J . Phys. Chem. 1984, 88, 2595-2599 actions of the type considered here, more realistic potentials should probably be used, which means that the empirical value of y will probably have to be reevaluated. Second, the success of potential VI,,suggests that some mixing in of the charge-transfer surface is occurring in these reactions and that the resulting polarity in the transition state is the reason for the correlation of radical ionization potentials with rate constants. Additional evidence to
2595
support this conclusion is presented in the following paper.17 Acknowledgment. We thank the National Science Foundation for support ofthis work under grants C H E 78-23867 and C H E 81-20834. Registry No. 1-Propyl, 2143-61-5; 2-propy1, 2025-55-0; oxygen, 7782-44-7.
Rates of Reaction of Alkyl Radicals with Ozone R. Paltenghi, E. A. Ogryzlo,? and Kyle D. Bayes* Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90024 (Received: September 16, 1983)
The rate constants for a series of alkyl radicals reacting with ozone have been measured at 298 K and 2 torr by using a cm3 molecule-' s-l) are 2.53 photoionization mass spectrometer. The radical (R) + ozone rate constants (in units of 0.54 for CH3, 25.3 5.8 for C2H5,24.4 f 5.9 for l-C3H7,46.5 f 10.6 for 2-C3H7, and 54.5 f 11.4 for t-C4H,. As was observed for the R + O2reactions, the R + O3reactions show a trend of increasing rate constant kl with decreasing ionization potential (IP) of the radical. When log ( k , ) vs. IP(R) - EA(Oz or 0,) is plotted, where EA represents electron affinity, the two families of rate constants are brought into close proximity (Figure 1). In addition, rate constants for fluorescence quenching of substituted benzenes by O2are cited which extend the log ( k ) vs. IP - EA plot to lower ionization potential. Adiabatic channel model calculations have been done by using a long-range potential resulting from the perturbation between and R + O3surfaces. These calculations give good agreement with the experimental cross sections (Figure the R+ + 0,2) and they predict rate constants faster than those derived from the classical harpoon model at low IP - EA.
*
*
Introduction Rate constants have been measured for the reaction of several alkyl radicals with ozone in the gas phase. Except for previous studies of the CH3 O3 reaction,' there have been no other measurements of alkyl radical-ozone rate constants. In the present work, the radicals were formed by laser flash photolysis and their concentation was followed as a function of time by using a photoionization mass spectrometer. The variation of the rate constants with radical structure is closely analogous to that observed for Some possible these same alkyl radicals reacting with 02.2,3 reasons for this unexpected trend are discussed below. Radicals are thought to be formed as intermediates during the reaction of ozone with The fate of these radicals depends on the ratio of 03/02 in the ambient gas and the respective rate constants. The measurements reported below suggest that any alkyl radicals formed in ozone-olefin mixtures will react primarily ratio is greater than 0.1 or the total with Oz, unless the 03/02 pressure is very low.
+
Description of Experiment The experimental system has been described previously1a*6and will be discussed only briefly here. Radical precursor molecules were transported in a flow system with 2 torr of H e carrier gas into a cylindrical reaction cell of about 50-cm3 volume. Inside the cell, the precursors were subjected to dissociating radiation at 193 nm from an A r F exciplex laser (Lumonics T E 261-2). Typically, an alkyl radical was generated from photolysis of the corresponding nitroalkane except for tert-butyl, which was made by dissociating 2,4,4-trimethyl-l-pentene.A 0.2 mm diameter pinhole in the rear window of the cell allowed a small fraction of the cell contents to escape into a high-vacuum region where the radicals were photoionized by vacuum-ultraviolet radiation from rare gas resonance Methyl radicals were ionized with a Kr lamp (MgF2 window) and the other radicals were ionized with a Xe lamp (sapphire window). The ions were mass selected with a quadrupole mass filter (Extranuclear 270-9) and Permanent address: Department of Chemistry, University of British Columbia, Vancouver, British Columbia, V6T 1W5, Canada.
