Reaction asymmetry

Since there have been no previous studies of spin-polarized electron induced reaction asymmetries in adsorbed chiral molecules, the exact manner by which the enhancement occurs is unclear. If the orbital occupied during DEA is sufficiently diffuse so as to sample the regions of the molecule responsible for the chiral structure [92] then enantiomeric specific dissociation will result. On the other hand, it has been theorized that two enantiomers will be ionized at different rates by longitudinally spin-polarized electrons [126]. If there are sufficient numbers of higher energy spin-polarized secondary electrons and the final state reached following ionization is dissociative, then this could lead to chiral enhancement. 

Chiral compounds can behave as catalysts in organic reactions. For example, chiral nitrogen bases, chiral crown ethers or Lewis adds bearing chiral residues catalyze diverse types of reactions. Asymmetry can also be induced in transition-metal-catalyzed reactions if the metal bears dural ligands. These possibilities will be described in sequence. 

The effect of an increasing reaction asymmetry is illustrated in Fig. 6.14(d)-(f). When the asymmetry is small, the HD and DH processes are almost equally fast, and again characterized by approximately twice the rate constant of the DD process. When the asymmetry becomes larger, the HD curve merges rapidly with the DD curve, and eventually the DH curve with the HH curve. 

Transition state theory (TST) can be applied in the solvent coordinate for the 1= 0 curve in Fig. 10.6 and for the corresponding curves for different thermodynamic reaction asymmetry AG xn [2d. 3b], and the rate constant for the adiabatic PT reaction is then given by [2-4, 6, 7]... 

Figures 10.8(a) and (b) also indicate that the TS position A along the solvent coordinate shifts with reaction asymmetry. This is due to the fact that the addition of the ZPE to an asymmetric (cf. Fig. 10.8(b)) shifts the maximum of G away from the maximum of at AE = 0, in the direction consistent with the Hammond postulate [15], e.g. later for endothermic reactions AGrxn>0- This indicates that the ZPE contribution at A to the free energy barrier AGl in the solvent coordinate will increase with increasing reaction asymmetry, a crucial qualitative characteristic [3] to which we will return. Also visible in Fig. 10.8(b) is the isotope dependence of the shift AEi- and the associated increase in ZPE at AEi- with increasing reaction asymmetry the latter leads to a KIE reduction, since the ZPE contribution at A will become more and more similar to that of the reactant. Here one can see that the variation in ZPE along the reaction coordinate and its isotopic difference plays a significant role in the reaction free energy barrier variation, and hence the KIE as well.

The TS structure s variation with reaction asymmetry is described by the Bronsted coefficient slope a, the derivative of Eq. (10.12) with respect to AGrxn evaluated for the symmetric reaction. In this manner, cifor the PER in Eq. (10.12) is linearly related to the reaction asymmetry... 

The isotope dependence of the Bronsted slope is most conveniently discussed in terms of the derivative of the expression involving force constants Eq. (10.14). These force constants certainly depend on the variation of the ZPE along the solvent reaction coordinate via Eq. (10.8). Accordingly, a can be cast in terms of these slopes plus the variation in the ZPE value at the reactant and TS positions with reaction asymmetry [4]. Since the ZPE variation is largest in the TS region, the first term in Eq. (10.14) is the most significant, and thus, the essential point is that the isotope difference is approximately proportional to... 

The KIE behavior versus reaction asymmetry for adiabatic PT follows directly [4] from insertion of the isotopic difference between the PER curves described in Eqs. (10.18) and (10.19). The general feature that the KIE is maximal for AGrxn 0 follows from a Bronsted coefficient for a symmetric reaction that is isotope-independent, Sq = 1/2, which reflects the symmetric nature of the electronic structure of the reacting pair at the TS (cf. Eq. (10.12)) [48]. The decrease from the maximum, characterized by a gaussian fall-off with increasing reaction asymmetry, is due to the isotope dependence a <,H > 5 oD- As discussed in Section 10.2.2, this isotope dependence is primarily due to the differential rate of change of ZPEl-versus reaction asymmetry between H and D. 

