Through-space acceleration

When looking for the velocities of points on a rigid body, the method of instantaneous centers can often be used. If the velocity of two points on the body are known, those points and all other points on the body can be considered to be rotating with the same angular velocity about some motionless central point. This central point is called the instantaneous center of zero velocity. The instantaneous center generally moves through space as a function of time and has acceleration. It does not represent a point about which acceleration may be determined. 

Results of a study of electrostatic acceleration of enolization in cationic ketones have implications for enzymatic catalysis of enolization.136 Rate constants determined for water-, acetate- and hydroxide ion-catalysed enolizations of cationic ketones (79) (pK 11.13) and (80) (pK 11.90) have been compared with those for (81). It has been estimated that the inductive effects of the charged lings lower the p/y,s of (81) and (79) by 4.2 and 1.2 log units, respectively, whereas for (79) the electrostatic effect lowers the pAa by 6.3 log units, and enhances oh by 330-fold relative to a typical methyl ketone. The rate of enolization of (81) is enhanced 2.3 x 104-fold by the through-space electrostatic effect. 

The cis isomer 52 was found to react about 450 times faster than its unsilylated analogue 51 in 97% trifluoroethanol. However, the turns isomer 53 showed essentially no acceleration. The secondary deuterium isotope effect observed with the fi tetradeuterated analogue of the cis isomer 52 confirmed that the molecule reacts via the diequatorial conformation. In this conformation the back lobes of the Si—C bond at the 3-position can interact with the developing p orbital at the 1-position. This through-space interaction is often referred to as homohyperconjugation. 

Enolization of cationic ketones is accelerated by electrostatic stabilization of the enolate anion. Rate constants for water-, acetate-, and hydroxide ion-catalysed enolization of 2-acetyl- 1-methylpyridinium ion (94) have been measured13811 and compared with a 2-acetylthiazolium ion (95), a simple analogue of 2-acetylthiamine pyrophosphate.13811 For (94), qh = 1.9 x 102 M-1 s 1, about 1.1 x 106 times that for a typical methyl ketone such as acetone. Thermodynamically, it is >108 times more acidic (pAa values of 11.1 vs 19.3). These increases in kinetic and thermodynamic acidity are derived from through-bond and through-space effects, and the implications for enzymatic catalytic sites with proximal, protonatable nitrogen are discussed. The results for (94) suggest a pAa value of 8.8 for (95), a value that cannot be measured directly due to competing hydrolysis. 

As the shaman spoke, Valdes (who had only experienced a few brief visions which he hadn t described) saw a black sky with brightly colored objects floating in it. He suddenly found himself speeding toward one and actually felt he was accelerating through space past the rest. The light turned out to be a Mazatec village similar to that of the curandero. 

The curvature/strain modes method hold the promise of detecting damage from the processing of experimental data without a structural model. The premise of the method is that damage in thin-wall structures induces local discontinuities that affect strongly the curvature of the flexural modes of the structure [71]. The curvamre of the modes (i.e. the curvature modes) can be determined through space-wise double differentiation of the measured displacement/velocity/acceleration modes. They can be also measured directly with surface mounted strain gauges. 

The potential for cation stabilization provided by delocalization through space is significant. For example, a properly positioned alkene provides dramatic acceleration (10") of ionization of anti C-X bonds with perfect stereospecificity of substitution. ... 

The introduction of an >-substituent (CN, Cl, or OH) into a primary n-alkyl chloride considerably enhances the rate of 5 n2 chloride exchange in the gas phase. Reactivity trends suggest that the acceleration is due primarily to through-space solvation of the transition state, especially charge-dipole interactions. Potential-energy surfaces are discussed. In further work by the same group, the translational energy dependence of the rate constants of several gas-phase 5 n2 and carbonyl addition-elimination reactions has been measured by FT-ICR spectroscopy. The results were interpreted by RRKM calculations. 

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