Effective Two-State Model Based on Adiabatic-to-Diabatic Transformation

A novel effective two-state model is proposed and applied to several multistate interacting systems. In this model, two effective diabatic states are obtained from a pair of adiabatic wave functions, and the adiabatic-to-diabatic (ATD) transformation matrix is deduced from two kinds of coefficients, i.e., the configuration interaction expansion coefficients of the adiabatic states and the partitioning coefficients, where the latter is also deduced from the former. The model is very simple but might be quite useful since it is available not only for constructing effective diabatic wave functions but also for evaluating various diabatic properties including energy, electronic coupling, potential energy surfaces (PESs) and their crossings, etc. A series of molecules, [NH₂-(CH₂)_n-NH₂]⁺, n = 1, 2, . . ., 5, the hydrogen abstraction (H-abstraction) reaction and the semiglobal PESs in H₃, and the Diels-Alder reaction of 1,3-butadiene and ethylene were used as test examples to display the versatility of the model. Moreover, the effects of electronic coupling on the barriers and the chemical reactivity of reactions in the test molecules are also discussed. Therefore, the effective two-state model can serve as a practical theoretical tool for analyzing bridge-assisted multistate electron transfer (ET) reactions and chemical reactions that involve simultaneous bond-breaking and bond-making.