A perspective on phase space electronic structure theory—from its surface hopping origins to its future promise

We trace the history of phase space electronic structure theory (PSEST), highlighting how this powerful approach emerged from fundamental questions in semiclassical surface hopping dynamics and evolved into an alternative to standard Born–Oppenheimer-based electronic structure theory (with moving instead of frozen nuclei). Our goal herein is not to recapitulate the mathematical details of phase space electronic structure calculations, and few equations are presented so as to maximize readability. Instead, our goal is to provide intuition for those new to the field—both (i) regarding the physics present when solving the Schrödinger equation in a non-inertial frame and (ii) regarding why PSEST is a necessary step forward toward understanding chemical problems involving spin (with limited practical alternatives). We further highlight some of the many open questions in this fast developing area, which will hopefully inspire new practitioners in this field. This intuitive perspective lacks many equations and is meant to complement (rather than replace) the more technical review given in Bian et al. [Chem. Phys. Rev. 7, 011303 (2026)].