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This leads to a Hermitian QED-TDDFT coupling matrix that is expected to facilitate the future development of analytic derivatives. Through a Gaussian atomic basis implementation of the QED-TDDFT method, we examined the effect of dipole self-energy, rotating-wave approximation, and the Tamm\u2013Dancoff approximation on the QED-TDDFT eigenstates of model compounds (ethene, formaldehyde, and benzaldehyde) in an optical cavity. We highlight, in the strong coupling regime, the role of higher-energy and off-resonance excited states with large transition dipole moments in the direction of the photonic field, which are automatically accounted for in our QED-TDDFT calculations and might substantially affect the energies and compositions of polaritons associated with lower-energy electronic states.<\/jats:p>","DOI":"10.1063\/5.0057542","type":"journal-article","created":{"date-parts":[[2021,8,11]],"date-time":"2021-08-11T09:54:06Z","timestamp":1628675646000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":75,"title":["Quantum-electrodynamical time-dependent density functional theory within Gaussian atomic basis"],"prefix":"10.1063","volume":"155","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6726-6538","authenticated-orcid":false,"given":"Junjie","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Chemistry and Biochemistry, University of Oklahoma 1 , Norman, Oklahoma 73019, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6400-7522","authenticated-orcid":false,"given":"Qi","family":"Ou","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University 2 , Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zheng","family":"Pei","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University 3 , Xiamen 361005, People\u2019s Republic of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9436-4013","authenticated-orcid":false,"given":"Hua","family":"Wang","sequence":"additional","affiliation":[{"name":"Homer L. 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