Symmetric transitions

Symmetrical transition states are the lowest energy eon figuration w ithin th at syrn m etry. If a geometry optim i/ation starts off with in that sym m etry, th en th e calcu latio n can fin d th e trail sition state. 

Symmetrical transition states are the lowest energy configuration within that symmetry. If a geometry optimization starts off within that symmetry, then the calculation can find the transition state. 

Although the above work showed that for the symmetrization reaction (and its reverse reaction) the mechanism is SE2 with two steps of dissimilar rate, a symmetrical transition state (XLIII),... 

The reaction of RHgX with HgX2, another exchange,23 can be accounted for by a symmetric transition state... 

The reaction is insensitive to steric effects, but kj increases with the number of alkyl substituents although it is not influenced by position of the alkyl groups (unlike oxidation by TI(III)) . In these respects Cr(VI) oxidation resembles bromination, chlorination and epoxidation and a symmetrical transition state of the type depicted is favoured. 

Kinetic Parameters" for the Symmetric Transition in the Improved Condon Approximation... 

Kinetic Parameters for the Symmetric Transition Taking Account of the Modulation of the Zeroth-Order Electron Densities (Beyond the Condon Approximation)... 

First, we shall consider the model where the intermolecular vibrations A—B and intramolecular vibrations of the proton in the molecules AHZ,+1 and BHZ2+1 may be described in the harmonic approximation.48 In this case, using the Born-Oppenheimer approximation to separate the motion of the proton from the motion of the other atoms for the symmetric transition, Eq. (16) may be... 

The region near < —< and r — r gives the major contribution to the integrals. For the symmetric transition, the saddle point is equal to 0 = 5. It is convenient to choose the origin of the coordin-... 

First, consider the symmetric transition of a particle between unexcited vibrational states assuming classical behavior of the medium atoms which form the microstructure near the tunneling particle and determine its potential energy. The states of the system corresponding to the localization of the particle in the initial and... 

Thus, the allowance for the dependence of the resonance integral on qsk may not be reduced in general to averaging the transition probability over the distribution function in Eq. (102). The function s(qk) plays the role of the distribution function for the coordinates qk in the case of the symmetric transition. In the classical limit, the results of Flynn and Stoneham62 can be obtained from Eq. (103), and in the low-temperature limit, the result of Kagan and Klinger64 can be obtained. 

First, we will consider the symmetric transition and will assume that proton transfer occurs between unexcited vibrational states, the other part of the vibrational subsystem being described by classical mechanics. Then we obtain67... 

Using equations of this type, the expressions for the average transition probability at an arbitrary value of the electron resonance integral V were obtained.77 For the symmetric transition, Wlf has the form... 

Fig. 18. Top transition coordinates (with symmetry species) of conformational transition states of cyclohexane (top and side views). Hydrogen displacements are omitted. The displacement amplitudes given are towards the C2v-symmetric boat form, and towards >2-symmetric twist forms (from left), respectively. Inversion of these displacements leads to the chair and an equivalent T>2-form, respectively. Displacements of obscured atoms are given as open arrows, obscured displacements as an additional top. See Fig. 17 for perspective conformational drawings. Bottom pseudorotational normal coordinates (with symmetry species) of the Cs- and C2-symmetric transition states. The phases of the displacement amplitudes are chosen such that a mutual interconversion of both forms results. The two conformations are viewed down the CC-bonds around which the ring torsion angles - 7.3 and - 13.1° are calculated (Fig. 17). The displacement components perpendicular to the drawing plane are comparatively small. - See text for further details.

This term is independent of the coherence order p. Furthermore, it vanishes for all symmetric transitions (q = 0), and thus can be disregarded when describing the SQ CT coherence or the symmetric MQ coherence. Note, however, that this is not the case for the STs (q 0), which are therefore strongly affected by the first-order quadrupolar interaction, except when the sample is spun at the magic angle. 

In addition to conventional ab initio methods, techniques based on the density functional theory (DFT) have also been used to study the Diels-Alder reaction between butadiene and ethylene97-99. With these kinds of methods, a concerted mechanism through a symmetric transition state is also predicted. Several kinds of density functionals have been used. The simplest one is based on the Local Density Approach (LDA), in which all the potentials depend only on the density. More sophisticated functionals include a dependence on the gradient of the density, such as that of Becke, Lee, Yang and Parr (BLYP). 

Supercritical water (SCW) presents a unique combination of aqueous and non-aqueous character, thus being able to replace an organic solvent in certain kinds of chemical synthesis. In order to allow for a better understanding of the particular properties of SCW and of its influence on the rate of chemical reactions, molecular dynamics computer simulations were used to determine the free energy of the SN2 substitution reaction of Cl- and CH3C1 in SCW as a function of the reaction coordinate [216]. The free energy surface of this reaction was compared with that for the gas-phase and ambient water (AW) [248], In the gas phase, an ion-dipole complex and a symmetric transition... 

The large isotope effect suggested that carbon-hydrogen bond cleavage occurs via a linear and symmetrical transition state, while the loss of stereochemical integrity via epimerization suggested the involvement of an intermediate. A mechanism that is consistent... 

In the transition state a boat like structure appears and there will be a suprafacial cis addition to the termini of the n bond. The ene reaction does not have a symmetrical transition state and it is a thermally allowed concerted reaction. Its transition state involves a suprafacial interaction of six electrons (4 from the k bonds and two from the o bond) So it is a Huckel system and transition state is aromatic. In the terminatlogy of Woodward and Hoffmann it can be regarded as o2s + n2s + 7t2s reaction. 

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