Calculated reaction paths

Czerminski R and R Elber 1990. Self-A voiding Walk Between 2 Fixed-Points as a Tool to Calculate Reaction Paths in Large Molecular Systems. International Journal of Quantum Chemistry 824 167-186. 

Benzyne shares a feature with A in the [2+2] cycloaddition reactions. The HOMO-LUMO interaction prefers the three-centered interaction (Scheme 4) [115]. This is in agreement with the calculated reaction path [116]. 

Our calculated reaction path may reasonably well represent the overall reaction of pyrite as it oxidizes, but it does little to illustrate the steps that make up the reaction process. Reaction 31.2, for example, involves the transfer of 16 electrons to oxygen, the electron acceptor in the reaction, from the iron and sulfur in each FeS2 molecule. Elementary reactions (those that proceed on a molecular level), however, seldom transfer more than one or two electrons. Reaction 31.2, therefore, would of necessity represent a composite of elementary reactions. 

The Calculated Reaction Path of the Alcoholytic Ring Opening of Azlactones... 

Figure 5.18. Calculated reaction path and optimized structures using DFT for (a) N—H dissociation and (b) N—CH3 dissociation of dimethylamine on the one-dimer silicon cluster. Figure reused with permission from Collin Mui, Journal of Chemical Physics, 114, 10170 (2001). Copyright 2001, American Institute of Physics [279].

FIGURE 2a. Calculated reaction path for the head-to-head and head-to-tail dimerization of silene (at TCSCF/DZ + d or CCSD/DZ + d, respectively, relative energies in kcal mol-1)186... 

SGF-LCGO calculations for the nucleophilic addition of hydride ion to formaldehyde to yield methanolate anion (H + CH2 = 0 CHjO ) have been carried out (83, 84). Interestingly, the calculated reaction path for this reaction shows striking similarities to that derived from structural correlations for amine addition to a ketone function. 

A potential surface is a graphical representation of the energy of the system as a function of its geometry. For a lucid account on potential energy surfaces, transition states, methods for calculating reaction paths, etc., see Chapter 2 in ref. 7. 

The idea of constrained dynamics performed for a set of points along such a reaction path , i.e. for a set of fixed values of the reaction coordinate, A, is not specific to MD. Similar approaches have been commonly used in computational studies based on static quantum-chemical calculations. Such approaches are known as linear transit calculations, reaction path scans, etc. A set of constrained geometry optimizations with the constraint driving the system from reactants to products is a popular way to bracket a transition state, for instance. 

Calculated reaction paths from actual weight loss of oxygen ... 

Calculated reaction paths from oxygen supplied by AgMnOi according to (A) 2AgMn04 —> 1.502 ... 

FIGURE 2. AMI-calculated reaction path for the aldol reaction of acetaldehyde with propionalde-hyde, using complex 150b as a model for the intermediate boron enolate complex 150a. Reproduced from Y. Makino, K. Iseki, K. Fujii, S. Oishi, T. Hirano and Y. Kobayashi, Tetrahedron Lett., 36, 6527. Copyright 1995, courtesy of Elsevier... 

Fig. 16. Comparison of calculated reaction paths with experimentally observed compositions for butene isomerization. The points are observed composition and the solid lines are calculated reaction paths.

We shall use the hypothetical four component system discussed in Section III,C to illustrate the method. In particular, the location of the maxima in the component Ai for an initial composition of pure Ai will be computed and compared with the location determined from the calculated reaction paths (Fig. 18). For an initial composition of pure Ai, we have... 

R. Czerminski and R. Elber, Self avoiding walk between two fixed points as a tool to calculate reaction paths in large molecular systems. Int. J. Quant. Chem. 24, 167 186 (1990). 

To operate EQPS on an EQ6 calculated reaction path, the user selects the boundary constraints affecting a process (open vs. closed system, isotopic equilibrium or disequilibrium between redox subsets, and precipitation pathway accompanying redox reactions), inputs initial solution or system reactant(s) composition(s), and specifies an input file generated from an EQ6 run. The EQ6 data consists of solution composition and mineral amounts at discrete points on a reaction pathway. EQPS can either be set to calculate at the points produced by EQ6, or use a curve crawler technique to produce pseudo-continuous isotopic pathways at user definable granularity. Accuracy of either computational procedure depends most on the step size executed by EQ6 and only slightly on the step size selected during the... 

Fig< 10.2.1 Comparison of calculated reaction paths with experimentally observed compositions for butene isomerization. The points are observed composition and the solid lines are calculated reaction paths. [From James Wei and Charles D. Prater, Adv. in Cat., 13, 256 (1962). Reprcxiuccd with permission.]... 

Some examples of the use of these methods for iron-sulfur complexes will be discussed later. The methods have utility for redox potentials, p/fa calculations, reaction path energetics, and understanding how surrounding protein side chains (or main chains) can stabilize an active site eluster electronically or geometrically. ... 

A step size 5s of 0.01 ao was used in the local quadratic approximation for following the reaction path for all of the systems. The accuracy of the calculated reaction path was tested by comparing computed rate constants (including tunneling effects) with at least one other reaction path determined with another step size. In all cases the rate constants for temperatures above 300 K are numerically converged to better than 50% and those at 200 K are numerically accurate to about a factor of 2. Tests were also made... 

Truhlar 6c coworkers have recently made available a program, POLYRATE, which, among other things, calculates reaction paths for chemical reactions (14). 

Thus, Seidl, Grev and Schaefer found a barrier for a concerted fully synchronous [2jts+2Tts reaction path of 5.2 kcalmol" (at CCSD/DZ+d+ZPE). At the same level of theory the head-to-taU dimerization is exothermic by 79.1 kcalmol" The transition state for this reaction appears very early on the reaction coordinate, i.e., the silene geometry being nearly conserved, as expected for a highly exothermic reaction. The calculated reaction path is shown in Figure 2a. 

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