detected with a Daly electrode? scintillator, and photomultiplier. The ion counts were accumulated and stored on a multichannel analyzer (Canberra 8 100) for later analysis by computer. The ozone was prepared by using a commercial ozonizer (Welsbach Style T-23) and trapped on silica gel at 196 K.I0 After the O2 was pumped off from the silica gel, the O3was allowed to expand into a 10-L bulb, diluted with He, and stirred by convection to give a homogeneous mixture. Before the ozone entered the reaction cell, its concentration was measured by absorption at 253.7 nm with a low-pressure H g lamp (Pen Ray), 254-nm interference filter, and photomultiplier. The O3 cross section at 253.7 nm was taken to be 1.157 X cm2/molecule.11 The pressure of the reactant ozone mixture was measured with a capacitance manometer (MKS type 77) and converted to absolute concentration by using the absorption data and separate flow calibrations. Typically 100-1000 laser flashes were necessary to accumulate enough radical signal for analysis. The laser intensity was kept sufficiently low so that radical-radical reactions were negligible. The radical decay was then a composite of reaction with 03, (1) (a) E. A. Ogryzlo, R. Paltenghi, and K. D. Bayes, Znt. J. Chem. Kinet., 13, 667 (1981); (b) R. Simonaitis and J. Heicklen, J . Phys. Chem., 79,298 (1975); (c) N. Washida, H. Akimoto, and M. Okuda, J . Chem. Phys., 73, 1673 (1980). (2) R. P. Ruiz and K. D. Bayes, J . Phys. Chem., preceding paper in this
issue. (3) T.M. Lenhardt, C. E. McDade, and K. D. Bayes, J . Chem. Phys., 72, 304 (1980). (4) F. J. Rik6czi and H. H. Gunthard, Chem. Phys. Lett., 67,173 (1979). (5) R. Atkinson, B. J. Finlayson, and J. N. Pitts, Jr., J . Am. Chem. SOC., 95. 7592 (1973). '(6) R. N. Pdtenghi, Ph.D. Thesis, University of California, Los Angeles, CA, 1982. (7) R. Gorden, Jr., R. E. Rebbert, and P. Ausloos, "Rare Gas Resonance Lamps", US.Department of Commerce, Washington, DC, 1969, NES Tech. Note (US.) No. 496. (8) H. Okabe, J . Opt. SOC.Am., 54, 478 (1964). (9) N. R. Daly, Rev. Sci. Instrum., 31, 264 (1960). (10) G. A. Cook, A. D. Kiffer, C. V. Klump, A. H. Malik, and L.A. Spence, Ada Chem. Ser., 21, 44 (1959). (11) W. B. DeMore and 0. Raper, J. Phys. Chem., 68, 412 (1964).
0022-3654/84/2088-2595$01.50/00 1984 American Chemical Society
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The Journal of Physical Chemistry, Vol. 88, No. 12, 1984
Paltenghi et al.
TABLE I: Radical + Ozone Rate Constants’ kl/(lO-LZcm3 radical T/K molecule-I s-l) CH3 243 f 4 2.11 & 0.39b 298 & 2 2.53 f 0.54b 2.82 f O S l b 341 f 3 384 f 4 2.83 f 0.4gb C2HS 298 f 2 25.3 f 5.8 1-c3H7 298 f 2 24.4 5.9 46.5 & 10.6 2-C3H7 298 & 2 t-C4Hg 298 f 2 54.5 f 11.4
*
‘Typical conditions were 2 torr of He, 0.01 torr of precursor, and sufficient ozone to give radical decay rates of 50-200 s-l. bThese rate constants are derived from previous work.15 reaction with 02,pumpout, and a small amount of wall reaction. The radical signal was fitted to a simple exponential of the form S = Soexp(-t/T)
0
+ SI
by using a least-squares fitting technique.12 The original O$He mixture contained some O2which gradually increased due to the thermal decomposition of O3to 02.Consequently, the radical decays contained a contribution from the R + O2reaction. Since [O,] varied with [ O , ] ,each value from the least-squares fit was corrected by subtracting k 2 [ 0 2 ] , where k2 is the R + O2rate c o n ~ t a n t and ~ ~ ~[O,] J ~ is the oxygen concentration for that particular decay. The correction was insignificant for the CH3 0,reaction and ranged from 5% to 40% for the other radicals. The corrected values of 1 / r were then plotted as a function of 0,number density. All rate constants were determined from a weighted leastsquares fit to the [ O , ] , 1/7 data.12*14In practice, since errors , was plotted as the in [ O , ] were larger than errors in 1 / ~ [O,] dependent variable with the ozone concentration errors used as weighting factors. The slopes obtained from the weighted least-squares fit were than inverted to give the bimolecular rate constants shown in Table I. The experimental uncertainties reported for the R 0,rate constants consist of the random statistical error in the [O,] vs. 1/7 plot obtained from Student’s t test and 90% confidence limits, the estimated absolute error in [O,],and the error in the product k z [ 0 2 ]used to correct 1 / for ~ reaction with 02.These were combined by using a standard propagation of errors treatment12 to yield the total uncertainty shown in Table I.
