On the Nonparametric Diabatization of Coupled Electronic States

The construction of quasi-diabatic potential energy matrices (DPEMs) from realistic adiabatic electronic structure data, a process also known as diabatization, is crucial for simulating quantum nonadiabatic molecular dynamics that goes beyond toy models. However, there is neither a unified approach to diabatization nor a reliable way to assess the quality of a DPEM due to the inherent nonuniqueness of the diabatic representation. In this paper, we introduce a method to obtain DPEMs solely from the definition that the diabatic wavefunctions must be smooth. The method relies on electronic properties (e.g., dipole moments) that are usually computed during electronic structure calculations at a negligible additional cost. We achieve nonparametric diabatization by enforcing the smoothness of diabatic molecular property functions through the minimization of a Lipschitz-type metric with mixed-integer programming. Importantly, this metric also provides a general and quantitative measure for systematically evaluating the quality of any DPEM. The method is demonstrated on a realistic molecular system.