Potential energy surface quantitative

Sun J-Q and Ruedenberg K 1993 Quadratic steepest descent on potential energy surfaces. I. Basic formalism and quantitative assessment J. Chem. Phys. 99 5257... 

Computer simulation techniques offer the ability to study the potential energy surfaces of chemical reactions to a high degree of quantitative accuracy [4]. Theoretical studies of chemical reactions in the gas phase are a major field and can provide detailed insights into a variety of processes of fundamental interest in atmospheric and combustion chemistry. In the past decade theoretical methods were extended to the study of reaction processes in mesoscopic systems such as enzymatic reactions in solution, albeit to a more approximate level than the most accurate gas-phase studies. 

A second point is that we. as yet, have no quantitative basis for the placement of the transition state along the horizontal axis. Figure 5-9 shows the transition state located slightly closer to the initial state than to the final state, in accordance with the argument of Section 5.1, Potential Energy Surfaces. This problem is dealt with later in the present section. 

For both statistical and dynamical pathway branching, trajectory calculations are an indispensable tool, providing qualitative insight into the mechanisms and quantitative predictions of the branching ratios. For systems beyond four or five atoms, direct dynamics calculations will continue to play the leading theoretical role. In any case, predictions of reaction mechanisms based on examinations of the potential energy surface and/or statistical calculations based on stationary point properties should be viewed with caution. 

The analytic potential energy surfaces, used for the Cl + CH3Clb and Cl + CHjBr trajectory studies described here, should be viewed as initial models. Future classical and quantum dynamical calculations of SN2 nucleophilic substitution should be performed on quantitative potential energy functions, derived from high-level ab initio calculations. By necessity, the quantum dynamical calculations will require reduced dimensionality models. However, by comparing the results of these reduced dimensionality classical and quantum dynamical calculations, the accuracy of the classical dynamics can be appraised. It will also be important to compare the classical and quantum reduced dimensionality and classical complete dimensionality dynamical calculations with experiment. 

The semiempirical nature of the methods used to construct multidimensional potential energy surfaces makes the quantitative validity of the results questionable. Hence the present state of the theoretical calculation of activation energies is unsatisfactory. 

We note at this point that the nonadiabatic-transition state method used here (6,19,77) is not expected to be able to give quantitative agreement with experimental rate constants. There are too many factors that are treated approximately (or not at all) in this theory for such performance to be possible. One of the key difficulties is that calculated rate constants are very sensitive to the accuracy of the potential energy surface at room temperature, an error of lkcalmol-1 on the relative energy of the MECP relative to reactants will equate, roughly speaking, to an error by a factor of five on the calculated rate constant. Even though we... 

The potential energy surfaces on which the electron-transfer process occurs can be represented by simple two-dimensional intersecting parabolic curves (Figure 6.23). These quantitatively relate the rate of electron transfer to the reorganisation energy (A.) and the free-energy changes for the electron-transfer process (AG°) and activation (AG ). 

The most accurate theories of reaction rates come from statistical mechanics. These theories allow one to write the partition function for molecules and thus to formulate a quantitative description of rates. Rate expressions for many homogeneous elementary reaction steps come from these calculations, which use quantum mechanics to calculate the energy levels of molecules and potential energy surfaces over which molecules travel in the transition between reactants and products. These theories give... 

The molecular potential energy surface is one of the most important concepts of physical chemistry. It is at the foundations of spectroscopy, of chemical kinetics and of the study of the bulk properties of matter. It is a concept on which both qualitative and quantitative interpretations of molecular properties can be based. So firmly is it placed in the theoretical interpretation of chemistry that there is a tendency to raise it above the level of a concept by ascribing it some physical reality. 

Even when the harmonic approximation is not quantitatively justified it provides a convenient starting point for exact treatments. Thus, even if the potential energy surface is anharmonic in the bottleneck, it is often smooth enough for there to be a principal saddle point that can be found by minimizing IVU 2. 

Multi dimensional quantum mechanical calculations are needed for the quantitative description of the effects discussed above. Rigorously stated, such calculations are very laborious. In this connection, considerable attention has been paid during the last two decades to the development of simplified methods for resolving the multi-dimensional problems. We refer, for instance, to the method of classic S-matrix [60] and the quantum-mechanical method of the transition state [61]. The advantage of these methods is the use of realistic potential energy surfaces the shortcoming is the fact that only... 

A brief comment on the accuracy of current approaches seems in order. For atomic systems in the first or second row of the periodic table, quantitative ( 0.01eV) studies have been carried out. For diatomic systems, constructed from these atoms, an accuracy of 1 kcal in the potential curves can be realized. For polyatomic systems the situation is less clear because of the great increase in computational difficulty. Accuracy of 5 to 10 kcal can probably be achieved for simple potential-energy surfaces, although very few surfaces have been examined in detail. 

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