Symmetrical transition states

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. 

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.

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). 

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. 

Neither of these vibrations corresponds to stretching vibrations of AH or BH. The antisymmetric vibrational mode represents translational motion in the transition state and has an imaginary force constant. The symmetric transition-state vibration has a real force constant but the vibration may or may not involve motion of the central H(D) atom2,12 13. If the motion is truly symmetric, the central atom will be motionless in the vibration and the frequency of the vibration will not depend on the mass of this atom, i.e. the vibrational frequency will be the same for both isotopically substituted transition states. It is apparent that under such circumstances there will be no zero-point energy difference... 

These reactions proceed through symmetrical transition states [H H H] and with rate constants kn,HH and kH,DH, respectively. The ratio of rate constants, kH,HH/kH,DH> defines a primary hydrogen kinetic isotope effect. More precisely it should be regarded as a primary deuterium kinetic isotope effect because for hydrogen there is also the possibility of a tritium isotope effect. The term primary indicates that bonds at the site of isotopic substitution the isotopic atom are being made or broken in the course of reaction. Within the limits of TST such isotope effects are typically in the range of 4 to 8 (i.e. 4 < kH,HH/kH,DH < 8). 

It used to be postulated that the magnitude of the alpha-carbon KIE in an Sn2 reaction is an indication of the transition state symmetry. The expectation was that this KIE reaches maximal value for a symmetric transition state and drops back to unity for extremely early or late transition states. That expected behavior is marked by the solid line in Fig. 10.10. However, recent calculations of the nucleophilic substitution of chloride from methyl chloride by a broad variety of nucleophiles... 

The singlet carbene, on the other hand, can add through a less symmetrical transition state in a slightly bent -approach, thus circumventing the barrier imposed by orbital symmetry ... 

Rate and equilibrium constant measurements for the enolization of 3-phenylcoumaran-2-one (82) in aqueous dioxane indicate an enol content of ca 0.1%, a pKg, of 8.9 (6.0 for the enol tautomer), and a fairly symmetrical transition state for enolate anion formation the Brpnsted Pb = 0.52 Below pH 5, enolization is independent of pH, occurring via O-protonation of the enolate. 

The Brpnsted coefficient /3b = 0.52 for deprotonation of 3-phenylcoumaran-2-one (108) by a series of bases in 50% (v/v) water-dioxane, and q bh = 0.48 for reprotonation by the conjugate acid of the buffer, are indicative of a fairly symmetrical transition state for proton transfer, although the primary KE, ku/ku = 3.81, found for proton abstraction by HO is lower than expected. " The moderate intrinsic rate constant for deprotonation of (108) suggests that generation of the charge in the transition state is accompanied by only a small amount of molecular and solvent reorganization. In acidic solution, below pH 5, O-protonation of (110) occurs initially to form (109)... 

Nitrile-forming anti eliminations from the (Z)-oximes (31) and (32) have also been found to proceed by the E2 mechanism the symmetrical transition state is little... 

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