Critical Assessment of Curvature-Driven Surface Hopping Algorithms

Trajectory surface-hopping (TSH) methods have become the most used approach in nonadiabatic molecular dynamics. The increasingly popular curvature-driven schemes represent a subset of TSH based on the implicit local diabatization of potential energy surfaces. Their appeal partly stems from compatibility with machine-learning frameworks that often provide only local PES information. Here, we critically assess the limitations of these curvature-based algorithms by examining three challenging scenarios: (i) dynamics involving more than two strongly coupled electronic states; (ii) trivial crossings; and (iii) spurious transitions arising from small discontinuities in multireference potential energy surfaces. Furthermore, we extend the Landau-Zener surface hopping (LZSH) method beyond two-state systems and introduce practical modifications to enhance its robustness. The performance is benchmarked on both low- and higher-dimensional model Hamiltonians, as well as realistic molecular systems treated with <i>ab initio</i> methods. While curvature-driven TSH using the explicit electronic coefficient propagation qualitatively captures the dynamics in most cases, we find no regime where it outperforms LZSH, especially when trivial crossings, multistate crossings, or discontinuities are encountered. Hence, we advocate for using a conceptually simple but solid LZSH method when nonadiabatic couplings are not available.