Following Reaction Paths

An IRC calculation examines the reaction path leading down from a transition structure on a potential energy surface. Such a calculation starts at the saddle point and follows the path in both directions from the transition state, optimizing the geometry of the molecular system at each point along the path. In this way, an IRC calculation definitively connects two minima on the potential energy surface by a path which passes through the transition state between them. 

Reaction path computations allow you to verify that a given transition structure actually connects the starting and ending structures that you think it does. Once this fact is confirmed, you can then go on to compute an activation energy for the reaction by comparing the (zero-point corrected) energies of the reactants and the transition state. 

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Gonzales C and Schlegel H B 1991 Improved algorithms for reaction path following higher-order implicit algorithms J. Chem. Phys. 95 5853... 

Schlegel H B 1994 Some thoughts on reaction-path following J. Chem. Soc. Faraday Trans. 90 1569... 

Figure 5.29 from Gonzalez C and H B Schlegel 1988. An Improved Algorithm for Reaction Path Following. The Journal of Chemical Physics 90 2154-2161. 

Fig. 5.29 Method for correcting the path followed by a steepest descents algorithm to generate the intrinsic reaction coordinate. The solid line shows the real path and the dotted line shows the algorithmic approximation to it. (Figure redrawn from Gonzalez C and H B Schlegel 1988. An Improved Algorithm for Reaction Path Following. Journal of Chemical Physics 90 2154-2161.)...

Reaction path following (using intrinsic reaction coordinates). 

We ll now use Gaussian s reaction path following facility to explore the H CO potential energy surface. There are many minima on this surface—including... 

Rotational Earner of Allyl Cation Reaction Path Following... 

The polarity of ground and transition states are a priori identical, because no charges are developed during the reaction path. Following this rule, spedfic micro-wave effects would not be expected for these reactions, as has been verified when the reactions were performed in a nonpolar solvent [5, 6]. Solvent effects in these reactions are also small, or negligible, for the same reasons (Fig. 3.6) [46]. 

The tertiary alcohol m,m,/ra ,v-perhydro-9h-phcnalcnol (7) is converted stereospecifically and in high yield (92%) to /ran.v,/ran.v,/ran.v-pcrhydrophcnalcnc (10) when treated with either triethylsilane or triphenylsilane and trifluoroacetic acid in dichloromethane (Eq. 15). Studies indicate that the reaction path follows the cation rearrangement 8 9 and that the trans trifluoroacetate ester related to... 

To obtain Vmin for a PFR, the T profile is chosen so that the reaction path follows the locus of maximum rates as fA increases that is, the rate is ( —rA)mflJ[ at each value of fA in the design equation (from equation 15.2-2) ... 

Fig. 4.5 Schematic projection of the energetics of a reaction. The diagram shows the Born-Oppenheimer energy surface mapped onto the reaction coordinate. The barrier height AE has its zero at the bottom of the reactant well. One of the 3n — 6 vibrational modes orthogonal to the reaction coordinate is shown in the transition state. H and D zero point vibrational levels are shown schematically in the reactant, product, and transition states. The reaction as diagrammed is slightly endothermic, AE > 0. The semiclassical reaction path follows the dash-dot arrows. Alternatively part of the reaction may proceed by tunneling through the barrier from reactants to products with a certain probability as shown with the gray arrow...

Although the traditional approach of transition structure determination and reaction path following is perfectly suited for gas phase reactions, which can also provide major insight into the mechanism of condensed phase reactions, (14-16) it is also important to specifically consider the fluctuation and collective solvent motions accompanying the chemical transformation in solution.(17, 18) One approach that has been used to address this problem is the use of an energy-gap reaction coordinate, A. -... 

To implement the reaction path following scheme in the EVB formalism, one defines a X-depcndcnl mapping... 

C. Gonzalez and H. B. Schlegel,/. Phys. Chem., 94,5523 (1990). Reaction-Path Following in Mass-Weighted Internal Coordinates. 

H. B. Schlegel, Reaction path following, in Encyclopedia of Computational Chemistry, Vol. 4, John Wiley Sons, Ltd, Chichester, 1998, p. 2432. 

C. Gonzalez et al., An improved algorithm for reaction path following. J. Chem. Phys. 90,... 

Gonzalez C, Schegel HBJ, Reaction path following in mass-weighted internal coordinates, J Phys Chem, 94, 5523-5527 (1990)... 

The actual reaction path followed becomes more evident if the corresponding hafnium complexes are used as substrates. In this case the crucial intermediate 29, which can react to form either product 30 or 17, can be isolated. The thermodynamically favored ( -m-butadiene)hafnocene (5b) (32) turns out to be inert toward ethylene under the conditions applied. Even heating to 120°C in an ethylene atmosphere (1 bar) for several hours does not result in consumption of the metal complex. In contrast, s-trans-rf-butadiene)hafnocene (3b) rapidly takes up 1 molar equivalent of C2H4 even at -10°C to yield a C—C coupling product, i.e., the five-membered metallacyclic cr-allylhafnocene complex 29b. Above 0°C, vinylhafnacy-clopentane reacts with additional ethylene to form bis(cyclo-pentadienyl)hafnacyclopentane (30b) and free butadiene. In the absence... 

Reactions of soluble metal complexes, whose mechanisms of catalysis appear to be reasonably well known, can serve as a guide to the main reaction paths followed on heterogeneous catalysts. Mononuclear complexes catalyze syn addition of H2 to alkynes to yield initially only cis isomers, as in equation (25). 5 More recently, Muetterties and coworkers showed that the dinuclear rhodium hydride complex ( yi-H)Rh[P(OPr )3]2 2 (38) converts alkynes to trans isomers as initial products (equation 26). The alkyne addition compound (39) was isolated its structure shows the vinyl group bonded to one rhodium atom by a a-bond and to the other by a ir-bond, while the substituents on the vinyl group are trans to one another. This structure resembles ones hypothesized earlier to explain the formation of trans isomers and alkanes. Hydrogenations of alkynes which are catalyzed by the dinuclear rhodium hydride are much slower than the hydrogenation of an alkene catalyzed by the dinuclear tetrahydride (40), which is formed rapidly from (38) in the presence of H2 (equation 11). ... 

Other examples from this study indicate that the reaction path followed by the nitrilium ion depends very much on the nature of the nucleophiles present. Thus, the allylindole (106) produced the imidate (107) through reaction of the nitrilium ion wiA methanol in preference to the electron-rich heterocyclic system (equation 45). In contrast, alcohol (108) underwent effective intramolecular cyclization (equation 46). 

The exclusion of hydrogen in the reduction step avoids any tungsten crystal growth via the volatile W02(0H)2- The reaction path follows the sequence WO3 (WO2 9) -> WO2.72 -> WO2 W W2C WC. The intermediately formed, needlelike WO2.72 decomposes to ultrafine WO2 nuclei, which are further transformed to WC of... 

Once again, these reaction paths follow elementary steps with very simple and predefined rules. They may be simply classified as isomerization and decomposition reactions. 

Reaction Path During Quench. Unfortunately, there is a sparsity of high-temperature kinetic data for the H—C—N system. Hence, one is unable to predict with certainty the reaction path followed as the atomic-species H, C, and N, are cooled from 15,000°K. to 500°K. in 10 msec., for example. After an examination of the experimental results in the succeeding sections, it may be possible to infer the important steps in the reaction sequence. 

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