Collinear Three Center Reactions

Jacobi Coordinates The Skew Angle in Three Center Collinear Reactions... 

The 1 1 reaction of 76 or 77 (R = Me, R = H) with bromine resulted in oxidation and the formation of a carbene complex of SBr2 (79) or SeBr2 (80), respectively (55, 58-62). The X-ray crystal structure of 79 has been reported and showed that this sulfurane possesses an almost collinear axial three-center geometry with elongated S-Br... 

Before discussing tunneling in VTST where the discussion will focus on multidimensional tunneling, it is appropriate to consider the potential energy surface for a simple three center reaction with a linear transition state in more detail. The reaction considered is that of Equation 6.3. The collinear geometry considered here is shown in Fig. 6.1a it is in fact true that for many three center reactions the transition state can be shown to be linear. The considerations which follow apply to a onedimensional world where the three atoms (or rather the three nuclei) are fixed to a line. We now consider this one-dimensional world in more detail. The Born-Oppenheimer approximation applies as in Chapter 2 so that the electronic energy of... 

Because of the success of the Marcus-Coltrin tunneling path for H + H2, the same procedure was applied to other collinear three center reactions including... 

Sn2 reactions of methyl halides with anionic nucleophiles are one of the reactions most frequently studied with computational methods, since they are typical group-transfer reactions whose reaction profiles are simple. Back in 1986, Basilevski and Ryaboy have carried out quantum dynamical calculations for Sn2 reactions of X + CH3Y (X = H, F, OH) with the collinear collision approximation, in which only a pair of vibrations of the three-center system X-CH3-Y were considered as dynamical degrees of freedom and the CH3 fragment was treated as a structureless particle [Equation (11)].30 They observed low efficiency of the gas-phase reactions. The results indicated that the decay rate constants of the reactant complex in the product direction and in the reactant direction did not represent statistical values. This constitutes a... 

This so-called stereoelectronic factor operates to maximize or minimize orbital overlap, as the case requires, to obtain the most favorable energy. This was evident from the three- and four-center systems we have discussed by the VB and HMO methods. It was also implicit in favored anti-1,2-additions, 1,3-cyclizations (Fig. 23), fragmentations (e.g. (174)), etc. Here we have selected several reaction types to illustrate the principle. In this and other sections, we show that the tendency for reaction centers to be collinear or coplanar stems largely from orbital symmetry (bonding), but may also derive from steric and electrostatic effects, as well as PLM. 

To examine the notion of steric requirements, consider the reaction H + D2 -> D + HD. At low energies it is an abstraction reaction, meaning that the potential energy of the three-atom system is such that the low-energy path to reaction is when the approach of H to D2 is nearly collinear. The impact parameter b is the miss-distance from H to the center of mass of the D2 molecule. At each value of b, all possible orientations of the axis of D2 with respect to the H-D2 distance are allowed. Owing to collisions with unfavorable orientations, P(b) will fail to reach the maximal value of unity. To account for such steric (and any other) requirements it is traditional to modify the simple, unit-step function by... 

N. Peripheral collisions. Reactions such as Cl + CH4 or H + HCl may be more likely to occur at higher impact parameters. This is because reaction requires the three atoms. Cl—H—C or H—H—Cl, to be nearly in a collinear configuration and this is easier to achieve for an off-center collision. Make a model where the center of mass of HCl is on the Cl atom. Place the bound H atom on a sphere about the center. Assume that reaction occurs when H—H—Cl is in a collinear configuration. Hence compute the opacity function vs. b [adapted from P. M. Aker and J. I Valentini, Is. J Chem. 30, 157 (1990)]. 

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