J . Phys. Chem. 1984, 88, 5221-5225
(H2
-
S
2H.
-+
H2S)
Conclusion Thus, our discussion based on various experimental results has shown that R u 0 2 on the n-type semiconductor works as a hydrogen-evolution catalyst in the water-splitting reaction and in any type of photocatalytic reaction in which hydrogen is evolved. Even in the oxygen-evolution reaction using a strong electron
5221
acceptor like Fe3+and Ag', it becomes a reduction site. Addition of a small amount of R u 0 2 or Pt seems to improve the efficiency of the charge separation at the metal/semiconductor interface. An excess amount of R u 0 2 on T i 0 2 suppresses the efficiency of photocatalytic reactions due to the property of R u 0 2 as a recombination center. Registry No. Ru02, 12036-10-1; Ti02, 13463-67-7; CdS, 1306-23-6; H,, 1333-74-0; 02, 7782-44-7; H,O, 7732-18-5; EtOH, 64-17-5; Pd, 7440-05-3; Pt, 7440-06-4; Ag, 7440-22-4; Fe, 7439-89-6.
Vibrational Energy-Transfer Probabilities of Highly Excited 1,1,2,2-Tetrafluorocyclopropane G . Arbilla, J. C. Ferrero,* and E. H. Staricco Instituto de Investigaciones en Fisicoquimica de C6rdoba (INFIQC), Departamento de F h c o Quimica, Facultad de Ciencias Quimicas, Universidad Nacional de G r d o b a , Sucursal 16, Casilla de Correo 61, 501 6 C6rdoba. Reptiblica Argentina (Received: April 10, 1984)
The collisional deactivation of tetrafluorocyclopropane produced with an average excitation energy of about 87 kcal/mol was studied at 300 K with five different bath gases (He, Ar, C02, CF4, and C2F6). The activated molecule is obtained by reaction of CH2(lAI)with C2F4and undergoes unimolecular decomposition to CF2and CF2CH2in competition with collisional deactivation. The relative measurement of both processes provides a convenient way of monitoring the collisional energy loss. Data obtained over a wide range of pressures permitted the assignment of the mean energy transferred per collision, ( AE)d, and the form of the transition probability distribution. For He and Ar the ( AE), values are 2.1 and 4 kcal/mol, respectively, and follow an exponential deactivation model. The plyatomic gases are more efficient, with (m)dvalues ranging from 5 to 10 kcal/mol and stepladder transition probabilities. Compared to other molecules, tetrafluorocyclopropane seems to be more easily deactivated. Several factors affecting the energy removal are analyzed.
Introduction In a previous work' we characterized the decomposition of highly vibrationally excited 1,1,2,2-tetrafluorocyclopropane(TFC), with an average excitation energy of about 87 kcal/mol, i.e. 39 kcal/mol above the critical energy for unimolecular reaction. The activated molecule was produced by reaction of CH2('A1) with C2F4, which acted as the bath gas. The competition between unimolecular decomposition and collisional deactivation was used to model the energy-transfer process and obtain information on the amount of energy removed per collision by the cold bath gas (C2F4). In fact, most of the data available at present on energy transfer at high energies come from this kind of work, which, if the unimolecular reaction is well characterized, provides a convenient way of studying the intermolecular energy-transfer process.2 These are reactive systems, and the activated molecule, initially produced in a rather narrow energy range, undergoes unimolecular reaction from different excited vibrational states, which are populated through the collisional cascade down to the critical energy for reaction. At adequate low pressure, this results in a dependence of k,, the unimolecular rate constant, with pressure, which is also dependent on the nature of the collider. Typically, a curvature in the plot of k, vs. pressure appears, as a consequence of the opportunities of reaction or the number of down steps in the cascade deactivation. In other words, the degree of curvature depends on the efficiency of the bath gas in removing the energy in excess of the critical energy. In general, the energy loss per collision increases with the number of atoms in the deactivating bath gas m ~ l e c u l e . ~Also, ~ ~ the energy-transfer ( I ) Arbilla, G.; Ferrero, J. C.; Staricco, E. H. J . Phys. Chem. 1983, 87, 3906. (2) Tardy, D. C.; Rabinovitch, B. S. Chem. Rev. 1977, 77, 369. (3) Marcoux, P. J.; Setser, D. W. J . Phys. Chem. 1978, 82, 97.
