Nonclassical reflection

In Equation 6.2 T(T) is equal to unity in classical TST, g(T) is a measure of the deviation from the assumption that reactant molecules are locally equilibrated, and k(T) describes the contribution from non-classical transmission through the barrier. k(T) is usually dominated by tunneling but also includes nonclassical reflections. 

CCVTST/SCT denotes CVTST plus a small curvature tunnel transmission (SCT) coefficient. dAll vibrations treated by classical mechanics, tunneling and nonclassical reflection are neglected. Alhambra, C. et al. (see Figs. 11.10 and 11.11) employ the term classical . 

Finally one calculates a transmission coefficient k (T) that accounts for tunneling and nonclassical reflection, and we use this in Eq. (31) to calculate the overall transmission coefficient y T). 

To incorporate multidimensional quantum effects arising from the motion of the system along the reaction coordinate, the CVT rate constant is multiplied by a ground state semiclassical transmission coefficient k t/g primarily accounts for reaction-path tunneling and nonclassical reflection [15,16,43,47]. The final semiclassical CVT rate constant is thus given by... 

In the previous sections, we quantized the F — 1 degrees of freedom in the dividing surface, but we still treated the reaction coordinate classically. As discussed, such quantum effects, which are usually dominated by tunneling but also include nonclassical reflection, are incorporated by a multiplicative transmission coefficient k(T). In this section, we provide details about methods used to incorporate quantum mechanical effects on reaction coordinate motion through this multiplicative factor. 

Nonclassical synthetic methods can also be used for tuning MCRs selectivity, and several successful examples will be reflected somewhat lower in our review. 

MC simulations can reflect the nonclassical critical fluctuations if the simulation box is sufficiently large or if special techniques are applied to analyze the fluctuations. Simulations for simple nonionic models such as the square-well fluid (SCF) [52] show that there is indeed a good chance to study details of criticality. As noted, MC simulations have also been profitably exploited... 

Actually, MC simulations should reflect the nonclassical critical fluctuations as well, thus allowing us to identify the critical exponents and the... 

MP2-FC/6-31G calculations reveal the symmetrically bridged 6-sila-2-norbomyl cation 1 not only to be a local minimum (Fig. 18), but also to be 17.2 kcal mof more stable than the 2-norbomyl cation (Eq. 3) at MP2-FC/6-31G + AZPE(SCF/6-31G 0.89). However, the inherently greater stability of silyl cations contributes to this difference. The Si NMR chemical shift of the bridging silicon atom, ca 1 ppm vs TMS (IGL0/H //MP2-FC/6-31G ), is very strongly shielded in comparison with ca 300 ppm expected for a free RSiH2 species [38]. Thus, the sila congener of the 2-norbomyl carbocation also possesses a nonclassical stracture which is reflected by its stracture as well as its NMR properties. 

Olah emphasizes that the division of cations into classical and nonclassical is frequently arbitrary, since in many cations there is an intenn liate range of delocalization ( partial carbonium-ion character ) as in the 2-methylnorbomyl ion. The author does not want to name classical ions carbonium because it is restricted to highest valeiK state carbocations this requirement is nwt by penta-and tetracoordinate carbocations but not trivalent ones. On the other hand, while in the formation of other onium ions the atom of the donor (nitrogen, oxygen etc.) increases its covalence by one unit upon addition of the acceptor (electrophile), in the formation of a classical ion the covalence of the carbon atom decreases from 4 to 3. As for the name carbenium ion, in the author s opinion it reflects the logical relationships between the carbene and the carbeiunm ion, between the alkene and the carbenium ion ... 

The diffusivity of hydrogen decreases with increasing mass of its isotope. The classical isotope effect reflects the square root of the mass ratio that is, Dh/ d would be expected to have a value of 1.41. However, hydrogen and deuterium exhibit nonclassical isotope effects in iron. The isotope effect in iron is a function of temperature, with Dh/ d decreasing from 1.8 at room temperature to 1.1 to 1.2 at temperatures around 700 °C [39, 48]. 

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