Reaction coordinate motion’along

When the molecular entity involved is a transition state, one of its normal coordinates is the reaction coordinate, motion along which is not opposed by a restoring force. The transition state is situated at a saddle point on the potential energy surface [25, Chap. 5] [26, pp. 101-107], at which A, the force constant for motion along the reaction coordinate is negative and is consequently imaginary, so a non-linear transition state can have no more than... 

The in-1 vibrational frequencies, C0 (s), are obtained from normal-mode analyses at points along the reaction path via diagonalization of a projected force constant matrix that removes the translational, rotational, and reaction coordinate motions. The B coefficients are defined in terms of the normal mode coefficients, with those in the denominator of the last term determining the reaction path curvature, while those in the numerator are related to the non-adiabatic coupling of different vibrational states. A generalization to non-zero total angular momentum is available [59]. 

For a reaction A+B=>[X ] the activated complex moves along the imaginable reaction coordinate (motion over the col is a translational motion) with a speed defined from classical mechanics... 

The SCP-IOS model is the semiclassical approximation of Miller and Smith applied to the reaction-path Hamiltonian. It has the appealing feature that it behaves qualitatively correctly both in the adiabatic limit, which is the situation if the transverse vibrational motion is much faster than motion along the reaction coordinate, and also in the sudden limit, which is the case if reaction-coordinate motion is much faster than transverse vibrational motion. For the case of a coll inear atom-diatom reaction it becomes the Hofacker-... 

The dependence of k on viscosity becomes even more puzzling when the time scale of motion along the reaction coordinate becomes comparable to that of solvent dipole reorientation around the changing charge distribution... 

Electi ocyclic reactions are examples of cases where ic-electiDn bonds transform to sigma ones [32,49,55]. A prototype is the cyclization of butadiene to cyclobutene (Fig. 8, lower panel). In this four electron system, phase inversion occurs if no new nodes are fomred along the reaction coordinate. Therefore, when the ring closure is disrotatory, the system is Hiickel type, and the reaction a phase-inverting one. If, however, the motion is conrotatory, a new node is formed along the reaction coordinate just as in the HCl + H system. The reaction is now Mdbius type, and phase preserving. This result, which is in line with the Woodward-Hoffmann rules and with Zimmerman s Mdbius-Huckel model [20], was obtained without consideration of nuclear symmetry. This conclusion was previously reached by Goddard [22,39]. 

It has been shown that there is a two-dimensional cut of the PES such that the MEP lies completely within it. The coordinates in this cut are 4, and a linear combination of qs-q-j. This cut is presented in fig. 64, along with the MEP. Motion along the reaction path is adiabatic with respect to the fast coordinates q -q and nonadiabatic in the space of the slow coordinates q -qi-Nevertheless, since the MEP has a small curvature, the deviation of the extremal trajectory from it is small. This small curvature approximation has been intensively used earlier [Skodje et al. 1981 Truhlar et al. 1982], in particular for calculating tunneling splittings in (HF)2- The rate constant of reaction (6.45a) found in this way is characterized by the values T<. = 20-25 K, = 10 -10 s , = 1-4 kcal/mol above T, which compare well with the experiment. 

Figure 5-3 is the reaction coordinate diagram for Fig. 5-2. Note the region of the maximum potential energy on the reaction coordinate this region assumes great importance in kinetic theory. At this point the reacting system is unstable with respect to motion along the reaction coordinate. However, at this same point the system possesses minimum energy with respect to motion along dashed line cd. This portion of the reaction coordinate is called the transition state of the reaction. (This concept was introduced in Fig. 1-1.)...

Values of and Qb can be calculated for molecules in the gas phase, given structural and spectroscopic data. The transition state differs from ordinary molecules, however, in one regard. Its motion along the reaction coordinate transforms it into product. This event is irreversible, and as such occurs without restoring force. Therefore, one of the components of Q can be thought of as a vibrational partition function with an extremely low-frequency vibration. The expression for a vibrational partition function in the limit of very low frequency is... 

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