A strict and internally consistent diabatic representation for coupled <i>N</i>-state diatomics: A hybrid asymptotic-property-based diabatization method

A robust regularization procedure for the radial non-adiabatic coupling (NAC) elements of the diatomic nuclear kinetic energy operator for the N-state diatomic problem is presented. This method ensures NACs are internally consistent with each other and with corresponding adiabatic properties, such as potentials or dipoles. Constructing a diabatic representation-where all components of the (radial) nuclear derivative couplings vanish-that is both physical and exactly equivalent to the adiabatic representation can be impossible due to inconsistencies between NACs and adiabatic properties. Such discrepancies arise from using different theory levels in ab initio molecular property calculations, convergence issues in quantum chemistry calculations, post-processing adjustments to computed property curves, and truncation errors when considering only a finite number of Born-Oppenheimer states. The presented regularization procedure leverages a hybrid asymptotic-property-based diabatization (HyAP), where the asymptotic behavior of diabatic properties is addressed and their smoothness maximized simultaneously. This is achieved through optimization of the trajectory of the adiabatic to diabatic transformation (AtDT) parameterized by the corresponding generator matrices (exponential mapping). The presented methodology is applied to the 3-state system of N2 [1Σ+1, 2Σ+1, and 3Σ+1] and the 4-state system of CH [CΣ+2, 2Σ+2, 3Σ+2, and 4Σ+2] via evolution of the AtDT, where a physical diabatization is achieved. The HyAP regularization, developed and tested for applications in spectroscopy, is guided by underlying electronic structure data to fulfill our pragmatic aim of constructing physical diabatic representations that effectively controls bound rovibronic molecular spectroscopy while remaining exactly equivalent to the adiabatic representation.