probabilities for the less efficient gases are well described by a model in which small step sizes are more probable than large step sizes (exponential model), while more complex molecules obey well a simple stepladder model, in which a particular down transition is much more probable than others. The nature of the activated molecule seems also to play a role, and in this sense Carr has shown that the amount of energy removed per collision, ( AE)d, has an inverse dependence with the number of atoms of the activated molecule; Le., smaller molecules are more easily deactivated than larger ones, when compared under the same experimental conditions.5 This is what the statistical theories on energy transfer predict and is related to the density of states of the collisional c o m p l e ~ . ~Thus, .~ if one compares deactivation of different molecules with the same bath gas, the energy transfer process will be governed by the density of states of the activated molecule, as has been invoked to account for the different behavior of CH2DCH2Cland CHD2CD2Br.8 Also, CF3CH is deactivated less easily than CH3CH2For CH2FCH2F,3,9 which have lower densities of states. Recently, two different techniques were reported which provide a direct measurement of the collisional loss of energy.4 In one of them,4a a pronounced dependence of ( AE)don the excitation energy was found, and in both reports the values were substantially lower than those obtained in experiments that rely (4) (a) Rossi, M. J.; Pladziewicz, J. R.; Barker, J. R. J . Chem. Phys. 1983, 78, 6695. (b) Hippler, H.; Troe, J.; Wendelken, H. J. J . Chem. Phys. 1983, 78, 6709. (c) Hippler, H.; Luther, K.; Troe, J.; Wendelken, H. J. J . Chem Phys. 1983, 79, 239. (5) Carr Jr., R. W. Chem. Phys. Lett. 1980, 74, 437. (6) Lin, Y . N.; Rabinovitch, B. S.J . Phys. Chem. 1970, 74, 3151. (7) Bhattacharjee, R. C.; Forst, W. Chem. Phys. 1978, 30, 217. (8) Nguyen, T. T.; King, K. D.; Gilbert, R. G. J . Phys. Chem. 1983,87, 494. (9) Richmond, G.; Setser, D. W. J. Phys. Chem. 1980, 84, 2699.
0022-3654/84/2088-5221$01.50/00 1984 American Chemical Society
5222 The Journal of Physical Chemistry, Vol. 88, No. 22, 1984
Arbilla et al.
on a comparison with unimolecular rate constants. However, the molecules studied with these techniques, azulene, toluene, and substituted cycloheptatrienes, are rather complex and the ( m ) d values do not deviate much from the general trend reported by Carr.’ It seems, then, that the properties of the molecules that facilitate the flow of energy to the transitional modes of the collisional complex are not well understood at present, partly because the theories on these processes are not developed enough and partly because more experimental data are necessary, mainly on different kinds of activated molecules. In our previous work we found ( AE)d = 9 kcal/mol for C2F4 as deactivating gas. This is a rather large value, and more information on the deactivation of TFC by different colliders seems desirable. We now report the characterization of the deactivation process of TFC by monoatomic and small polyatomic gases. The results show an increase in (A,?), with the number of atoms, and by comparison with other results in the literature, TFC seems to be more easily deactivated than other molecules. Experimental Section Materials. Ketene and C2F4 were obtained, as described previously,’ by the pyrolysis of acetic anhydride and polymeric C2F4, respectively. Both reactants were carefully distilled at low temperatures, C2F4 was also purified by gas chromatography on an alumina column followed by further purification on a silica gel column. The inert gases were commercially available. They were purified by trap-to-trap distillation, and