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Although models have been developed to understand cavity-modified reactions, fully quantum mechanical simulations remain out of reach for the collective regime that involves many molecules, a critical aspect of the phenomenon. Mixed quantum\u2013classical (MQC) simulations offer a scalable alternative, but their accuracy requires testing and potential improvements even in the single-molecule limit. In this work, we take this step by first introducing the mapping approach to surface hopping (MASH) to address the limitations of traditional MQC methods. Second, we incorporate a quantum treatment of the cavity mode, moving beyond the classical approximations often employed in previous studies. Results for a single-molecule model of vibrational polaritonic chemistry show that combining MASH with a quantum cavity mode yields the most accurate rates. However, this scheme may produce different long-time population dynamics at zero coupling depending on whether the cavity mode is quantized; a problem known as size-inconsistency in MASH. We address this problem by proposing the \u025b-MASH approach, which forbids hopping between states with negligible nonadiabatic couplings (NACs). Combining MASH with a quantum cavity mode thus provides a promising approach for scalable and accurate MQC simulations in the collective regime.<\/jats:p>","DOI":"10.1063\/5.0314264","type":"journal-article","created":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T13:28:57Z","timestamp":1772717337000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Toward accurate mixed quantum classical simulations of vibrational polaritonic chemistry"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2056-9942","authenticated-orcid":false,"given":"Muhammad R.","family":"Hasyim","sequence":"first","affiliation":[{"name":"Simons Center for Computational Physical Chemistry, New York University 1 , New York, New York 10003,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9088-2980","authenticated-orcid":false,"given":"Arkajit","family":"Mandal","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Texas A&M University 2 , College Station, Texas 77840,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5265-5637","authenticated-orcid":false,"given":"David R.","family":"Reichman","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Columbia University 3 , New York, New York 10027,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,3,5]]},"reference":[{"key":"2026030508285108100_c1","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1146\/annurev-physchem-082620-014627","volume":"73","year":"2022","journal-title":"Annu. 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