{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T20:27:18Z","timestamp":1783628838268,"version":"3.55.0"},"reference-count":126,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2025YFB3003603"],"award-info":[{"award-number":["2025YFB3003603"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12588301"],"award-info":[{"award-number":["12588301"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computer Physics Communications"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.cpc.2026.110260","type":"journal-article","created":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T15:22:58Z","timestamp":1781104978000},"page":"110260","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["A unified heterogeneous implementation of numerical atomic orbitals-based real-time TDDFT within the ABACUS package"],"prefix":"10.1016","volume":"327","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-8194-8914","authenticated-orcid":false,"given":"Taoni","family":"Bao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanbo","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zichao","family":"Deng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haotian","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Denghui","family":"Lu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yike","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chao","family":"Lian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lixin","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8071-5633","authenticated-orcid":false,"given":"Mohan","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cpc.2026.110260_bib0001","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1103\/PhysRevLett.52.997","article-title":"Density-functional theory for time-dependent systems","volume":"52","author":"Runge","year":"1984","journal-title":"Phys. Rev. Lett."},{"key":"10.1016\/j.cpc.2026.110260_bib0002","doi-asserted-by":"crossref","first-page":"4484","DOI":"10.1103\/PhysRevB.54.4484","article-title":"Time-dependent local-density approximation in real time","volume":"54","author":"Yabana","year":"1996","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.cpc.2026.110260_bib0003","series-title":"Time-Dependent Density-Functional Theory: Concepts and Applications","author":"Ullrich","year":"2012"},{"key":"10.1016\/j.cpc.2026.110260_bib0004","doi-asserted-by":"crossref","first-page":"B864","DOI":"10.1103\/PhysRev.136.B864","article-title":"Inhomogeneous electron gas","volume":"136","author":"Hohenberg","year":"1964","journal-title":"Phys. Rev."},{"key":"10.1016\/j.cpc.2026.110260_bib0005","doi-asserted-by":"crossref","first-page":"A1133","DOI":"10.1103\/PhysRev.140.A1133","article-title":"Self-consistent equations including exchange and correlation effects","volume":"140","author":"Kohn","year":"1965","journal-title":"Phys. Rev."},{"key":"10.1016\/j.cpc.2026.110260_bib0006","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1103\/RevModPhys.87.897","article-title":"Density functional theory: its origins, rise to prominence, and future","volume":"87","author":"Jones","year":"2015","journal-title":"Rev. Mod. Phys."},{"issue":"8","key":"10.1016\/j.cpc.2026.110260_bib0007","doi-asserted-by":"crossref","first-page":"5011","DOI":"10.1021\/jacs.3c08226","article-title":"Real-time time-dependent density functional theory for simulating nonequilibrium electron dynamics","volume":"146","author":"Xu","year":"2024","journal-title":"J. Am. Chem. Soc."},{"issue":"8","key":"10.1016\/j.cpc.2026.110260_bib0008","article-title":"Photoexcitation in solids: first-principles quantum simulations by real-time TDDFT","volume":"1","author":"Lian","year":"2018","journal-title":"Adv. Theory Simul."},{"issue":"9","key":"10.1016\/j.cpc.2026.110260_bib0009","doi-asserted-by":"crossref","first-page":"2856","DOI":"10.1021\/ct100289t","article-title":"Real-time TD-DFT simulations in dye sensitized solar cells: the electronic absorption spectrum of alizarin supported on TiO2 nanoclusters","volume":"6","author":"S\u00e1nchez-de Armas","year":"2010","journal-title":"J. Chem. Theory Comput."},{"issue":"23","key":"10.1016\/j.cpc.2026.110260_bib0010","doi-asserted-by":"crossref","first-page":"14734","DOI":"10.1021\/acs.jpcc.9b00296","article-title":"Real-time TDDFT investigation of optical absorption in gold nanowires","volume":"123","author":"Senanayake","year":"2019","journal-title":"J. Phys. Chem. C"},{"issue":"17","key":"10.1016\/j.cpc.2026.110260_bib0011","doi-asserted-by":"crossref","first-page":"3991","DOI":"10.1021\/acs.jpclett.7b01652","article-title":"Attosecond charge migration with TDDFT: accurate dynamics from a well-defined initial state","volume":"8","author":"Bruner","year":"2017","journal-title":"J. Phys. Chem. Lett."},{"key":"10.1016\/j.cpc.2026.110260_bib0012","article-title":"The role of collective motion in the ultrafast charge transfer in van der Waals heterostructures","volume":"7","author":"Wang","year":"2016","journal-title":"Nat. Commun."},{"issue":"16","key":"10.1016\/j.cpc.2026.110260_bib0013","doi-asserted-by":"crossref","first-page":"3868","DOI":"10.1021\/acs.jpclett.1c00772","article-title":"Bridged azobenzene enables dynamic control of through-space charge transfer for photochemical conversion","volume":"12","author":"Zhou","year":"2021","journal-title":"J. Phys. Chem. Lett."