Transition structure evaluation calculations

In the IPCM calculations, the molecule is contained inside a cavity within the polarizable continuum, the size of which is determined by a suitable computed isodensity surface. The size of this cavity corresponds to the molecular volume allowing a simple, yet effective evaluation of the molecular activation volume, which is not based on semi-empirical models, but also does not allow a direct comparison with experimental data as the second solvation sphere is almost completely absent. The volume difference between the precursor complex Be(H20)4(H20)]2+ and the transition structure [Be(H20)5]2+, viz., —4.5A3, represents the activation volume of the reaction. This value can be compared with the value of —6.1 A3 calculated for the corresponding water exchange reaction around Li+, for which we concluded the operation of a limiting associative mechanism. In the present case, both the nature of [Be(H20)5]2+ and the activation volume clearly indicate the operation of an associative interchange mechanism (156). 

To assess the reliability of the particular ONIOM scheme employed in the analysis of the aldol addition, Ojea and coworkers" considered the difference between the activation energies of the most stable transition structures 136 and 137 in the favored disolvated reaction channel (130 and 131) as a convenient parameter for the -value test proposed by Morokuma" . In this manner the error of the ONIOM(I) and ONIOM(II) extrapolations, with respect to their benchmark calculations at the B3LYP/6-31- -G //HF/6-31G level, were 0.86 and 0.60 kcalmol", respectively. When the geometry optimizations at the ONIOM(II) level were followed by single-point energy evaluations at the B3LYP/6-31-l-G level, the error was reduced to less than 0.10 kcalmoG. ... 

The experimental KIE can be compared with KIEs calculated from transition structures on the basis of the vibrational frequencies associated with specific bonds. This information is available from computed transition structures, and the comparison can provide a direct experimental means of evaluating the computed transition structures.The method has also been used to measure KIE in reactions such as the bromination of pentene and epoxidation of propene. Those transition stmctures that are inconsistent with the observed KIE can be excluded. 

Frank et al. [168] reported the formation of / -quinone + hydrogen atom via a transition state with a barrier that was estimated at 90 kcal mof and in which the O—O bridge is in para-position (Figure 6.6). Hadad et al. [32] reported a higher barrier of 127 kcal mof for this para-position transition state adduct. From G2M calculations, Tokmakov et al. [180] report a high barrier for this pathway as well (123 kcal mol ). Hadad et al. evaluated the transition state structure and determined the barrier to be around 138 kcal mof. The O—O bridge was found in the meta-position to form Y(C50 ) + CO. The third isomer is the ortho-position transition state structure. This structure was calculated in this work by different computational methods and by Hadad et al. It was found to be at the lowest energy (around 81 kcal mol ). 

In the first part of this chapter, we have reported a brief survey of the computational tools available to evaluate the geometries and relative energies of the stationary points (reactants, transition structures, and reaction intermediates) associated with the elementary steps of any transformation under the Born-Oppenheimer approximation. These computational data permit the calculation of individual kinetic constants associated with each step. In the second part, we have commented on several results obtained in our laboratory. These kinetic calculations involved up to 40 atoms and 160 electrons and in many cases included solvent effects. Under these conditions, the individual rate constants associated with each elementary step were expected not to be very accurate. However, since the error magnitudes along the different reaction coordinates were similar enough, the final relative rate constants reproduced surprisingly well the experimental observations, even when very subtle effects were studied. In addition, the possibility of evaluating each step of the different reactions permitted... 

The ° mn coefficients are the mean values of the generalized spherical harmonics calculated over the distribution of orientation and are called order parameters. These are the quantities that are measurable experimentally and their determination allows the evaluation of the degree of molecular orientation. Since the different characterization techniques are sensitive to specific energy transitions and/or involve different physical processes, each technique allows the determination of certain D mn parameters as described in the following sections. These techniques often provide information about the orientation of a certain physical quantity (a vector or a tensor) linked to the molecules and not directly to that of the structural unit itself. To convert the distribution of orientation of the measured physical quantity into that of the structural unit, the Legendre addition theorem should be used [1,2]. An example of its application is given for IR spectroscopy in Section 4. 

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