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Building on our previous work [Tsai et al., J. Phys. Chem. Lett. 14, 5924 (2023)], we extend the theory of the QED-NAE rate from a single cavity photonic mode to infinite photonic modes and calculate the QED-NAE rates of 9-cyanoanthracene at the first-principles level. To avoid the confusion, the quantum electrodynamic internal conversion process is renamed as \u201cQED-NAE\u201d in our present work. According to our theory, we identify three key factors influencing the QED-NAE processes: light\u2013matter coupling strength (mode volume), mass-weighted orientation factor, and photonic density of states. The mode volume is the primary factor causing rate differences between the two scenarios. In a single cavity with a small mode volume, strong light\u2013matter coupling strength boosts QED-NAE rates. In contrast, in free space with infinite photonic modes, weak coupling strength significantly reduces these rates. From a single cavity photonic mode to infinite photonic modes, the mass-weighted orientation factor only causes an 8\u03c0\/3-fold increase in the QED-NAE rate. In free space, the photonic density of state exhibits a flat and quadratic distribution, which slightly reduces the QED-NAE rate. Our study shows that cavities can significantly enhance non-adiabatic QED effects while providing a robust analysis demonstrating that QED vibronic effects can be safely ignored in free space.<\/jats:p>","DOI":"10.1063\/5.0238657","type":"journal-article","created":{"date-parts":[[2025,1,15]],"date-time":"2025-01-15T10:58:26Z","timestamp":1736938706000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Non-adiabatic quantum electrodynamic effects on electron\u2013nucleus\u2013photon systems: Single photonic mode vs infinite photonic modes"],"prefix":"10.1063","volume":"162","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-4338-8094","authenticated-orcid":false,"given":"Chih-En","family":"Shen","sequence":"first","affiliation":[{"name":"Institute of Atomic and Molecular Sciences, Academia Sinica 1 , Taipei 10617,","place":["Taiwan"]},{"name":"Department of Chemistry, National Taiwan University 2 , Taipei 10617,","place":["Taiwan"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-3182-704X","authenticated-orcid":false,"given":"Hung-Sheng","family":"Tsai","sequence":"additional","affiliation":[{"name":"Institute of Atomic and Molecular Sciences, Academia Sinica 1 , Taipei 10617,","place":["Taiwan"]},{"name":"Department of Chemistry, National Taiwan University 2 , Taipei 10617,","place":["Taiwan"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9165-1033","authenticated-orcid":false,"given":"Liang-Yan","family":"Hsu","sequence":"additional","affiliation":[{"name":"Institute of Atomic and Molecular Sciences, Academia Sinica 1 , Taipei 10617,","place":["Taiwan"]},{"name":"Department of Chemistry, National Taiwan University 2 , Taipei 10617,","place":["Taiwan"]},{"name":"Physics Division, National Center for Theoretical Sciences 3 , Taipei 10617,","place":["Taiwan"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2025,1,15]]},"reference":[{"key":"2025011510582028900_c1","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1039\/df9500900014","volume":"9","year":"1950","journal-title":"Discuss. 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