Extension of the fourfold way for calculation of global diabatic potential energy surfaces of complex, multiarrangement, non-Born–Oppenheimer systems: Application to HNCO(S,S1)

The fourfold way is a general algorithm for generating diabatic electronic wave functions that span the same space as a small set of variationally optimized adiabatic electronic wave functions and for using the resulting diabatic wave functions to generate diabatic potential energy surfaces and their couplings. In this paper we extend the fourfold way so it is applicable to more complex polyatomic systems and in particular to the calculation of global potential energy surfaces for such systems. The extension involves partitioning the active space into three blocks, introducing restricted orbital rotation within two of the blocks, introducing a specific resolution of the subspace containing molecular orbitals that are doubly occupied in all dominant configuration state functions, and introducing specific orientations of the coordinate systems for reference molecular orbitals and resolution molecular orbitals. The major strength of the improved method presented in this paper is that it allows the diabatic molecular orbitals to exhibit a gradual change of chemical character with smooth deformation along the reaction coordinate for a change of chemical arrangement while preserving the orbital character required for a physical ordering of the orbitals. This feature is required for the convenient construction of global potential energy surfaces for non-Born–Oppenheimer rearrangements. The resulting extended algorithm is illustrated by calculating diabatic potential energy surfaces and couplings for the two lowest singlet potential energy surfaces of HNCO.