Exact Rovibronic Equivalence of the Adiabatic and Diabatic Representations of N $$ N $$ -Coupled State Diatomic...

The Born-Oppenheimer approximation assumes nuclear motion evolves on single, uncoupled potential energy surfaces, widely used to solve the time-independent Schrödinger equation for atomistic systems. However, for near-degenerate same-symmetry electronic states, avoided crossings in the potential energy curves occur and non-adiabatic couplings (NACs) become significant. In such cases, the adiabatic approximation is unsuitable for high-resolution spectroscopy. A unitary transformation to the diabatic representation can eliminate NACs, resulting in smooth molecular property curves that may cross. Computing this adiabatic-to-diabatic transformation (AtDT) is desirable but non-analytic for multi-state coupled systems, necessitating numerical solutions. It remains unclear if current methods yield numerically exact AtDTs ensuring rovibronic energy level equivalence between adiabatic and diabatic pictures. We demonstrate (for the first time) numerically exact equivalence of adiabatic and diabatic representations for $N$ -state diatomic molecules using ab initio data for $N_2$ , CH, and a model 10-state system. We show how the equivalence can be efficiently used to assess the importance of non-adiabatic effects and the impact of omitting them when computing rovibronic energies of diatomic molecules. The adiabatic and diabatic representations of the spectroscopic model, including all coupling terms, have been implemented in the diatomic code Duo.