+
+
Discussion Comparison of Rate Constants. There are no previous rate constants for the reaction of alkyl radicals with ozone with which to compare the current values, except for the case of CH3 + O,, which has been discussed previously.la The rate constants for R + 0,show the same trend as that observed for R 0,; methyl ozone is the slowest and tert-butyl + ozone is the fastest. Comparing a given radical reacting with 0,or with 02, the ozone reactions are faster by factors of 1.3-5. The rate constant for tert-butyl ozone is very fast for a reaction between two polyatomic molecules. The rate constant of 5.4 X IO-” cm3 molecule-1 s-l corresponds to an effective cross section of 11 A2. For comparison, the ozone-isobutene reaction
+
+
+
(1 2) P. R. Bevington, ‘Data Reduction and Error Analysis for the Physical Sciences”, McGraw-Hill, New York, 1969. (13) I. C. Plumb and K. R. Ryan, Int. J . Chem. Kinet., 13,1011 (1981). (14) R. L. Scott, private communication. (15) The methyl radical rate constants represent revised calculations of measurements reported previously.1a This downward revision of approximately 4% resulted from a correction for the pressure drop along the flow tube between the reaction cell and the manometer. The expressions given in ref la should be revised as follows:
* 1.6) X k = (2.5 * 1.3) X
k = (5.1
exp((-210
A
* 84)/T)
cm3 moleculed
(T/300)0~68*0.37 cm3 molecule-’
s-I
s-l
4
2
8
6
(IP - E A)/eV
Figure 1. Rate constants plotted as a function of IP - EA. The circles ( 0 )represent R + OZ?the triangles (A)represent R O3 (this work), and the squares (m) are rate constants for quenching of fluorescence from substituted benzenes by O2.*O
+
is much slower, having a preexponential factor of only 3.2 X cm3 molecule-’ s-I.l6 Evidently, the radical-ozone reactions must have little or no activation energy and the transition states must be loose to explain such large rate constants. The close similarity between the R O3 and R 0,rate constants can be seen in Figure 1, where In ( k ) is plotted vs. IP(R) - E A ( 0 3 or 0 2 ) . When available, the vertical IP’s have been ~ s e d . ’ ~ J *By use of IP - EA, rather than just IP, the two sets of rate constants can be brought into close proximity. While the R O3rate constants do not vary as smoothly with I P - EA as do those of R + 02, the similar trend observed in Figure 1 suggests that the same mechanism is operating in the two sets of reactions.lg A third family of rate constants have been placed in Figure 1, namely, those for the fluorescence quenching of substituted The first excited singlet states of these benzenes benzenes by 02.20 are analogous to free radicals since for each of them there is a single loosely bound electron. The ionization potential of an electronically excited benzene is calculated from the IP of the ground state minus the electronic excitation energy. The rate constants for fluorescence quenching tend to be larger than those for either R 0,or R 0,although there is some overlap with the latter. Clearly, the fluorescence quenching rate constants extend the trend observed with the radical rate constants to lower ionization potential. Harpoon Model. The good correlation between In (k) and IP - EA invites comparison with the classical harpoon mode1.21,22 For this simple model, the interaction potential between molecules A B is assumed to be very small until they approach to within a distance r,, which is the distance at which the Coulomb attraction between A+ B- just equals IP(A) - EA(B). At distances shorter than r, the Coulomb potential drops below the potential curve for neutral A B. Since the Coulomb curve is very attractive, the harpoon model assumes that every collision for which the impact
+
+
+
+
+
+
+ +
