Potential energy surfaces unimolecular reaction rates

POLYRATE can be used for computing reaction rates from either the output of electronic structure calculations or using an analytic potential energy surface. If an analytic potential energy surface is used, the user must create subroutines to evaluate the potential energy and its derivatives then relink the program. POLYRATE can be used for unimolecular gas-phase reactions, bimolecular gas-phase reactions, or the reaction of a gas-phase molecule or adsorbed molecule on a solid surface. 

In order to better understand the detailed dynamics of this system, an investigation of the unimolecular dissociation of the proton-bound methoxide dimer was undertaken. The data are readily obtained from high-pressure mass spectrometric determinations of the temperature dependence of the association equilibrium constant, coupled with measurements of the temperature dependence of the bimolecular rate constant for formation of the association adduct. These latter measurements have been shown previously to be an excellent method for elucidating the details of potential energy surfaces that have intermediate barriers near the energy of separated reactants. The interpretation of the bimolecular rate data in terms of reaction scheme (3) is most revealing. Application of the steady-state approximation to the chemically activated intermediate, [(CH30)2lT"], shows that. 

These, and similar data for other systems, demonstrate the tremendous potential that the MICR technique has for the qualitative elucidation of potential energy surfaces of relatively complex organic reactions. Once implementation of the quadrupolar excitation technique has been effected to relax ions to the cell center, the technique will become even more powerful, in that the determination of highly accurate unimolecular decomposition lifetimes of chemically activated intermediates will also become possible. No other technique offers such a powerful array of capabilities for the study of unimolecular dissociation mechanisms and rates. 

In dynamical theories, one solves the equation of motion for the individual nuclei, subject to the potential energy surface. This is the exact approach, provided one starts with the Schrodinger equation. The aim is to calculate k(E) and kn(hi/), the microcanonical rate constants associated with, respectively, indirect (apparent or true) unimolecular reactions and true (photo-activated) unimolecular reactions. 

This is an approach for the calculation of the microcanonical rate constant k(E) for indirect unimolecular reactions that is based on several approximations. The molecule is represented by a collection of s uncoupled harmonic oscillators. According to Appendix E, such a representation is exact close to a stationary point on the potential energy surface. Furthermore, the dynamics is described by classical mechanics. 

It seems worthwhile to examine critically this transcription of the Slater method into the standard absolute reaction rate theory. In the simple unimolecular bond break, it does appear reasonable that the coordinate q between the tvfo atoms A and B must reach and go beyond a critical extension q0 in order that decomposition takes place. In Slater s calculations account is taken of the different energies involved in stretching q to q0. In regarding q as the mode of decomposition in the transition state method, one must, however, first look at the potential energy surface. The decomposition path involves passage over the lowest possible barrier between reactants and products. It does not seem reasonable to assume that this path necessarily only involves motion of the atoms A and B at the activated complex. Possibly, a more reasonable a priori formulation in a simple decomposition process would be to choose q as the coordinate which tears the two decomposition fragments apart. Such a coordinate would lead roughly to the relation... 

Theoretical chemistry is the discipline that uses quantum mechanics, classical mechanics, and statistical mechanics to explain the structures and dynamics of chemical systems and to correlate, understand, and predict their thermodynamic and kinetic properties. Modern theoretical chemistry may be roughly divided into the study of chemical structure and the study of chemical dynamics. The former includes studies of (1) electronic structure, potential energy surfaces, and force fields (2) vibrational-rotational motion and (3) equilibrium properties of condensed-phase systems and macromolecules. Chemical dynamics includes (1) bimolecular kinetics and the collision theory of reactions and energy transfer (2) unimolecular rate theory and metastable states and (3) condensed-phase and macromolecular aspects of dynamics. 

Since 1970, direct photolysis of molecules or ions in low-pressure, collisionless environments, has permitted molecules to be excited to well-defined energy levels, while the use of pulsed lasers or coincidence techniques has provided an accurate external time base with which to measure the dissociation rate constants over many orders of magnitude. It is often the case that more precise experimental results lead to fundamental changes in the theoretical models which describe the phenomena. This has not happened in the case of unimolecular reactions. The statistical theory has remained surprisingly robust. Most molecular systems that dissociate on a bound potential energy surface do so in a statistical fashion. What has changed in the past 25 years is our ability to apply the statistical theory. It is now possible to calculate Unimolecular rate constants with essentially no adjustable parameters and which are in quantitative agreement with experiments. 

The statistical dissociation rate constant can be calculated from the point of view of the reverse reaction, namely the recombination of the products to form a complex. This approach, commonly referred to as phase space theory (PST) (Pechukas and Light, 1965 Pechukas et al., 1966 Nikitin, 1965 Klots, 1971, 1972) is limited to reactions with no reverse activation energy, that is, reactions with very loose transition states. PST assumes the decomposition of a molecule or collision complex is governed by the phase space available to each product under strict conservation of energy and angular momentum. The loose transition state limit assumes that the reaction potential energy surface is of no importance in determining the unimolecular rate constant. 

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 MCTDH method allows for a treatment of quantum dynamics of (mainly) bound states in medium size molecular systems (with number of degrees of freedom up to 24). Many applications employing accurate potential energy surfaces are successfully achieved and compared with the relevant experimental spectral data, such as vibrational absorption, vibronic spectrum and so on. The method, however, is known not necessarily to work well for the evaluation of reaction rate in case of unimolecular dissociation with chaotic motions and hard recombination reaction systems. In these systems it is quite difficult to reproduce the d5mamics accurately in terms of a small number of reference multireference orbitals. 

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. 

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