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The resulting Q-ADC(2) method explicitly accounts for both opposite-spin and same-spin contributions, thereby retaining a fully ab\u00a0initio nature. The approach is based on a seminumerical decomposition of the four-index electron-repulsion integrals into products of molecular-orbital amplitudes evaluated on a molecular integration grid and a three-center electric-field integral over the remaining orbital pair. In combination with a Laplace transform treatment of the energy denominators, this enables more efficient contraction schemes through decoupling of orbital indices. Construction of the large virtual-virtual block of the three-index integrals is avoided, improving computational efficiency. In addition, the formulation is well suited for parallelization on distributed-memory architectures. A mixed-order Q-ADC(2\/1) scheme is developed, providing access to ground-to-excited-state transition moments at an additional computational cost that scales only cubically. The accuracy of the method with respect to ADC(2) is assessed for excitation energies and oscillator strengths across different molecular integration grids. Its applicability is further demonstrated by calculations on larger representative fluorophores with up to 2806 basis functions.<\/jats:p>","DOI":"10.1063\/5.0343564","type":"journal-article","created":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T10:58:38Z","timestamp":1789469918000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Q-ADC(2): A parallel quadrature-based second-order algebraic diagrammatic construction method for electronic excitations with fourth-order scaling"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7744-5038","authenticated-orcid":false,"given":"Antonia","family":"Papapostolou","sequence":"first","affiliation":[{"name":"Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University Heidelberg , Im\u00a0Neuenheimer Feld 205, 69120 Heidelberg,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1106-8716","authenticated-orcid":false,"given":"Adrian L.","family":"Dempwolff","sequence":"additional","affiliation":[{"name":"Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University Heidelberg , Im\u00a0Neuenheimer Feld 205, 69120 Heidelberg,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5862-5113","authenticated-orcid":false,"given":"Andreas","family":"Dreuw","sequence":"additional","affiliation":[{"name":"Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University Heidelberg , Im\u00a0Neuenheimer Feld 205, 69120 Heidelberg,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,15]]},"reference":[{"key":"2026091506583297200_c1","doi-asserted-by":"publisher","first-page":"2395","DOI":"10.1103\/physreva.26.2395","article-title":"Beyond the random-phase approximation: A new approximation scheme for the polarization propagator","volume":"26","year":"1982","journal-title":"Phys. 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