Formation of enantiomeric excess upon irradiation

All the three scenarios of formation of enantiomeric excess (EE) in racemic mixtures exposed to circularly polarized light or subjected to beta-radiol ysis are considered. The major dimensionless parameters allowing for the EE value and dynamics of EE accumulation are chiral polarization (CP) eta = D -L/D+L, where D and L are the concentrations of enantiomers, and advantage factor (AF) g = k(D)-k(L)/k(D)+k(L), where k(D) and k(L) are the rate const ants for mirror conjugate reactions of D and L enantiomers. Dynamic equations eta(tau) governing asymmetric destruction of the enantiom ers, their racemization, and synthesis from the achiral substrate are prese nted. Racemizing processes, if any occur ((eta) over dot = -kappa eta), imp ose severe restrictions on the stationary CP values: eta((s)) less than or equal to g similar to 10(-2) (for CPL; for beta-radiolysis, g much less tha n 10(-2)); at g much greater than kappa, there may form transition states s uch that eta(max) much greater than eta((s)). It is emphasized that there i s a fundamental difference between EE accumulation, i.e., conversion of rac emic mixtures into mixtures of "dominant" and "recessive" enantiomers, and attainment of chiral purity of an optically active system. In actual conditions, racemizing processes dominate over AF (g much less th an a), and chiral purity is attainable only by the bifurcation mechanism, i .e., through spontaneous breaking of mirror symmetry. This peculiar sort of phase transition can occur even at g = 0. The evolutionary way of attaining chiral purity is through gradual accumula tion of EE, which is possible in the case that racemizing processes are sup pressed almost completely (9 much greater than kappa). In this context, of particular interest is the impact of local and global a symmetric factors on systems amenable to optical activation at very low tem peratures, when all thermally activated processes are suppressed, and in ad dition, tunneling racemization is considerably inhibited by interactions of chiral molecules with cold environment.