(16) R. E. Huie and J. T Herron, Int. J . Chem. Kinel., Symp. 1, 165 (1975). (17) F. A. Houle and J. L. Beauchamp, J . Am. Chem. SOC.,101, 4067 (1979). (18) H. M. Rosenstock, K. Draxl, B. W. Steiner, and J. T. Herron, J. Phys. Chem. Re$ Data, 6, Suppl. 1 (1977). (19) A similar trend in reactivity with changing electron affinity has been
noted for reactions of sodium atoms with various chlorinated molecules; K. R. Wilson and D. R. Herschbach, Nature (London), 208, 182 (1965). (20) R. G. Brown and D. Phillips, J. Chem. SOC.,Faraday Trans. 2, 70, 630 (1974). (21) J. L. Magee, J . Chem. Phys., 8, 687 (1940). (22) R.D. Levine and R. B. Bernstein, ”Molecular Reactions Dynamics”, Oxford University Press, Oxford, 1974.
The Journal of Physical Chemistry, Vol. 88, No. 12, 1984 2597
Rates of Reaction of Alkyl Radicals with Ozone
(IP-E A)/eV
k-I = ( k T / h ) Q * / Q c
(4)
where h is Planck‘s constant, Qc is the partition function for the R03 molecule, and Q* is the partition function for the transition state. Expression 4 is combined with that for the equilibrium constant to give eq 5. In this expression, QA and QB are partition
ki = ( kT / h)(Q*/ QAQB) exp(-AEoe / k r )
(5)
functions of the reactants, R and 03,all referenced to their individual vibrationless states, and AEoe is the change in internal and products energy for the reaction with both reactants (R + 0,) (RO,) in their standard states at 0 K. As will be seen below, it is not necessary to know a numerical value for AEoe in order to apply the ACM to calculate k l . The partition functions in eq 5 could be calculaied if one knew the vibrational frequencies and geometries of R, O,, and the transition state. Since these are not known, a series of approximations are used to evaluate the Qs. The total partition functions are assumed to be factorable in the usual way
Q = (qtr/V)qelqw
Figure 2. Reactive cross sections as a function of log [(IP - EA)/eV]-2. The symbols used for the three sets of reactions are identified in the caption of Figure 1. The cross sections predicted by the classical harpoon model are shown by the dashed straight line. The solid and hyphenated curves are calculated by using the adiabatic channel model with the potential given by eq 16.
parameter is less than r, results in a reaction. Thus, the cross section becomes u
= rrr2 = rr[e2/(IP - EA)I2
(2)
The effective cross sections for the radical reactions have been calculated by dividing the experimental rate constants by the average relative velocity. u =
k1(~~/8kT)’/’
(3)
In eq 3 k is the reduced mass of the collision complex, k is Boltzmann’s constant, and Tis the absolute temperature. The cross sections are plotted on a logarithmic scale in Figure 2 against log [(IP - EA)-2]. The form of this plot is such that the harpoon model gives a straight line as is shown. Both the R + O3and the R O2cross sections are seen to be well below the harpoon cross sectigns, but they appear to approach the harpoon model for small IP - EA. The fluorescence quenching cross sections shown in Figure 2 are comparable to or slightly above those of the harpoon model. Clearly, the simple harpoon model does not have the flexibility necessary to fit the range of cross sections shown in Figure 2. However, the good correlation between u and IP - EA suggests some common mechanism for these three families of reactions. If there is a common mechanism, then it should be capable of giving both large cross sections at low I P - EA and small cross sections at high IP - EA. The adiabatic channel model with an appropriate long-range potential is capable of rationalizing the behavior shown in Figure 2. Adiabatic Channel Model Theory. The rate constants for the R + 0, reactions were modeled by using a modified form of the adiabatic channel model (ACM) proposed by Quack and T r ~ e . ~ , As originally outlined, the ACM calculates a unimolecular rate constant; for the present reactions, this would be the rate constant, k-l, for the thermal decomposition of the hypothetical RO, molecule.