their purity was verified by gas chromatographic analysis. He and Ar were passed through pyrogallol, concentrated H2S04,and a trap cooled with liquid nitrogen before storage. Apparatus and Procedure. The experiments were performed in a greaseless high-vacuum system. Pressure was measured with a capacitance manometer (MKS Baratron 220 B). The pressures of ketene and C2F4 were measured in a calibrated reservoir of 16.43 cm3 and transferred to the reaction vessel by condensation in liquid N2. Oxygen was added by expansion from a calibrated volume. The desired amount of inert gas was introduced into the reaction vessel by condensation in liquid N2 (C2F6,CF4, C 0 2 ) or by expansion from a known volume (Ar, He). The partial pressure of inert gas was such that contribution to collisions by other species was negligible. The reactant ratio was CH2CO:C2F4:02= 1:16:1.3, and the following bath gas/C2F4 ratios were used, on a collisional basis: C2F6:CzF4= 30:1, CF4:C2F4= 30:1, C02:CzF4= llO:l, He:C2F4= 150:1, Ar:C2F4 = 150:l. The CF4 experiments at pressures higher than 1500 torr were made with a ratio CF4:C2F4= 50: 1. Runs were performed in Pyrex vessels with calibrated volumes varying from 1.01 to 500 cm3. All of them were previously seasoned to obtain reproducible results. The samples were photolyzed at room temperature with a 500-W high-pressure mercury lamp. Reaction time varied from 20 s to 15 min., depending on the conditions of the experiment. In every case the conversioa was kept lower than 2%. Analysis of the reaction products was carried out by gas chromatography. The procedure was described in detail previously.’ Experimental Results Photolysis of ketene in the presence of C2F4 results in the production of CH,CF2 and 1,1,2,2-tetrafluorocyclopropane,as the products of interest. For the present purposes, the important reaction steps are the following: CH2CO hv CH2 C O (1)
+
CH2(’AI) TFC*
+
-+
+ C2F4
-+
TFC*
(2)
-% CH2=CF2 + CF2
(3)
I
I
I
I
I I I I I
103
I
I I I U
1
loo0 PRESSURE,Torr
Figure 1. Experimental rate constants ( k , = P ( D / S ) vs. pressure for 1,1,2,2-tetrafluorocycIopropane.The curves are the least-squares fit from eq 6: (0) C P 6 , ( 0 )CF,, (v)COz.
10
I
I
I
I
1
l
l
l
l
5000
1000 PRESSURE, Torr
Figure 2. Experimental rate constants ( k , = P(CF,CH,/TFC)) vs. pressure for 1,1,2,2-tetrafluorocyclopropane. The curves are the leastsquares fit from eq 6 : (A)He, (+) Ar. can decompose to yield CH2CF2(D)or, by collisions with M, stabilize to TFC (S). From the measurement of the D / S ratio, the apparent unimolecular rate constant for decomposition, k,, can be obtained through the following equations:
k , = ( D / S ) w , s-l
or k , = ( D / S ) P , torr
(4)
where w is the collision frequency and P the total pressure.I0 The experimental results, m a wide pressure range, are shown in Figures 1 and 2, for the different bath gases used. Clearly,
(5) In this mechanism TFC* indicates a chemically activated molecule of TFC and M represents a collider molecule. TFC*
(10) (a) Forst, W. “Theory of Unimolecular Reactions”; Academic Press: New York, 1973. (b) Robinson, P. J.; Holbrook, K. A. “Unirnolecular Reactions”; Wiley-Interscience: London, 1972.
kdM)
TFC*+M-TFC+M CH2(3Bl) + 0
2
+
CO, C02, H2, HzO,
...
rhe Journal of Physical Chemistry, Vol. 88, No. 22, 1984 5223
Energy-Transfer Probabilities of Highly Excited TFC TABLE I: Lennard-Jones Parameters molecule TFC C2F4
He Ar
co2
cF4
C2F6
A
dk, K
4.74 4.14 2.57 3.41 4.47 3.23 4.10 4.40 4.65 3.63 4.81 5.19
187 157 10.8 119 188 134 134 166 229 155 155 201 283
u,
6.25
10-7kM, torr-'
s-I
0.85 1.50 0.91 1.96 0.69" 0.88 0.94 1.07 0.70° 0.86 1.03 1.36
ref 1 1 12 12 12 11 11 4b 3 11 11 4b 3
OThese values represent the best fit.
