Toward Community-Driven Benchmarking and Ranking of Nonadiabatic Dynamics Methodologies

Assessment, benchmarking, and ranking of nonadiabatic quantum dynamics (NAQD) methods have long fascinated researchers and stimulated comprehensive assessment works. However, only recently has the NAQD community begun to move toward a consistent, systematic, and genuinely community-driven approach to this challenging problem. Progress in this direction requires establishing a coherent framework for assessing NAQD methodologies. This perspective focuses on such evaluation strategies. The concepts of the test case is introduced along with the metrics for quantifying test-case complexity and evaluating errors of NAQD methods, including Shannon and Kozachenko-Leonenko entropies. It is argued that reduced density-matrix-based error metrics may be preferable to those derived from other properties or observables, and several specific approaches are compared. The application of the Elo concept in the context of NAQD method assessment is demonstrated, and further improvements are discussed. Finally, an Elo-N-Tasks platform for a semiautomated community-driven ranking of methods and test-cases is proposed.