+
The ACM starts with a transition-state theory expression for k-l: (23) M. Quack and J. Troe, Eer. Eunsenges. Phys. Chem., 81,329 (1977).
(6)
where the subscripts tr, el, and rv refer to translation, electronic, and rotation-vibration, and Vis the volume. To evaluate the position of the transition state, the simplified form of the ACM sets up the electronic and rotation-vibration partition functions of the collision complex to be functions of the reaction coordinate r, here taken to be the distance between the radical carbon atom and the nearest oxygen atom in ozone. Then the transition state is located by using the criterion of a maximum in the free energy, or equivalently, a minimum in the value of the partition function of the collision complex, Q(r). The transition state is identified with the qinimum in the function
f ( r ) = In ( k T / h ) + In ( Q ( r ) )- In
(QAQB)
- AEoe/kT
(7)
The translational partition functions in eq 7 can be combined to give (qtr/V)C/[(qtr/V)A(qtr/V)BI
= h 3 / ( 2 r r k k r ) 3 / 2 (8)
Similarly, combining the electronic partition functions in eq 7 gives
(qel)C/ [(qel)A(qel)B]= gC/(gAgB) exP(-V’(r)/kr)
(9)
where the g’s represent electronic degeneracies and V’(r) is the potential energy function for the reaction coordinate, referenced to zero at the vibrationless state of the R 0 3 molecule. For the present case, the degeneracy of ozone is one, and those of R and R 0 3 are both assumed to be two so that these terms cancel out in eq 9. When the potential energy, V’(r),is combined with the AEoe in eq 7, the result is V(r) = V’(r)
+ AEoe
-
(10)
-
and now V(r)is the potential energy of interaction between R and O3referenced to zero for the separated products, i.e., V(r) 0 as r a. By using V(r)rather than the usual V’(r) we emphasize that it is only the long-range potential between R and O3 that determines the rate of recombination; the overall depth of the potential well is not a critical parameter except as it influences the long-range potential. This point is important for the present calculations since the bond strength of the hypothetical R 0 3 molecule is not known. The rotation-vibration partition functions are approximated by using the methods of Quack and T r ~ e . ~Two , of the rotational degrees of freedom of the colliding R + 0,are assigned to a pseudodiatomic molecule with a rotational partition function of the form
qcent(r)= 8rrZkTpr2/h2
(1 1)
where r,, the distance between the centers of mass of R and 03, is approximated by the expression
r? = A
+ Br + r2
(12)
The constants A and B are determined by average geometries and
2598
The Journal of Physical Chemistry, Vol. 88, No. 12, I984
Paltengbi et al.