k , depends on the bath gas pressure, which is indicative of a multistep collisional deactivation process. It is evident from these plots that the limiting high-pressure region could not be reached, even at a pressure of about 7000 torr. This is unfortunate as the value of k , is especially important in modeling the deactivation process and in calculating the relative collisional efficiency of bath gases. Then, k , had to be calculated by regression analy~is.~ The experimental points were computer fit to a polynomial where Po = k,". In this way k," could be obtained for the different bath gases, with the exception of He. In this case, the limited pressure range accessible and rate constants too far from the limiting high-pressure region precluded a satisfactory extrapolation. In order to obtain k , in units of s-l it is necessary to evaluate the bimolecular collision frequency, w , as the product of collision number kM and pressure. The collision number is calculated from the collision diameter and the Lennard-Jones constants. For TFC these values were used as estimated in ref 1, while for the bath gases they were obtained from the literature. However, one main difficulty arises because of the various values reported in different works for CF, and C2F6.3,49'1The selection of these parameters directly affects the calculated value of k , (in s-l) and alters the estimation of Eminand ( A E ) , . As a consequence, calculations were made with the different values of kM in order to determine the effect on ( A,!?),. The calculated collision numbers for the different bath gases and the Lennard-Jones parameters are shown in Table I and were used as reported by Hirschfelder, Curtis, and Bird12 except for CF4 and C2F6. Assignment of Collisional Deactivation Models The computation of the RRKM rate constant at a specific energy, kE, requires the selection of a model for the activated complex, the calculation of the density of vibrational states of the molecule, and the total number of states of activated complex.I0 This was made by direct count, with a seven-frequency model, up to 10 kcal/mol and by the Haarhoff approximation thereafter. The grain size in most of the calculations was 1 kcal/mol, but for the exponential deactivation model lower values were used when required. The vibrational frequencies for the activated complex were the same as before' and selected to fit the experimental Arrhenius parameters (log k = 15.28 - 48480/(4.5767')).13 The critical energy for decomposition was calculated to be Eo = 46.3 kcal/mol. The decomposition to stabilization ratio, D / S , was computed from the matrix f o r m ~ l a t i o n ' ~ D / S = (l/w)C[k(I
-
P
+ k/w)-'fl,
I
(11) Ireton, R. C.; Rabinovitch, B. S.J . Phys. Chem. 1974, 78, 1979.
S/D
Figure 3. Effect of the calculated kM upon ( A E ) d for CF4 and C2F6.The parameters were taken from the following: (0)CF4, ref 11; ( 0 )CF4, ref 11; ( 8 )CF4, ref 4b; ( 0 )CF4, ref 3; (0)C2F6, ref 11; ( 0 ) C2F6ref 11; (El) C2F6, ref 4b; (m) C2F6,ref 3.
where k is a diagonal matrix with elements k,, I is the unit matrix, P is a matrix with elements Pi,, and f is a vector with elements f(E),the energy distribution function of TFC. The collisional transition probabilities, Pi,, require the selection of a model for the deactivation process. In this work they were calculated with both the stepladder and the exponential deactivation models. In the stepladder model the elements Pij are defined as
P.. = 1.0 - Pji 1J Pi, = 0
for i - j = ( A E ) , for i - j # ( A E ) ,
while for the exponential model
Pij =
c exp(-AE/
(AE)d)
( A E ) , is the average down energy transferred per collision, and AE is the energy difference between Ei and E,. The conditions of detailed balance, Pij/Pji = (gi(gj) exp(-(Ei - E , ) / k T ) , and completeness, C P i j = 1.0, were imposed on the calculations. The distribution function of TFC* was calculated as before, with a model for the reverse of reaction 2, assuming that reactants are in thermal equilibrium.1° Thus, no excess energy of reacting C H 2 is ~0nsidered.l~The average energy of TFC* is given by ( E ) = Emin (Eth),where (Eth),the average thermal energy, is computed from the distribution function mentioned above and Emin is the critical energy for the reverse of the activation process, assuming that Eo for the latter step is zero. With Emin= 85 kcal/mol, ( E ) = 87.4 kcal/mol, as calculated before.' With these values, calculations were performed with both the stepladder and the exponential deactivation models, for different values of (A@,. Comparison of the computed results with the experimental points requires the change of k , to units of s-'. This is accomplished with the calculation of the collision number for each bath gas, which in the case of CF, and C2F6 is subject to considerable uncertainty. The effect of the calculated k M upon ( A,!?),, for a stepladder model, is shown in Figure 3 for CF, and C2F6and four different sets of Lennard-Jones parameters (Table I). The result is a systematic change of the best fit to the ( A E ) , curves. For C2F6, ( h E ) d varies from 10 to 6 kcal/mol when kMchanges from 0.697 X lo7 to 1.365 X lo7 s-' torr-', and for CF,, ( A E ) , = 8 kcal/mol with kM = 0.69 X lo7 s-' torr-' and (A#!?), = 6 kcal/mol with kM = 1.07 X lo7 s-l torr-'. However, the best fit is obtained with the lower k M for both CF4 and C2F6, and these values are used hereafter. It must be noted that the selection of k Mfor CF4 and C2F6, according to the above consideration, is based on Emin = 85 kcal/mol and the Arrhenius parameters reported by Trot-
+
(12) Hirschfelder, J. 0.;Curtis, C . F.; Bird, R. B. "Molecular Theory of
Gases and Liquids"; Wiley: New York, 1965. A.; Trotman-Dickenson, A. F. J . Chem. SOC. (13) Herbert, F. P.; Kerr, .I. 1965, 5710.
