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(14) M. S. Spencer, unpublished.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