Hybridization kinetics second-order

Me2pyo[14]trieneN4 (CR) ligand (Fig. 6a) catalyzes the hydrolysis of the triester diphenyl 4-nitrophenyl phosphate in aqueous acetonitrile solution.221 This reaction is first-order in zinc complex and phosphate ester. On the basis of pH-rate studies, which revealed a kinetic pifa value of 8.7,40 the active zinc complex is proposed to be [(CR)Zn-OH]+. A hybrid mechanism in which the zinc center of [(CR)Zn-OH]+ serves to provide the hydroxide nucleophile, and also electrophilically activates the phosphoryl P O bond, is favored for this system. This type of bifunctional mechanism was proposed based on the fact that the second-order rate constant for the [(CR)Zn-OH]+-catalyzed reaction (2.8 x 10 1 M-1 s 1) is an order of magnitude larger than that of free hydroxide ion-catalyzed hydrolysis (2.8 x 10 2M 1 s 1). As OH- is a better nucleophile than the zinc-coordinated hydroxide, Lewis acid activation of the substrate is also operative in this system. 

Kinetic studies of the reaction of a mononuclear N2S(thiolate)-ligated zinc hydroxide complex (PATH)Zn-OH with tris(4-nitrophenyl) phosphate in 33% ethanol-water and 7=0.10 (NaN03) also point to a hybrid-type mechanism (Fig. 43).228 Overall, this reaction is second order and a pH-rate profile indicates that the zinc hydroxide species (PATH)Zn-OH is involved in the reaction. The maximum rate constant for this reaction (16.1(7) M-1 s-1) is higher than that reported for free hydroxide ion (10.7 +0.2 M 1 s-1).225 This implies that a simple mechanism involving nucleophilic attack is not operative, as free OH- is a better nucleophile. Studies of the temperature dependence of the second-order rate constants for this reaction yielded activation parameters of A77 = 36.9(1) kJ mol-1 and AS = —106.7(4) JmolK-1. The negative entropy is consistent with considerable order in the transition state and a hybrid-type mechanism (Fig. 43, bottom). 

In order to make improvements over the LSDA, one has to assume that the density is not uniform. The approach that has been taken is to develop functionals that are dependent on not only the electron density but also derivatives of the density. This constitutes the generalized gradient approximation (GGA) and is the second rung on Jacob s Ladder. The third rung, meta-GGA functional, includes a dependence on the Laplacian of the density (V p) or on the orbital kinetic energy density (t). The fourth row, the hyper-GGA or hybrid functionals, includes a dependence on exact (HF) exchange. Finally, the fifth row incorporates the unoccupied Kohn-Sham orbitals. This is most widely accomplished within the so-called double hybrid functionals. 

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