RRKM calculations potential energy surface

Variational RRKM calculations, as described above, show that a imimolecular dissociation reaction may have two variational transition states [32, 31, 34, 31 and 36], i.e. one that is a tight vibrator type and another that is a loose rotator type. Wliether a particular reaction has both of these variational transition states, at a particular energy, depends on the properties of the reaction s potential energy surface [33, 34 and 31]- For many dissociation reactions there is only one variational transition state, which smoothly changes from a loose rotator type to a tight vibrator type as the energy is increased [26],... 

Fig. 28. Schematic of potential energy surfaces of the vinoxy radical system. All energies are in eV, include zero-point energy, and are relative to CH2CHO (X2A//). Calculated energies are compared with experimentally-determined values in parentheses. Transition states 1—5 are labelled, along with the rate constant definitions from RRKM calculations. The solid potential curves to the left of vinoxy retain Cs symmetry. The avoided crossing (dotted lines) which forms TS5 arises when Cs symmetry is broken by out-of-plane motion. (From Osborn et al.67)...

Rice et al. [99] developed a global potential energy surface based on the Mowrey et al. [103] results and performed extensive classical trajectory calculations to study the dynamics of the CH2NN02 dissociation reactions. They calculated rates for reactions (III) and (IV) with classical barriers of 35 and 37 kcal/mol, respectively. They found that N-N bond fission dominates at low energy but that HONO elimination is competitive. Chakraborty and Lin [104] predict the opposite on the basis of their ab initio barriers and RRKM theory calculations. The two dissociations channels are closely competitive and it is not clear that ab initio methods are sufficiently reliable to distinguish between two reactions that have such similar energy requirements. Also, the Zhao et al. results [33] are not in accord with the theoretical predictions. 

Laser-induced formaldehyde dissociation has been intensively studied experimentally and theoretically in the last decade.51-54 Detailed calculations of the potential energy surface have been reported and various studies have been undertaken regarding the possibility of mode selective decay, The low density of vibrational states at the typical energies studied make H2CO an interesting candidate for possible non-RRKM effects, a point to which we return later. 

Calculations on electrophilic additions to acetylene were reported for a number of hydrocarbon cations, including CH" [129], C3H3" [130, 131], and phenylvinylium ion [132]. It was predicted that the cyclopropenylium cation, the most stable form of C3H, forms an ion-molecule complex with acetylene but does not undergo further addition [131]. The linear propargyl cation, however, reacts with acetylene without an apparent barrier, to form many different C5H5 isomers [130,131]. Wang et al. computed the AMI potential energy surfaces and carried out RRKM and microcanonical variational transition-state analysis for the rate of reaction of phenylvinylium ion with acetylene [132]. 

See, for example, D. L. Bunker, /. Chem. Phys., 40,1946 (1963). Monte Carlo Calculations. IV. Further Studies of Unimolecular Dissociation. D. L. Bunker and M. Pattengill,/. Chem. Phys., 48, 772 (1968). Monte Carlo Calculations. VI. A Re-evaluation erf Ae RRKM Theory of Unimolecular Reaction Rates. W. J. Hase and R. J. Wolf, /. Chem. Phys., 75,3809 (1981). Trajectory Studies of Model HCCH H -P HCC Dissociation. 11. Angular Momenta and Energy Partitioning and the Relation to Non-RRKM Dynamics. D. W. Chandler, W. E. Farneth, and R. N. Zare, J. Chem. Phys., 77, 4447 (1982). A Search for Mode-Selective Chemistry The Unimolecular Dissociation of t-Butyl Hydroperoxide Induced by Vibrational Overtone Excitation. J. A. Syage, P. M. Felker, and A. H. Zewail, /. Chem. Phys., 81, 2233 (1984). Picosecond Dynamics and Photoisomerization of Stilbene in Supersonic Beams. II. Reaction Rates and Potential Energy Surface. D. B. Borchardt and S. H. Bauer, /. Chem. Phys., 85, 4980 (1986). Intramolecular Conversions Over Low Barriers. VII. The Aziridine Inversion—Intrinsically Non-RRKM. A. H. Zewail and R. B. Bernstein,... 

The first of the theoretical chapters (Chapter 9) treats approaches to the calculation of thermal rate constants. The material is familiar—activated complex theory, RRKM theory of unimolecular reaction, Debye theory of diffusion-limited reaction—and emphasizes how much information can be correlated on the basis of quite limited models. In the final chapt, the dynamics of single-collision chemistry is analyzed within a highly simplified framework the model, based on classical mechanics, collinear collision geometries, and naive potential-energy surfaces, illuminates many of the features that account for chemical reactivity. 

The introduction of an >-substituent (CN, Cl, or OH) into a primary n-alkyl chloride considerably enhances the rate of 5 n2 chloride exchange in the gas phase. Reactivity trends suggest that the acceleration is due primarily to through-space solvation of the transition state, especially charge-dipole interactions. Potential-energy surfaces are discussed. In further work by the same group, the translational energy dependence of the rate constants of several gas-phase 5 n2 and carbonyl addition-elimination reactions has been measured by FT-ICR spectroscopy. The results were interpreted by RRKM calculations. 

Figure 5.3 depicts potential energy surface of OH -1- NO2 reaction obtained by quantum chemical calculation (Pollack et al. 2003). Reaction rate constants calculated by RRKM calculation using the electronic structure of the transition state has been compared with the observed values (Sumathi and Peyerimhoff 1997 Chakraborty et al. 1998), and Golden et al. (2003) reported that recently calculated rate constants reproduced well the temperature and pressure dependence obtained by experiments. It has not been elucidated yet, however, if the reaction intermediate HOONO isomerizes to HONO2 or it regenerates more reactive chemical species by photolysis or reaction with other reactive species in the atmosphere, which would affect the ozone formation efficiency in the troposphere. 

Both the Slater and the rrkm treatments are inappropriate for calculations of °°, since the dissociation is not characterized by a critical extension of one bond, but rather by the transition from one potential surface to another. In such a case the observed activation energy at high pressures will be lower than the energy threshold for reaction110. From their high-pressure data Olschewski et a/.109 calculate that E0 = 63 kcaLmole-1 and that the transition matrix-element is 100 caLmole-1, which is in good agreement with the spin-orbit interaction term for O atoms. 

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