Basis set methods for calculating dynamic polarizabilities and excitation energies via coupled Kohn–Sham equations within time-dependent density functional theory are introduced. The methods can be employed after solving the ground state Kohn–Sham equations with a fitting function approach. Successful applications of the methods to test molecules are presented. Coupled Kohn–Sham methods based on the linear response of the Kohn–Sham density matrix are derived from the standard coupled Kohn–Sham equation based on the linear response of the electron density and the relations between the two types of coupled Kohn–Sham equations are investigated. The choice of norm functions associated with basis set representations of the coupled Kohn–Sham equations is discussed and shown to be a critical point of basis set approaches to time-dependent density functional theory.

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New very effective results on the liquid-phase oxidation of cyclohexene to cyclohexanone by nitrous oxide are analyzed using the B3LYP/6-31G* approximation to predict a two-step reaction mechanism correlated with the experimental data.

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The various quantum chemical models of catalytic active site in Cu-ZSM-5 zeolites are analyzed. The density functional theory (DFT) is used to calculate the electronic structure of molecular cluster (HO) 3 Al-O-Cu-O-Cu modeling the catalytic active site in Cu-ZSM-5 zeolites and study the interaction and decomposition of NO. It is assumed that the rate-determining stage of the low-temperature selective catalytic reduction of NO is the formation of the π-radical (N 2 O 2 ) -on electron donor sites of Cu-ZSM-5 catalysts. This is in good agreement with the high electron affinity of the molecular dimer ONNO (E a ) -1.5 eV) and is confirmed by the experimental data on the formation of surface anion π-radical (N 2 O 2 ) -on electron donor sites of supported organo-zirconium surface complex. The DFT calculated electronic structure and excitation energy spectra for the model system (HO) 3 Al-O-Cu-O-Cu show that it is a satisfactory model for description of experimental UV-vis spectra of Cu-ZSM-5, containing (-O-Cu-O-Cu-) chain structures in the zeolite channels. The calculated reaction energy profile of ONNO adsorption and decomposition on the model catalytic active site shows the possibility of the low-temperature decomposition of dimer (NO) 2 with low activation energy and the important role of copper oxide chains (-O-Cu-O-Cu-) in the channels of Cu-ZSM-5 zeolite during selective reduction of NO.