Figure 10.10(a), which displays the H versus D KIE (T = 300 K) for the Fig. 10.8 PT system, makes these points concrete. The calculated KIE is maximum at AGrxn = 0 drops off symmetrically as the reaction asymmetry is increased. The maximum KIE for the symmetric reaction and the KIE magnitude throughout the whole range are both consistent with experimental observations, (ii) and (iii), respectively. The origin of this last aspect is as follows. The intrinsic KIE magnitude in the adiabatic PT view is directly related to the isotopic difference TS-R ZPE difference AZPEl-<, = - 2 (see Eqs. (10.15) and (10.17)), whose...

A first significant point is that the adiabatic PT form in Eq. (10.24) has the same important feature as the standard picture, via Eq. (10.2) the Swain-Schaad relation is independent of temperature. We first examine the symmetric case AGrxn = 0, for which the adiabatic PT expression via Eq. (10.15) shows that the magnitude is related solely to the reactant and TS ZPE difference. These ZPE differences were shown to obey the same mass scaling used to derive the Swain-Schaad relations, cf Eq. (10.16) hence the Fig. 10.10(b) plot maximum is dose to the traditionally expected value. While Fig. 10.10(b) also shows that there is a small variation with reaction asymmetry, in the adiabatic PT perspective, of the Swain-Schaad slope. This has a minimal net effect, however, as discussed in Ref. 

Kinetic Isotope Effect Magnitude and Variation with Reaction Asymmetry... 

Before presenting the KIE variation with reaction asymmetry for nonadiabatic PT, it will prove useful to first discuss the individual isotope PT rate constant Eq. (10.36) s variation with reaction asymmetry, which must include tunneling prefactor terms as well as the activation free energy. This behavior was analyzed up through quadratic terms in [5] to find... 

For illustrative purposes, the same system as in Fig. 10.16 was taken, and T was varied (T = 300-350 K), while keeping the reaction asymmetry constant, AGrxn = 0- The apparent Arrhenius rate and KIE behavior obtained in this limited T range are displayed in Fig. 10.19. The apparent activation energies for H and D differ considerably, with almost twice Ea E = 5.7 kcal moH and Ead = 10.6 kcal moki this results in a significant effective activation energy for the KIE Efijo - E u = 5.0 kcal moTi, displayed in Fig. 10.19(b). These slopes can be quantitatively analyzed [5] to determine the contributions from the H-bond and proton vibration excitations. 

Ead = 11.2 kcal mol 1, which differ by less than 10% from the obtained numerical values. The decomposition of these apparent activation energies via Eq. (10.46) is useful [5] in determining which contributions are most important and how these contributions change with T, tuoQ, reaction asymmetry, and solvent reorganization energy Fg, as now reviewed. 

The second term in Eq. (10.53), the activation free energy barrier AGI lo.o- is for the present system also significant for both H (39%) and D (25%). Of course, the magnitude of this term changes ivith reaction asymmetry, decreasing as the reaction goes from endo to exo-thermic (cf. Eq. (10.33)). 

Excited state contributions described by Pi have a key characteristic in that they increase with increased reaction asymmetry AG])xn decreased reorganization energy Eg [5]. Eurthermore, the isotopic disparity pu< also increases with these trends, resulting in an increase in significance of the third difference in Eq. (10.55) with increased AGrxn 3tid decreased Eg [5]. 

The Marcus relation, Eq. (19.6), is clearly not a linear relationship between the activation energy and the reaction asymmetry but a quadratic one. The first derivative of AEt with respect to is equivalent to the Bronsted coefficient a in Eq. 

It turns out that charge-transfer reactions, such as this, follow the linear response approximation in solution [51a, 52] and in enzymes [50a, 53], meaning that the diabatic energy curves are quadratic. Consequently, the (kinetic) activation free energy on the adiabatic surface is related to the (thermodynamic) reaction asymmetry according to Eq. (19.12). 

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