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Curvature-driven approximations provide an appealing alternative by evaluating TDCs from adiabatic potential energies or gradients along nuclear trajectories, motivated by the one-dimensional Baeck\u2013An model. In this work, we examine curvature-based TDC approximations within trajectory surface hopping (TSH) and coherent switching with decay of mixing (CSDM), and introduce a modified gradient-based curvature-only formulation that retains the directional-curvature contribution to the TDC while omitting the explicit acceleration-dependent term at all times in the coupling evaluation. The performance of energy-based, gradient-based, and curvature-only TDCs is evaluated for four benchmark systems of increasing dynamical complexity: ethylene, DMABN, fulvene, and SO2. For ethylene, all curvature-driven schemes closely reproduce reference dynamics obtained with analytic nonadiabatic couplings. For DMABN and fulvene, which involve repeated nonadiabatic passages and back-transfer, the curvature-only approximation yields improved agreement with reference populations by reducing overpopulation effects observed with standard curvature formulations. In the multistate singlet\u2013triplet dynamics of SO2, standard curvature-based TDCs introduce spurious population transfer to the ground state, an artifact that is significantly decreased by the curvature-only scheme in both TSH and CSDM. Overall, the results show that removing the acceleration-dependent contribution leads to a more robust curvature-driven TDC approximation across a wide range of nonadiabatic regimes, while retaining the conceptual simplicity and efficiency of curvature-based approximations.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c01219","type":"journal-article","created":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T11:01:31Z","timestamp":1789038091000},"page":"9290-9301","source":"Crossref","is-referenced-by-count":0,"title":["Gradient-Based\nCurvature-Only Time-Derivative Coupling\nfor Surface Hopping and Coherent Switching with Decay of Mixing: Application\nto SO2 and Molecular Tully Models"],"prefix":"10.1021","volume":"22","author":[{"given":"Feven-Alemu","family":"Korsaye","sequence":"first","affiliation":[{"name":"University of Vienna , , Wa\u0308hringer Stra\u00dfe 17 , ,","place":["Vienna, Austria, 1090"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5112-794X","authenticated-orcid":true,"given":"Leticia","family":"Gonza\u0301lez","sequence":"additional","affiliation":[{"name":"University of Vienna , , Wa\u0308hringer Stra\u00dfe 17 , ,","place":["Vienna, Austria, 1090"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,10]]},"reference":[{"key":"2026092209073361800_cit1","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1063\/1.459170","article-title":"Molecular\ndynamics with electronic transitions","volume":"93","author":"Tully","year":"1990","journal-title":"J. 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