A Theoretical and Experimental Study of the CN + NO Association ...

chemistry.emory.edu
  • No tags were found...

A Theoretical and Experimental Study of the CN + NO Association ...

CN + NO Association Reaction J. Phys. Chem. A, Vol. 102, No. 35, 1998 6979Figure 6. Plot of the temperature dependence for the high-pressurelimiting thermal association rate constant. The filled squares denotethe CN vibrational relaxation data of Sims and Smith, 43 the circlesdenote the Troe-based extrapolations of the present work, the crossesand pluses denote the corresponding extrapolations of Sims and Smith, 7and the triangles denote the present RRKM estimates. The lines areprovided as a guide to the eye.experimental data shown in Figures 3 and 4 with the aboveequations using F c ) 0.6 gave rise to the limiting values of k ∞and k 0 , which are summarized in Figures 6 and 7, respectively.For most temperatures, increasing F c by 0.1 yields about a 40%decrease in k ∞ and about a 3% decrease in k 0 . For T ) 207 Ksuch an increase in F c instead yields only an 7% decrease in k ∞and an 18% decrease in k 0 .Also included in Figures 6 and 7 are the extrapolated resultsof Sims and Smith employing similar extrapolation techniques(in which the fitting parameters for the pressure fall-off wereestimated separately). 7 These rate constants and the pressuredependency depicted in Figures 3-5 are compared below withtheoretically predicted results.B. Comparison of Theory and Experiment. The pressuredependence of the theoretically predicted association rateconstants k eff are compared with both the present experimentaldata and the prior experimental data of ref 7 in Figures 3-5,for temperatures of 740, 430, 297, 207, 145, and 102 K. Someof the experimental data of Sims and Smith 7 corresponds to aslightly different temperature from that plotted, but only minorcorrections would be expected. The data of ref 7 and the presentexperimental data are in remarkably good agreement in theregions of their overlap. This agreement provides strong supportfor the accuracy of both sets of data.For each temperature the predicted and observed pressuredependencies are seen to be in satisfactory agreement. Notably,the average energy-transfer parameter 〈∆E〉 down , which providesthis agreement, decreases quite substantially with decreasingtemperature. The best fit values are about -500, -300, -200,-140, -70, and -35 cm -1 for temperatures of 740, 430, 297,207, 145, and 102 K, respectively. A slight increase in 〈∆E〉 downwith increasing temperature is perhaps to be expected giventhe increasing average collision energy. However, the magnitudeof this increase (and of the actual values at the highesttemperatures) are so large as to be suggestive of some failurein the theoretical model, perhaps related to the treatment of theangular momentum dependence of either the dissociation rateconstants or the energy-transfer process. It would be interestingto examine such possibilities in future studies.In Figure 6 a plot of the temperature dependence of the highpressurelimiting rate constant is provided. Consideration ofthe TST values presented therein suggests that the high-pressureFigure 7. Plot of the temperature dependence of the low-pressurelimiting thermal association rate constant. The circles, pluses, andcrosses are as in Figure 6. The filled squares denote the present RRKMestimates employing at each temperature the 〈∆E〉 down value thatprovides the best fit to the observed pressure dependence (cf. Figures3-5).limit is never closely approached in the present experiments.The closest approach is for a temperature of 207 K where theexperimental data at a pressure of 800 Torr is only 2.5 timeslower than the TST estimated high-pressure rate constant. Inthis instance it is difficult to accurately extrapolate the experimentaldata to the high-pressure limit and it is not surprisingthat the experimental extrapolations are not in good agreementwith the theoretical estimates.An alternative indirect experimental measure of the highpressurerate constants is provided by the experiments of Simsand Smith, which probe the rate of vibrational relaxation ofCN in V)1 arising from collisions with NO. 47 This relaxationrate would be expected to correlate quite closely with the rateof complex formation and thus with the high-pressure limitingrate constant. These experimental relaxation rate constants arealso plotted in Figure 6 and are about 40% higher than thetheoretical estimates. This reasonably minor discrepancy againmay be an indication of errors in the treatment of angularmomentum effects for the transition state. Notably, a theoreticalmodel that yields a somewhat greater high-pressure rate constantat the higher temperatures (in agreement with these relaxationrate constants) would also require somewhat smaller energytransferparameters at higher temperatures.The temperature dependence of the various estimates for thelow pressure limiting rate constant is illustrated in Figure 7. Inthis instance, the TST results for the fitted average energytransfercoefficients are seen to be in good agreement with thoseobtained from the present Troe-based extrapolations of theexperimental data. The similar extrapolations of ref 7 predictonly slightly higher rates.V. Concluding RemarksThe good agreement between the present experimental resultsand those of Sims and Smith 7 where the two experiments overlap


