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This chapter concentrates in the computation of rate constants of elementary chemical reactions with accurate quantum wave packet theories, with special focus on the derivation of the rate constant for nonadiabatic reactive systems from our recently developed nonadiabatic quantum wave packet theories and related computational codes, in parallel with some progresses in electronic structure theory and computational capacity. In nonadiabatic chemical reactions, the strong interaction among multiple electronic states leads to a breakdown of the Born–Oppenheimer approximation in describing quantum reaction dynamics and electronically nonadiabatic transitions contribute to the underlying mechanism. Our developed nonadiabatic wave packet theories can treat the electron-nuclei coupled motion dynamics arising from strong nonadiabatic couplings well, providing an efficient computational tool with which to obtain accurate rate coefficients for nonadiabatic chemical reaction. Illustrations of the quantum wave packet theories, particularly the nonadiabatic ones, in predicting rate constants for tri-atomic, tetra-atomic and polyatomic reactions are shown, in conjunction with our efforts on developing a tetra-atomic diabatic potential matrix. Comparisons are also made to existing experimental and calculation data. This has provided much more information on rate constants and improved our understanding of the adiabatic quantum reaction dynamics and the nonadiabatic quantum reaction dynamics that are quite beyond the Born-Oppenheimer approximation.

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