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We focus on a conical intersection involving two collective modes tuning the energy of each excited state, and we revisit the transformation of the initial correlated tuning baths to de-correlated shared baths in order to reduce the computational resources. While a completely frequency-dependent transformation poses problems for HEOM, we find that in some particular cases, an optimal approximate frequency-independent transformation may be derived. On the contrary, T-TEDOPA is very efficient and allows us to use this frequency-dependent transformation at the price of managing long-range couplings in the tensor chain. An illustrative application is shown by using the linear vibronic coupling model of a planar symmetrical (phenylethynyl)benzene dimer.<\/jats:p>","DOI":"10.1063\/5.0340260","type":"journal-article","created":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T12:21:43Z","timestamp":1782908503000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Revisiting crossed-correlated baths in open quantum systems simulated by HEOM or T-TEDOPA"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6004-0758","authenticated-orcid":false,"given":"Brieuc","family":"Le D\u00e9","sequence":"first","affiliation":[{"name":"Institut des Nanosciences de Paris, Sorbonne Universit\u00e9, CNRS 1 , F-75005 Paris,","place":["France"]},{"name":"Department of Chemistry and Biochemistry, University of California 2 , Merced, California 95343,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1640-6713","authenticated-orcid":false,"given":"Etienne","family":"Mangaud","sequence":"additional","affiliation":[{"name":"MSME, Universit\u00e9 Gustave Eiffel, UPEC, CNRS 3 , F-77454 Marne-La-Vall\u00e9e,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7741-5915","authenticated-orcid":false,"given":"Alex W.","family":"Chin","sequence":"additional","affiliation":[{"name":"Institut des Nanosciences de Paris, Sorbonne Universit\u00e9, CNRS 1 , F-75005 Paris,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6199-7401","authenticated-orcid":false,"given":"Mich\u00e8le","family":"Desouter-Lecomte","sequence":"additional","affiliation":[{"name":"Institut de Chimie Physique, Universit\u00e9 Paris-Saclay-CNRS, UMR8000 4 , F-91400 Orsay,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,7,1]]},"reference":[{"key":"2026070108043601100_c1","volume-title":"The Theory of Open Quantum Systems","year":"2002"},{"key":"2026070108043601100_c2","volume-title":"Quantum Dissipative Systems","year":"2012"},{"key":"2026070108043601100_c3","volume-title":"Charge and Energy Transfer Dynamics in Molecular Systems","year":"2011"},{"key":"2026070108043601100_c4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/revmodphys.59.1","article-title":"Dynamics of the dissipative two-state system","volume":"59","year":"1987","journal-title":"Rev. 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