6980 J. Phys. Chem. A, Vol. 102, No. 35, 1998 Klippenstein et al.demonstrates the validity of both experiments. The implementationof the Troe factorization method provides an estimatefor the high-pressure rate constant (k ) 6.16 × 10 -7 T -1.50 exp-(-332/T)cm 3 s -1 ), which is essentially identical to that obtainedby Sims and Smith. 7 The expression k ) 3.4 × 10 -10 exp-(120/T)cm 3 s -1 provides a good representation of the transitionstatetheory estimates for the high-pressure rate constant in the207-740 K region.The theoretical study suggests the importance of anharmoniceffects and of the secondary CNNO association channel inyielding a net increase in the density of states by a factor ofabout 2. The variational RRKM results employing a simplemodel potential provide a completely satisfactory descriptionof the experimental results for both the dissociation and theassociation. The agreement for the association results reliesupon fitted values for 〈∆E〉 down that decrease in magnitude from-500 to -35 cm -1 from T ) 740 to 102 K.Acknowledgment. S.J.K. acknowledges the support of thisresearch through NSF Grant CHE-9423725 and through anEmerson fellowship from the Cherry Emerson Center at EmoryUniversity. S.K. and M.C.L. acknowledge the support of thiswork by the Caltech Multidisciplinary University ResearchInitiative under Office of Naval Research Grant No. NOOO14-951-1338. We thank the Cherry Emerson Center for ScientificComputation for the use of computing facilities and variousprograms.References and Notes(1) Melius, C. F. 25th JANNAF Combustion Meeting (Proceedings);1988; Vol. II, pp 155-62.(2) Melius, C. F. Philos. Trans. R. Soc. London A 1992, 339-365.(3) He, Y.; Wu, C. H.; Lin, M. C.; Melius, C. F. Schock WaVes @Marseille; Brown, R., Dumitrescu, L. Z., Eds.; Springer-Verlag: BeinHeidelberg, 1995; pp 89-94.(4) Colket, M. B. Int. J. Chem. Kinet. 1984, 16, 353.(5) Natarajan, K.; Roth, P. Symp. (Int.) Combust. (Proc.) 1986, 21,729.(6) Wang, N. S.; Yang, D. L.; Lin, M. C. Chem. Phys. Lett. 1989,163, 484.(7) Sims, I. R.; Smith, I. W. M. J. Chem. Soc., Faraday Trans. 1993,89, 1.(8) Nadler, I.; Noble, M.; Reisler, H.; Wittig, C. J. Chem. Phys. 1985,82, 2608. Qian, C. X. W.; Noble, M.; Nadler, I.; Reisler, H.; Wittig, C. J.Chem. Phys. 1985, 83, 5573. Reisler, H.; Wittig, C. Annu. ReV. Phys. Chem.1986, 37, 307. Qian, C. X. W.; Ogai, A.; Reisler, H.; Wittig, C. J. Chem.Phys. 1989, 90, 209.(9) Khundkar, L. R.; Knee, J. L.; Zewail, A. H. J. Chem. Phys. 1987,87, 77.(10) Klippenstein, S. J.; Khundkar, L. R.; Zewail, A. H.; Marcus, R. A.J. Chem. Phys. 1988, 89, 4761.(11) Yang, D. L.; Lin, M. C. In The Chemical Dynamics and Kineticsof Small Molecules; Liu, K., Wagner, A. F., Eds.; World Scientific: RiverEdge, NJ, 1996; Vol. I, pp 164-213.(12) Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry: Introductionto AdVanced Electronic Structure Theory; McGraw-Hill: New York,1982.(13) Hehre, W. J.; Radom, L.; Schleyer, P. V. R.; Pople, J. A. Ab InitioMolecular Orbital Theory; Wiley-Interscience: New York, 1986.(14) Møller, C.; Plesset, M. S. Phys. ReV. 1934, 46, 618.(15) Pople, J. A.; Binkley, J. S.; Seeger, R. Int. J. Quantum Chem. Symp.1976, 10, 1.(16) Krishnan, R.; Pople, J. A. Int. J. Quantum Chem. 1978, 14, 91.(17) Krishnan, R.; Schlegel, H. B.; Pople, J. A. J. Chem. Phys. 1980,72, 4654.(18) Raghavachari, K.; Pople, J. A. Int. J. Quantum Chem. 1981, 20,167.(19) Cizek, J. AdV. Chem. Phys. 1969, 14, 35.(20) Bartlett, R. J. Annu. ReV. Phys. Chem. 1981, 32, 359. Purvis, G.D.; Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910.(21) Paldus, J. In New Horizons of Quantum Chemistry; Löwdin, P.-O., Pullman, B., Eds.; Reidel: Dordrecht, 1983; p 31.(22) Bartlett, R. J.; Dykstra, C. E.; Paldus, J. In AdVanced Theories andComputational Approaches to the Electronic Structure of Molecules;Dykstra, C. E., Ed.; Reidel: Dordrecht, 1984; p 127.