(14) Hoare, M. J . Chem. Phys. 1963, 38, 1630. (15) Simmons, J. W.; Curry, R. Chem. Phys. Lett. 1976, 38, 121.
5224
The Journal of Physical Chemistry, Vol. 88, No. 22, 1984
Arbilla et al.
TABLE 11: High-pressure Rate Constants and ( U )Values , for
1,1,2,2-Tetrafluorocyclopropane
Id'
k,"(exptl)" bath gas C2F4 He
torr 5.88
S-'
5.01
(AE)d,
l0-I0(calcd),b
kcal/mol 9 (SL) 2.1 (Exp) 4 (EXP)
4.89
I $
S-I
23.3
14.29 13.1 12.2 5 (SL) 6.75 C02 3.39 6.65 8 (SL) 5.16 5.30 CF4 7.68 5.08 10 (SL) 4.67 C2F6 7.29 "These rate constants were obtained by regression analysis of the experimental points (see text). Calculated for the transition probabilities models and ( AE)d values indicated, in the high-pressure region. Ar
man-Dickenson, and any change of these may produce a fit with different values of kM affecting the determination of ( h E ) d . To study the effect of the uncertainties of E,, kM,and the Arrhenius parameters on (m)drequired a great deal of computation since any choice of one of these three variables affects the selection of the others. The results of these calculations are presented after considering those which represent the best fit, according to our estimation. The computed results together with the experimental points, obtained with the parameters given above, are presented in Figure 4, for the stepladder (SL) and the exponential (Exp) models. A good fit is obtained, and with Emin= 85 kcal/mol, the ( A E ) d values range from 2.1 to 10 kcal/mol, the lower value corresponding to He and the higher to CzF6. These results are shown in Table 11, where the (AE)d for CzF4 was also included. As expected, the behavior of the inefficient bath gases is represented better by the exponential deactivation model, while the more complex colliders follow the stepladder model. As the main goal of this work was to obtain ( h E ) d for different bath gases, and even though the fit in Figure 4 is remarkably good, the influence of the variations of parameters in the model calculations of ( AE)dwas extensively explored. Regarding the selection of the Lennard-Jones parameters for CF4 and CzF6, the best fit is obtained with the lower kM (Table I) when Emin= 85 kcal/mol and log A = 15.28 and Eo = 46.3 kcal/mol. The ( h E ) d are 10 and 8 kcal/mol for C2F6and CF,, respectively. Changing kM for CF4 and C2F6 resulted in a good fit to the curves computed with the following values: for C2F6 with kM calculated from ref 4b, Emin= 87 kcal/mol and ( = 10 kcal/mol; with k M from ref 11, Emin= 86 kcal/mol and (AE)d= 10 kcal/mol. For CF,, the only good agreement, in addition to the calculations with E~ = 85 kcal/mol, was obtained with kMfrom ref 11 and Emin= 87 kcal/mol, yielding (AE), = 10 kcal/mol. A series of computations with a set of lower values of Arrhenius parameters (log A = 14.6 and Eo = 44.0 kcal/mol) and varying Emin up to 95 kcal/mol did not produce satisfactory results with any value of k,. In this case, the computed results show quite a different curvature than the experimental points. It seems, then, that the uncertainties in kM for CF4 and C2F6 are not so serious as to introduce an error in (AE)dlarger than the error associated with the uncertainties in Eminand the Arrhenius parameters. In fact, Efi, is the variable that more directly affects the determination of (AE)d; Le., either an increase or
Figure 4. Comparison of experimental data with calculations,with E , = 85 kcal/mol: (0) C2F6, ( 0 ) CF4, (V) C02, (+) Ar, (A) He.
decrease in Efinresults in curves that with higher or lower values of ( m ) d produce a reasonably good fit to the experimental results, within certain limits. In the present case, variations of Eminin 1 2 kcal/mol results in an error in ( A E ) , of about 20%.
