By taking the energy to be a Morse-like function of the number of electrons, E(N) = α{1 - e(-β(N-δ))}(2) - κ, the electronic chemical potential and global hardness values for a set of atoms and some molecules are calculated from the accurate definitions of these two concepts and using the hybrid B3LYP functional and 6-311++G** basis set. By a comparison between the obtained hardnesses and the corresponding experimental values, it is found that the proposed model yields better values for hardnesses with respect to those that are obtained from the other frequently used methods. It is claimed that the difference between the calculated and experimental hardness values may arise from the approximate equation used for the evaluation of experimental hardnesses. Both of the calculated and experimental molecular hardnesses are used to investigate the change of hardness during the course of some exothermic reactions according to the maximum hardness principle (MHP). It is shown that the obtained hardnesses of reactions from the calculated hardnesses (Δη(calc)) are more successful in predicting the directions of these reactions than those that are evaluated from the experimental hardnesses (Δη(exp)).

Effect of a range of t-butyl perbenzoates bearing electron-withdrawing and electron-donating substitutions on the phenyl ring and HZSM-5 as a porous additive at 0 °C in enantioselective allylic C–H bond oxidation of cyclic and acyclic olefins in the presence of Cu (I)-(S,aS,S) complexes of biphenyl bisoxazoline ligands, produced easily through the chelation-induced process, were investigated. The enantioenriched allylic esters were obtained in reasonable times with excellent enantioselectivities and yields using electron-withdrawing substituted peresters in the presence of Cu (I)-(S,aS,S)-1a complex, containing phenyl groups at the stereogenic centers of the oxazoline moieties. To reach a better insight on geometry, chemical activity, enantioselectivity, and thermodynamic stability of the Cu (I)-BOX complexes, DFT calculations with B3LYP-D3/6-31G (d, p) level of theory were applied to them. Moreover, NBO analysis was used to illustrate interactions between orbitals.

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