Electronuclear basis for three-dimensional electronic nonadiabatic chemical reactions

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Abstract
The quantum mechnical theory of electronic nonadiabatic atom–diatomic molecule reactive collisions in three dimensions is discussed with emphasis on the reaction F(2P3/2,2P1/2)+H2(1Σ+g,v,j). It is known that the first two excited electronic adiabatic surfaces of the FH2 system are very close to the ground state surface at large F–H2 distances. Only the ground state surface, however, can lead to reaction at subdissociative energies. The importance of considering the exchange of flux between these surfaces is discussed. An electrorotational basis set {ΩJMα} is formulated for use in a quantum mechanical, reactive scattering calculation for systems of this type. These basis functions are formed by starting with good total angular momentum (nuclear plus electronic) kets in the space‐fixed frame. Then, these functions are written in terms of the body‐fixed natural collision (NCC) coordinates, and the Euler angles that orient the body frame with respect to the space frame. One feature of the {ΩJMα} setting them apart from other basis sets typically used in scattering calculations is that they cannot be factored into products of nuclear and electronic parts. It is then shown how the ΩJMα may be written in terms of adiabatic electronic basis functions used in the ’’diatomics‐in‐molecules’’ (DIM) treatment of atom–diatom systems. By writing the {ΩJMga} in terms of DIM basis functions, matrix elements of the type 〈ΩJMα′‖Ĥel‖ΩJMα〉 are evaluated as linear combinations of pure electronic matrix elements of Ĥel in the DIM basis. Four nonmixing parity types are found for the ΩJMα. Plots of selected matrix elements 〈ΩJMα′‖Ĥel‖ΩJMα〉 as functions of the reaction coordinate s and vibrational coordinate ρ are presented for F+H2. Matrix elements of T̂rot (the nuclear rotational kinetic energy operator expressed in NCC) are also evaluated in the electrotational basis. The method of conversion from the electrotational basis to an adiabatic electronic basis is formulated. This transformation should be useful after the system passes the zone where electronic transitions are significant.