| In the recent years, experimental chemists have found that transition-metal cations M+ and their oxide cations MO+ have peculiar activations to the N-O, C-C and C-O bonds of small compounds in the gas phase using an inductively-coupled plasma selected-ion flow tube (ICP/SIFT) tandem mass spectrometer. Recently, theoretical approaches to gas-phase transition-metal chemistry indicated that often the reactants, possible intermediates, and products had ground states of different spin multiplicities, and the transformations of spin multiplicities occurs frequently in reactions. Namely, the reactions did not obey"spin conservation law". Although the necessity to explicitly consider surface hopping as a mechanistic step in chemistry was pointed out more than 10 years ago, the assumptions of either strict spin conservation or its complete neglect prevailed until 1994. This was in part due to difficulties in the appropriate theoretical descriptions of spin crossover in polyatomic metal compounds and, more importantly, the lack of unambiguous experimental examples for a violation of spin conservation along the reaction path, which provoked the necessity to tackle"two-state reactivity (TSR)". This was in part due to the restriction of experimental conditions in the early phases and, more importantly, the dominant status of spin conservation along the reaction path. Today, TSRs have attracted a great deal of interest in the world for the sake of exact reaction mechanisms. In this paper, we chose several typical reactions(Ir+,FeO+with N2O and CO)which have been carefully studied using quantum methods, obtained some interesting results.In the paper, on the basis of the molecular orbital theory, the tradition transition state theory as well as Armentrout,B?hme,Schwarz and Schr?der's experimental results, the systems choosed have been carefully investigated using Density Functional (DFT) Methods. The structures of the reagents, the reaction products and the transition states along the reaction paths have been obtained, then obtained the reaction surfaces, the spectrum datum, the thermodynamic datum as well as the information of orbitals. The reaction mechanism has been argued deeply using these data.The whole paper consists of four chapters. Chapter 1 describes the progeess and application of quantum chemistry as well as the development and the present situation of two-state reactivity (TSR). In Chapter 2, introduces elementary theory and quantum chemistry computation methods, which mainly contained the reaction surface, crossing rules of the potential energy surfaces, tradition transition state theory, spin-orbit coupling mechanism, rules for intersystem crossing and natural bond orbital theory. The contents of the two chapters were the basis and background of our studies and offer us with useful and reliable quantum methods.In Chapter 3, 4, the reactions of Ir+,FeO+ with N2O and CO , which are selected as a representative system of reactions of the third and first-row lately transition-metal ions and oxide ions with N2O and CO, have been studied carefully using UB3LYP methods. The activation of C-O bonds, N-O bonds and ability of O capture by transition-metal ions and oxide ions have been emphasized. The involving potential energy surface crossing has been discussed detailedly. We have analyzed potential energy surfaces (PES) crossing scenario, and have found the CPs by means of single-point computations. In the study courses, Firstly, the O-atom affinities of the correlative species were calculated, which testified that the cyclic, catalytic function of Ir+ and FeO+ were thermodynamically allowed. Secondly, the reaction path channels have been studied on the two potential energy surfaces (PESs). Thirdly, the PES crossing dramatically affecting reaction efficiency and the reaction rate has been studied by means of the Hammond postulate and the intrinsic reaction coordinate (IRC) approach used by Yoshizawa et.al. and a series of crossing points (CPs) involving the structures and energy values have been located. Finally, in order to have a deep understanding of the spin inversion, we discuss the action of frontier molecular orbital for CP, and calculating natural population of the species for the best reaction channel by NBO analysis.
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