Discussion The results obtained for the collisional deactivation of highly vibrationally excited TFC agree with earlier works in the sense that monoatomic gases remove less energy than polyatomic molecules and follow an exponential transition probability modeL2 The removal of energy by polyatomic gases is well described by the stepladder model with (aE)dincreasing with the number of atoms in the collider. This effect has been observed in other studies with different excited molecules, and in general, there is a linear correlation between ( m ) d and the number of atoms in the collider m ~ l e c u l e . ~The , ~ most notorious difference in the TFC system is that more energy is removed by the same bath gas in comparison with the case of other activated molecules (Table 111). Note, however, that the ( h E ) d values for TFC are quite similar to those reported for the butyl radical. An explanation to this behavior is not immediate, and several experimental evidences influencing the energy-transfer process have to be considered. In addition to the relation of ( M ) with , the number of atoms in the collider, Carr presented evidence of the importance of the complexity of the activated m o l e c ~ l e .A~ plot of ( A E ) , vs. the number of atoms of the activated molecule shows that the amount of energy transferred decreases with increasing complexity of A*, when compared under the same experimental conditions and with efficient colliders (at least with 10 atoms). Direct comparison of our data for TFC is not feasible because the largest deactivator
TABLE 111: Comparison of ( A E ) d for Various Activated Molecules
bath gas He Ar
co2 cF4
CH,CH2Fn 1.0 (Exp) 2.0 (SL)
CH2FCH2F" 1.0 (Exp) 1.0 (Exp) 2.5 (SL)
4 (EXPI 2.0 (Exp) 5 (SL)
6 (SL)
C2F6
( E ) , kcal/mol Eo, kcal/mol
CH,CF,b 1.0 (Exp)
CH2C1CH2CIc 1.4 (Exp) 4 (EXPI 5 (SL)
TFC
C-C3H6d
2.1 (Exp) 4 (EXPI
4 (EXPI 6 (ExP)
5 (SL) 8 (SL) 10 (SL)
CH3CH2CHCH3e 1.5 (Exp) 2.6 (Exp) 4 (SL, Exp) 8.6 (SL)
91
92.5
102
89
87.4
100
43
57
62
68
60
46.3
62.1
33.0
"The data were taken from the tabulation given in ref 9. bFrom ref 3. CFromref
2 and
9. dFrom ref
2 and 17. eFrom ref 2 and 18.
J . Phys. Chem. 1984,88, 5225-5228
5225
used in this work was C2F6, for which ( A E ) d = 10 kcal/mol. However, an extrapolation of our results to N = 10 yields ( h E ) d = 13 kcal/mol. Although this value falls in the general trend presented by Carr, it is also higher than for C-C& CH3CF3,and CH2FCHzFwhich are molecules of the same or less complexity than TFC. In addition, for the less efficient colliders, our ( h E ) d values are higher (by a factor of -2) than those reported for CH3CF3and CHzFCH2F (see Table 111). In a study on chemically activated l,l-dichlorocyclopropane,I6the deactivation by CH2CC12and C3F8 resulted in values of 7.2 and 14.4 kcal/mol, respectively, which are closer to those for TFC*. Unfortunately, not much attention was given to the energy-transfer process in that work as it was mainly concerned with the chemical aspect. Most of the chemical activation studies on energy transfer are with excitation energies of about 100 kcal/mok5 however, for TFC, ( E ) = 87 kcal/mol. Even though the difference in energy is not large, a possible dependence of the energy-transfer process of ( E ) might be considered. Until recently, most of the data supported an independence of on ( E ) . 2 However, in a study on photoactivated azulene at two different excitation energies (50 and 87.4 kcal/mol), Barker et al. found a pronounced effect of ( E ) , with the large (&)d corresponding to the higher excitation energy.4a If this finding is confirmed, then the effect is just opposite to what one would need to explain the ( h E ) dvalues for TFC. However, azulene in a nonreactive system, and the question remains as to whether the energy-transfer process is also dependent on excitation above the critical energy for reaction or not, as pointed out by Barker. The opposite situation arises from other direct measurements on toluene and substituted cycloheptatrienes in which dependence of was not f o ~ n d . ~In~all , ~these works, ( m ) d values much smaller than expected were reported. Deciding if this is a consequence of the complexity of the molecule or of the experimental technique is speculative at present, and more experimental data seem desirable. However, it must be noted that the measurements of energy loss with these direct methods were performed with rather large excited molecules ( N = 15, 18, 21, and 24) and that the ( h E ) d values, low as they are, seem to fall