TABLE II: Parameters Used in the Adiabatic Channel Model Calculations for R parameter CH3 C2Hs ASe/ (cal/ (mol K) 1 -36 -37 A(HTe - Hoe)/(kcal/mol) -1.61 -1.21 A/A2 1.234 0.309 0.804 0.804 B/A -7.62 -8.33 W IP/eV 9.84 8.51
+ Osu 1-C3H7 -38 -1.28 0.588 0.804 -8.68 8.10
2-C3H7 -36 -1.19 1.234 0.804 -7.98 7.69
t-C4H, -34 -1.18 1.234 0.804 -6.92 6.92
"Parameters that were common to all calculations include A 9 = -58 kcal/mol, w = 1050 cm-', and p = 2.42 A-'. The electron affinity of ozone was taken to be 2.14 eV. The ionization potentials listed are the vertical IP, except for 1-C3H7.l7*'* the law of cosinesa6 The remaining rotational and vibrational degrees of freedom are accommodated by using the overall change in thermodynamic properties for the reaction. It is assumed that the dependence of the logarithm of the partition function on the reaction coordinate is of the form W e x ~ ( - y ( r - re)) where y is an empirical parameter that Quack and Troe have evaluated to be 0.75 A-1, and W is given by the expression w = - In (qcent(re1) + In 11 - exp(-w/kT)l + In [gC/(g&B)] + a e / R - A ( H T ~ Hoe)/RT + 1.5 In (p/amu) + 2.5 In (T/K) - 3.665 (13)
TABLE III: Comprison of Calculated and Experimental Rate Constants for R 03" Morse potential radical Potentialb from ea 16 exptl
In this equation, qcent(re)is given by evaluating eq 11 at r = re, the equilibrium C-O distance in the R 0 3 molecule, and the A on the thermodynamic properties is to be taken in the sense (R03) minus (R 0 3 ) . Following the approximations of Quack and Troe, the final form of eq 7 is
(H = 0.124 eV), the results shown in the middle column of Table I11 are obtained. The rationalization for this type of potential has been given in the preceding paper.2 The calculated rate constants now reproduce the observed trend of kl with radical I P and they differ from the experimental values by an average factor of 1.6. This same potential was successful in ACM calculations for the R O2reactions, although with a diffetent value for the perturbation parameter, H. The dominant parameter in these ACM calculations is the long-range potential between the radical and 0, or 02.This can be shown by selecting the parameters for the 2-propyl + O3 reaction and using a potential of the form of eq 16, but treating I P - EA as a continuous variable. When this is done, the solid curve shown in Figure 2 is generated. As can be seen, this calculation gives a reasonable fit to all of the R + O3rate constants. A similar calculation was done for the R + O2 family by using the parameters for 2-C3H7, but again treating IP - EA as a continuous variable; the result is shown as a hyphenated curve in Figure 2 and is seen to represent well the observed trend of rate constants. For comparison, the cross sections predicted by the classical harpoon model are indicated in Figure 2 by the dashed straight line. One interesting result of the ACM calculations can be seen in Figure 2. At small IP - EA, the ACM cross sections rise above the harpoon model cross sections. Such supraharpoon cross sections are known experimentally. Most of the quenching cross sections for the substituted benzenes shown in Figure 2 are larger than those predicted by the harpoon model. Similarly, cross sections for alkali metal atoms reacting with halogen molecules are consistently ~upraharpoon:~as are those for metastable rare gas atoms reacting with halogens.28 These latter two families of experimental rate constants would fall close to the ACM curves shown in Figure 2. Supraharpoon cross sections can be understood by considering the form of the potential used. As a result of the perturbation between the Coulomb curve of R+ 03-and the neutral curve of R 03,the latter becomes attractive at distances larger than the classical crossing point. Consequently, the transition state for the reaction occurs a t distances larger than the classical crossing, resulting in a larger cross section. Thus, by recognition of the extended nature of the perturbation between the two curves, cross sections larger than those derived from the classical harpoon model are predicted. This mechanism has been called the "orbiting
+
f(4 = In (kT/h)
- V(r)/kT
Wexp(-y(r
+ In
(C7ce"tW)
+
- re)) - 1.5 In (2r&T/h2) (14)
After choosing a form for the potential, V(r), and assigning values for the quantities that make up W, one minimizesflr) to give the ACM value for In (kl). Adiabatic Channel Model Calculations. The choice of parameters for the R + O3reactions is not straightforward because the R 0 3 molecules are not known experimentally. We have approximated the properties of R 0 3 by the known or estimated properties of the corresponding alkyl nitrite, RONO. The values selected for AS', A(HTe- Hoe), and other parameters are collected in Table 11. The choice of a function to represent the long-range potential, V(r), is somewhat arbitrary. The original ACM used a Morse potential V(r) = De(-2 exp(-@(r - re)) exp(-2@(r - re))) (15) where De is the total well depth (=-AEoe + w/2) and @ is a parameter related to the C-0 bond force c o n ~ t a n t . ~ "On ~ ~ the basis of the corresponding values for RONO, we have used uniform values of 58 kcal/mol for De, 2.42 A-' for @, and 1.44 A for re. Using the Morse potential in eq 14 together with the parameters in Table I1 results in the calculated rate constants shown in the first column of Table 111. When compared to the experimental rate constants in the last column of Table 111, the ACM rate constants calculated with the Morse potential are too large by factors of 3-100. More importantly, the calculated rate constants show no evidence of the observed trend of kl with radical IP. A similar failure was noted when the Morse potential was used to model the R O2 reactions.* If a potential of the form V(r) = -@/[(IP - EA) - e2/r] #/(IP - EA) (16)
+
+
+
is used in eq 14 and the parameter H varied to give the best agreement between calculated and experimental rate constants laboe, D. Jones, and E. R. Lippincott, Spectrochim. Acta, Part
+
CH3 C2HS 1-C3H7 2.C3I-f~ t-C,H,
25 17 15 17 19
0.34 1.2 1.5 5.0 14
0.25 2.5 2.4 4.7 5.5
"All rate constants given in units of lo-" cm3 molecule-' s-'. bEquation 15.