(23) Scuseria, G. E.; Scheiner, A. C.; Lee, T. J.; Rice, J. E.; Schaefer,H. F., III. J. Chem. Phys. 1987, 86, 2881.(24) Scheiner, A. C.; Scuseria, G. E.; Rice, J. E.; Lee, T. J.; Schaefer,H. F., III. J. Chem. Phys. 1987, 87, 5361.(25) Parr, R. G.; Yang, W. Density-Functional Theory of Atoms andMolecules; Oxford: Oxford, 1989.(26) Labanowski, J. K., Andzelm, J. W., Eds. Density FunctionalMethods in Chemistry; Springer-Verlag: New York, 1991.(27) Becke, A. D. J. Chem. Phys. 1993, 98, 5648; Ibid. 1992, 97, 9173;Ibid. 1992, 96, 2155; Ibid. 1988, 88, 1053. Lee, C.; Yang, W.; Parr, R. G.Phys. ReV. B1988, 37, 785.(28) Curtiss, L. A.; Raghavachari, K.; Pople, J. A. J. Chem. Phys. 1993,98, 1293.(29) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J.Chem. Phys. 1991, 94, 7221.(30) Durant, J. L., Jr.; Rohlfing, C. M. J. Chem. Phys. 1993, 98, 8031.(31) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.;Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M.A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley,J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.;Stewart, J. J. P.; Pople, J. A. Gaussian 92/DFT, Revision G.1; GaussianInc.: Pittsburgh, PA, 1992.(32) Landolt-Börnstein, Physical Constants for Atoms and Molecules;Springer: Berlin, 1983; Part II (Suppl.).(33) Dickinson, R.; Kirby, G. W.; Sweeny, J. G.; Tyler, J. K. J. Chem.Soc., Faraday Trans. 1978, 74, 1393.(34) Bak, B.; Nicolaisen, F. M.; Nielsen, O. J. J. Mol. Struct. 1979, 51,17.(35) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular RecombinationReactions; Blackwell Scientific: Oxford, 1990. (b) Holbrook, R. A.; Pilling,M. J.; Robertson, S. H. Unimolecular Reactions, 2nd edition; Wiley:Chichester, 1996. (c) Robertson, S. H.; Pilling, M. J.; Baulch, D. L.; Green,N. J. B. J. Phys. Chem. 1995, 99, 13452.(36) Klippenstein, S. J. J. Phys. Chem. To be submitted.(37) Strictly speaking we should compare the harmonic frequencies withthe corresponding harmonic experimental frequencies. However, the anharmonicitiesfor CN and NO are both quite small (13.1 and 14.1 cm-1,respectively) and so are of negligible importance in considering the largedeviations between the experimental and theoretical estimates. One mayexpect the anharmonicities in NCNO, which are unknown, to be of asimilarly minor importance in such comparisons.(38) Klippenstein, S. J. Chem. Phys. Lett. 1990, 170, 71; J. Chem. Phys.1991, 94, 6469; 1992, 96, 367.(39) Klippenstein, S. J. In The Chemical Dynamics and Kinetics of SmallRadicals; Liu, K., Wagner, A. F., Eds.; World Scientific: River Edge, NJ,1996.(40) Klippenstein, S. J. J. Phys. Chem. 1994, 98, 11459.(41) Bai, Y. Y.; Segal, G. A. Chem. Phys. Lett. 1988, 151, 31.(42) Hirschfelder, J. O.; Wigner, E. J. Chem. Phys. 1939, 7, 616. Miller,W. H.; J. Chem. Phys. 1976, 65, 2216. Chesnavich, W. J.; Bass, L.; Su, T.;Bowers, M. T. J. Chem. Phys. 1981, 74, 2228. Rai, S. N.; Truhlar, D. G.J. Chem. Phys. 1983, 79, 6046.(43) A thermal average over the reactant rotational states could havebeen performed in the theoretical analysis. However, the variation of therate constant with J in this low J limit essentially reduces to an uncertaintyin the dissociation threshold corresponding to the thermal rotational energyof the reactants. In this case, this uncertainty corresponds to only a fewcm -1 in the energy scale of Figure 2 and so was deemed unimportant.(44) Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory ofGases and Liquids; 4th printing; Wiley: New York, 1967.(45) Troe, J. J. Phys. Chem. 1979, 83, 114.(46) Troe, J. Ber. Bunsenges. Phys. Chem. 1983, 87, 161. Gilbert, R.G.; Luther, K.; Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 169.(47) Sims, I. R.; Smith, I. W. M. J. Chem. Soc., Faraday Trans. 2 1988,84, 527.

More magazines by this user
Similar magazines