in the general trend of the plot given by Carr. Thus, it seems so far, that ( h E ) d depends not only on the bath gas but also, though to a lesser extent, on the nature of the activated molecule and, possibly, the critical energy for unimolecular reaction. This leads to the conclusion that the amount of energy transferred depends on the properties of the collisional complex, in accordance with the predictions of the quasi-statistical theories on energy t r a n ~ f e r . ~Common ,~ to these theories is the central idea of a finite lifetime of the complex, during which the energy is redistributed from the activated molecule into the transitional modes, subject to certain constraints. These theories have been successful in obtaining calculated values in agreement with experiment and predict a dependence of the energy-transfer probabilities with the density of states of the activated m ~ l e c u l e . ~The - ~ difference in the density of vibrational states was used to explain the behavior of CH2DCH2Clas compared with that of CHDzCD2Br,when deactivated by the same bath gas.8 The density of vibrational states of TFC at the average excitation energy is quite large (-9 X 10l2 states/cm-') when compared, for instance, with CF3CH3(-2 X 1Olo states/cm-I). On a statistical basis one would then expect that deactivation of TFC should be more difficult than CF3CH3, with the same collider, at variance with experiment. This reassures our idea that the energy-transfer process depends on the properties of the activated molecule in an indirect fashion through the properties of the collisional complex, which should also be dependent on the interaction potential. In conclusion, the properties of TFC responsible of its behavior in collisional energy transfer cannot be isolated, due to the lack of data on related molecules and to the various factors on which the deactivation process seems to depend, according to the present experimental evidence. We think, however, that the data reported here are valuable as they provide information on a different kind of molecule. Unfortunately, the theories on energy transfer at high levels of excitation are not enough developed, but even at their present state they may provide some insight into these processes. We postpone further considerations and modeling with these theories until the study with more complex gem-difluorocyclopropanes is completed.
(16) Eichler, K.; Heydtmann, H. Int. J . Chem. Kinet. 1981, 13, 1107. (17) Setser, D. W.; Rabinovitch, B. S.; Simons, J. W. J . Chem. Phys. 1964, 40, 1751. (18) Kohlmaier, G. H.; Rabinovitch, B. S.J . Chem. Phys. 1963, 38, 1692.
Acknowledgment. This work was partially supported by CONICET (Argentina) through INFIQC. Registry No. 1,1,2,2-Tetrafluorocyclopropane,3899-7 1-6.
Molecular Structure of CuOH and Cu(OH),-.
An Ab Initio Study
F. Illas,* J. Rubio, Department Quimica Fhica, Facultat de Q u h i c a de Tarragona, Tarragona, Spain
F. Centellas, and J. Virgili Department Quimica Fhica, Facultat de Quimica de Barcelona, Barcelona-28, Spain (Received: April 17, 1984) The geometries of CuOH and CU(OH)~have been optimized at the SCF level with a basis of double { quality. The C, geometry of CuOH is more stable than C ,,, and a C2geometry is predicted for CU(OH)~-; this geometry is like that for H 2 0 2but with the Cu atom lying in the middle of the 0-0 bond. Dissociation energies have been calculated at the SCF and CI levels. While the SCF dissociation of CuOH only accounts for 60% of the experimental value, good agreement between calculated and experimental data is found at the CI level. Introduction Copper(1) hydroxide seems to play an important role in several industrial processes,i-3 as well as in the process of inhibiting
formaldehyde c~ndensation.~Likewise, both CuOH and Cu(0H), (referred to as I and 11) have been postulated as intermediates in the anodic formation of Cu,O. From an electrochemical viewpoint, and depending on the particular technique used, the
(1) Rogic, M. M.; Demmin, T. R. Aspects Mech. Organomel. Chem., [Proc. Symp.] 1978, 141. ( 2 ) Shenai, V. A.; Sharma, K. K. J . Appl. Polym. Sci. 1976, 20, 377.
(3) Takeda, T.; Matsumoto, K.; Nogata, M. Japanese Patent 77 96, 531; C.A. 88/81834s, 1978. (4) Morozov, A. A. Kinet. Katal. 1973, 14, 193.
0022-3654/84/2088-5225$01.50/0
0 1984 American Chemical Society