+
+
+
(27) J. Maya and P. Davidovits, J . Chem. Phys., 61, 1082 (1974). (28) J. E. Velazco, J. H. Mots, and D. W. Setser, J . Chem. Phys., 69,4357 (1978).
J. Phys. Chem. 1984,88, 2599-2605 collision curve crossing" mechanism (ref 28 and references therein). However, the adiabatic channel model with the potential given in eq 16 extends the orbiting collision curve crossing model by incorporating the change in internal degrees of freedom during the reaction (the term in eq 14 involving W). It is this additional term that allows the adiabatic channel model to predict much smaller cross sections when the transition state occurs at smaller internuclear distance. Equation 16 is a gross simplification of the real long-range potential of a neutral pair perturbed by a Coulomb curve. It neglects normal chemical bonding and van der Waals forces (this is a particularly serious failing for the slower reactions). The perturbation integral H is treated as a constant when it should be a function of the distance between the two molecules.29 Attempts to calculate H as a function of r have been confined to diatomic interaction^.^^,^^ More realistic potential functions are needed for polyatomic systems of the type studied above. The success of eq 16 in fitting the R O3and R + O2rate constants suggests that the perturbation between the neutral and Coulomb surfaces should be a significant factor in these long-range potentials, even for pairs of reactants that do not have large cross sections.
+
(29) R. Grice and D. R. Herschbach, Mol. Phys., 27, 159 (1974). (30) R. K. Janev and A. Salin, J . Phys. B, 5, 177 (1972).
2599
Conclusions In this paper we have reported the first measurements of rate constants for ozone reacting with alkyl radicals larger than methyl. The bimolecular R O3reactions are closely analogous to the high-pressure R O2reactions in that both show a definite trend of increasing rate constant with decreasing radical ionization potential. When In ( k ) vs. I P - EA is plotted, the two sets of rate constants become close neighbors (Figure 1). The adiabatic channel model with a simple long-range potential involving IP - EA is capable of reproducing the experimental rate constants for both R O3and R 02.At low IP - EA this model merges with the orbiting collision curve crossing model, giving cross sections that are larger than those calculated from the classical harpoon model. At high IP - EA, the adiabatic channel model has the versatility to give smaller cross sections for those reactions with tight transition states. Clearly, more work is needed to develop suitable and realistic long-range potentials between polyatomic molecules.
+
+
+
+
Acknowledgment. This work was supported by the National Science Foundation under grants CHE-7823867 and CHE8120834. E.A.O. received financial assistance from the National Science and Engineering Research Council. Registry No. CH3, 2229-07-4; CzHS,2025-56-1; l-C&, 2-C3H7, 2025-55-0; t-C,H,, 1605-73-8.
