives an rms deviation of 12.7 cm-l. We conclude that the observed ozone spectrum does not recommend the new, algebraic coupling over the traditional, Darling-Dennison coupling. The algebraic coupling has a somewhat more complicated form and is introduced in a purely phenomenological way without theoretical foundation. Occam’s razor dictates against its use unless some compelling evidence for its superiority is given. Acknowledgment. This work was supported by the National Science Foundation. Registry No. Ozone, 10028-15-6. (4) A. B a r k , C. Secroun, and P. Jouve, J. Mol. Spectrosc., 49, 171 (1974).
Kevin K. Lehmann Department of Chemistry Harvard University Cambridge, Massachusetts 021 38 Received: April 26, 1983; In Final Form: May 1 1 , 1983
Received: August 22, 1983: In Final Form: November 3, 1983
Reply to the Comment on “High-Lying Levels of Ozone via an Algebraic Approach” Comment on “Hlgh-Lying Levels of Ozone vla an Algebraic Approach” Sir: In a recent Letter,’ Benjamin, Levine, and Kinsey report an analysis of two coupled oscillators utilizing an algebraic approach. This formalism leads to the conventional anharmonic expansion (wi and Xij),but with a slightly different form for the off-diagonal Darling-Dennison2 coupling. They report that the algebraic coupling does much better than the traditional Darling-Dennison coupling at fitting the recently observed, high overtone states of ozoneS3 However, their Table (1) I. Benjamin, R. D. Levine, and J. L. Kinsey, J . Phys. Chem., 87, 727 (1983). (2) B. T. Darling and D. M. Dennison, Pfiys. Rec., 57, 128 (1940). (3) D. G . Imre, J. L. Kinsey, R. W. Field, and D. H. Katayama, J . Pfiys. Cfiem., 86, 2564 (1983).
0022-3654/84/2088-1047$01.50/0
Sir: The algebraic approach provides a Hamiltonian whose exact eigenvalues can be computed and compared to the observed spectrum. Such comparisons have now been carried out for the high vibrational states of 03,HCN, and HzO. The advantages of the algebraic approach are that, on the one hand, exact eigenvalues (rather than an anharmonic expansion) can be obtained and, on the other, it can be interpreted in terms of a potential function. Our results’ for the high-lying vibrational energy levels of ozone (and of other molecules such as HCN2 or H203) are the exact (1) I. Benjamin, R. D. Levine, and J . L. Kinsey, J . Phys. Cfiem., 87, 727
(19x31 \ - _ _ _ .
( 2 ) 0.s. van Roosmalen, F. Iachello, R. D. Levine, and A. E. L. Dieprink,
J . Cfiem. Pfiys., 79, 2515 (1983). (3) I. Benjamin and R. D. Levine, Cfiem. Pfiys. Lett., 101, 518 (1983).
0 1984 American Chemical Society
1048 The Journal of Physical Chemistry, Vol. 88, No. 5, 1984
eigenvalues of a Hamiltonian. While not discussed in our Letter,' we also generate the corresponding wave functions. Also not discussed therein is the interpretation of the algebraic Hamiltonian in geometrical terms4 Another feature of interest is the prediction2 of bound vibrational states above the nominal dissociation energy. The density of such states does decline, however, with increasing energy. In his Comment, Lehmann5 notes that by using a phenomenological anharmonic expansion formula plus a Darling-Dennison correction term6 he can equally well fit the observed7 high-lying states of ozone. However, his formalism results from an expansion retaining different orders in perturbation theory for different terms of the Hamiltoniane6 We have also compared our results with such an expansion using parameters derived in a study of a potential function for ozone.* The use of the parameters of ref 8 (4) 0. S. van Roosmalen, R. D. Levine, and A. E. L. Dieprink, Chem. Phys. Letf., 101, 512 (1983). ( 5 ) K. K. Lehmann, J . Phys. Chem., preceding comment in this issue. (6) B. T. Darling and D. M.Dennison, Phys. Rev., 57, 128 (1940). (7) D. G. Imre, J. L.Kinsey, R . W. Field, and D. H. Katayama, J. Phys. Chem., 86, 2564 (1982).
Additions and Corrections is explicitly mentioned in our work. The purpose of our Letter was to draw attention to the capabilities of the algebraic approach. We provided a Hamiltonian9 whose eigenvalues fit the observed spectrum (rms deviation 7.9 cm-' vs. experimental accuracy of f 1 O cm-I). Registry No. Ozone, 10028-15-6. ( 8 ) A. Barbe, C. Secroun, and P. Jouve, J. Mol. Spectrosc., 49, 171 (1974). (9) In the notation of ref 1 the parameters are wp = 1054.99 cm-I, wp = 1108.43 cm-l, N , = 92, N, = 197, x = -4.75, and y = -30.1 cm-I. Note indeed that there is a misprint in Table I of ref 1 and that the observed energy value for the (3,0,4) level is 6897 cm-'. Also the sign of x should be negative.
I. Benjamin R. D. Levine* The Fritz Haber Molecular Dynamics Research Center The Hebrew University Jerusalem 91 904, Israel Receiued: October 1 , 1983
ADDITIONS AND CORRECTIONS 1983, Volume 87
P. H. Wine* and D. H. Semmes: Kinetics of C1(2PJ) Reactions with the Chloroethanes CH3CH2C1,CH3CHC12,CH2ClCH2Cl, and CH2C1CHCl2. Page 3575. The parameters K and /3 in eq 9 are improperly defined. Equation 9 should read [c1(2PJ)]f - ( K [c1(2pJ)10
-
+ Xl)eXI' - ( K + X2)e"' XI
- A2
(9)
where
K = kj[CI,]
+ k k + k,[RHCl] + k ,
XI = 0.5{(a2- 4@)'12- a)
h2 = -0.5{(a* - 4P)'/2
= ki[RHCl]
+ a)
+ K + k7
P. H. Wine* and D. H. Semmes: Kinetics of C1(2PJ) Reactions with the Chloroethanes CH,CH2C1, CH3CHC12,CH2ClCH2CI, and CH2CICHCI2.