2143-61-5;
Ordered Forms of Dianionic Guanosine 5'-Monophosphate with Na+ as the Structure Director. 'H and 3iP NMR Studies of Hydrogen Bonding and Comparisons of Stacked Tetramer and Stacked Dimer Models Judith A. Walmsley,t Richard C. Barr, Elene Bouhoutsos-Brown, and Thomas J. Pinnavaia* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 (Received: December 14, 1982; In Final Form: December 8, 1983)
The ordered forms of the guanosine 5'-monophosphate dianion in the presence of Na+ as the structure-directing cation (Na+/S'-GMP = 2.0) have been investigated in H 2 0 solution by 'H NMR spectroscopy. The resonances assigned to H-bonded N(1)H (11.1-11.3 ppm) and N(2)H (8.8-10.4 ppm) in the ordered nucleotide have normalized intensities of 0.96 i 0.12 and 1.1 i 0.1 protons per ordered 5'-GMP, respectively. This results is compatible with the interbase H-bonding scheme expected for planar tetramer units (I) and supports the proposal that the ordered forms are isomeric octamers formed by stacking of tetramer units. An additional resonance at 7.69 ppm has been assigned on the basis of chemical shift, line width, and spin saturation transfer results to a ribose OH involved in extratetramer H bonding. The normalized intensity of the ribose OH proton (0.33 & 0.06) is equal within experimental uncertainty to the normalized intensity of an unusually high-field line at 2.2 ppm in the 31PNMR spectrum (0.30 & 0.06), suggesting that a phosphte oxygen on an adjacent tetramer may be acting as the hydrogen acceptor. Several plausible alternatives for the extratetramer H bond also are discussed. Finally, the merits of the stacked tetramer model are shown to be superior to those of a recently proposed stacked asymmetric dimer model when the two models are compared in light of all the relevant data.
Introduction Nucleosides and nucleotides containing guanine exhibit aggregation phenomena distinctly different from those containing other nucleic acid bases. One manifestation of these differences is the ability of guanosine and guanosine monophosphate (GMP) to form pH-dependent ordered structures.' In weakly acidic solution (pH 5), guanosine monophosphates form anisotropic gels similar to those formed by guanine nucleosides in the presence of certain electrolytes.2 However, in neutral or slightly basic solution where guanosine monophosphtes exist as dianions, soluble ordered aggregates have been ~ b s e r v e d . ~ Several models have been proposed for the solution The favored models involve coaxial stacking of two or more tetramer units (I) formed by hydrogen bonding between donor
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Present address: Department of Chemistry, The University of Toledo, Toledo. OH.
0022-3654/84/2088-2599$01.50/0
positions N(1)H and N(2)H and the acceptor positions O(6) and N(7).'*13 Extensive stacking of tetramer units is known to occur in the gel structures of guanine nucleoside^'^ and nucleotide^,'^ (1) Guschlbauer, W. Jerusalem Symp. Quantum Chem. Biochem. 1972, 4, 297, and references therein. (2) Chantot, J. F.; Guschlbauer, W. Jerusalem Symp. Quantum Chem. Biochem. 1972 4 , 205. (3) Miles, H. T.; Frazier, J. Biochem. Biophys. Res. Commun. 1972, 49, 199. (4) Pinnavaia, T. J.; Miles, H. T.; Becker, E. D. J. Am. Chem. SOC.1975, 97, 7198. (5) Pinnavaia, T. J.; Marshall, C. L.; Mettler, C. M.; Fisk, C. L.; Miles, H. T.; Becker, E. D. J . Am. SOC.1978, 100, 3625. (6) Paris, A.; Laszlo, P. C.R. Hebd. Seances Arad. Sci.,Ser. C. 1978, 286, 717. (7) Borzo, M.; Laszlo, P. C.R. Hebd. Seances Acad. Sei, Ser. C 1978, 287, 415. (8) Paris, A.; Laszlo, P. Am. Chem. SOC.Symp. Ser. 1976, 34, 418. (9) Petersen, S. B.; Led. J. J.; Johnston, E. R.; Grant, D. M. J. Am. Chem. SOC.1982, 104, 5007.
0 1984 American Chemical Society