},{"key":"10.1016\/j.cpc.2026.110260_bib0014","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.103.043117","article-title":"Enhancement of high-order harmonic generation in two-dimensional materials by plasmonic fields","volume":"103","author":"Wu","year":"2021","journal-title":"Phys. Rev. A"},{"key":"10.1016\/j.cpc.2026.110260_bib0015","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.118.087403","article-title":"Impact of the electronic band structure in high-harmonic generation spectra of solids","volume":"118","author":"Tancogne-Dejean","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"10.1016\/j.cpc.2026.110260_bib0016","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.99.184306","article-title":"Cooperative evolution of intraband and interband excitations for high-harmonic generation in strained MoS2","volume":"99","author":"Guan","year":"2019","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.cpc.2026.110260_bib0017","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.105.224311","article-title":"Nonadiabatic electron-phonon coupling and its effects on superconductivity","volume":"105","author":"Hu","year":"2022","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.cpc.2026.110260_bib0018","article-title":"Directional pumping of coherent phonons and quasiparticle renormalization in a dirac nodal-line semimetal","volume":"15","author":"Wang","year":"2025","journal-title":"Phys. Rev. X"},{"key":"10.1016\/j.cpc.2026.110260_bib0019","doi-asserted-by":"crossref","DOI":"10.1016\/j.physb.2025.417202","article-title":"Resonant electron-phonon coupled responses to single-shot driver: ab initio TDDFT study of diamond","volume":"710","author":"Kazempour","year":"2025","journal-title":"Phys. B: Condens. Matter"},{"key":"10.1016\/j.cpc.2026.110260_bib0020","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1103\/RevModPhys.81.163","article-title":"Attosecond physics","volume":"81","author":"Krausz","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0021","doi-asserted-by":"crossref","DOI":"10.1016\/j.cpc.2024.109349","article-title":"QRCODE: massively parallelized real-time time-dependent density functional theory for periodic systems","volume":"305","author":"Choi","year":"2024","journal-title":"Comput. Phys. Commun."},{"issue":"5","key":"10.1016\/j.cpc.2026.110260_bib0022","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1109\/JPROC.2008.917757","article-title":"GPU computing","volume":"96","author":"Owens","year":"2008","journal-title":"Proc. IEEE"},{"issue":"16","key":"10.1016\/j.cpc.2026.110260_bib0023","doi-asserted-by":"crossref","first-page":"2618","DOI":"10.1002\/jcc.20829","article-title":"Accelerating molecular modeling applications with graphics processors","volume":"28","author":"Stone","year":"2007","journal-title":"J. Comput. Chem."},{"key":"10.1016\/j.cpc.2026.110260_bib0024","doi-asserted-by":"crossref","first-page":"11169","DOI":"10.1103\/PhysRevB.54.11169","article-title":"Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set","volume":"54","author":"Kresse","year":"1996","journal-title":"Phys. Rev. B"},{"issue":"32","key":"10.1016\/j.cpc.2026.110260_bib0025","doi-asserted-by":"crossref","first-page":"2581","DOI":"10.1002\/jcc.23096","article-title":"Accelerating VASP electronic structure calculations using graphic processing units","volume":"33","author":"Hacene","year":"2012","journal-title":"J. Comput. Chem."},{"issue":"19","key":"10.1016\/j.cpc.2026.110260_bib0026","doi-asserted-by":"crossref","DOI":"10.1063\/5.0007045","article-title":"CP2K: an electronic structure and molecular dynamics software package - quickstep: efficient and accurate electronic structure calculations","volume":"152","author":"K\u00fchne","year":"2020","journal-title":"J. Chem. Phys."},{"issue":"10","key":"10.1016\/j.cpc.2026.110260_bib0027","doi-asserted-by":"crossref","first-page":"2378","DOI":"10.1021\/acs.jcim.1c01538","article-title":"Performance analysis of CP2K code for ab initio molecular dynamics on CPUs and GPUs","volume":"62","author":"Yokelson","year":"2022","journal-title":"J. Chem. Inf. Model."},{"issue":"46","key":"10.1016\/j.cpc.2026.110260_bib0028","article-title":"Advanced capabilities for materials modelling with Quantum ESPRESSO","volume":"29","author":"Giannozzi","year":"2017","journal-title":"J. Phys.: Condens. Matter"},{"issue":"15","key":"10.1016\/j.cpc.2026.110260_bib0029","doi-asserted-by":"crossref","DOI":"10.1063\/5.0005082","article-title":"Quantum ESPRESSO toward the exascale","volume":"152","author":"Giannozzi","year":"2020","journal-title":"J. Chem. Phys."},{"issue":"13","key":"10.1016\/j.cpc.2026.110260_bib0030","first-page":"20","article-title":"Effects of easy hybrid parallelization with CUDA for OpenMX","volume":"98","author":"Parq","year":"2014","journal-title":"Int. J. Comput. Appl."},{"issue":"12","key":"10.1016\/j.cpc.2026.110260_bib0031","doi-asserted-by":"crossref","DOI":"10.7566\/JPSJ.94.124003","article-title":"GPU Acceleration of collinear and noncollinear DFT using a numerical atomic orbital-based DFT code","volume":"94","author":"Kawai","year":"2025","journal-title":"J. Phys. Soc. Jpn."},{"issue":"1","key":"10.1016\/j.cpc.2026.110260_bib0032","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.cpc.2012.08.002","article-title":"The analysis of a plane wave pseudopotential density functional theory code on a GPU machine","volume":"184","author":"Jia","year":"2013","journal-title":"Comput. Phys. Commun."},{"key":"10.1016\/j.cpc.2026.110260_bib0033","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.jcp.2013.05.005","article-title":"Fast plane wave density functional theory molecular dynamics calculations on multi-GPU machines","volume":"251","author":"Jia","year":"2013","journal-title":"J. Comput. Phys."},{"issue":"12","key":"10.1016\/j.cpc.2026.110260_bib0034","doi-asserted-by":"crossref","first-page":"7447","DOI":"10.1021\/acs.jctc.1c00562","article-title":"INQ, a modern GPU-accelerated computational framework for (time-Dependent) density functional theory","volume":"17","author":"Andrade","year":"2021","journal-title":"J. Chem. Theory Comput."},{"key":"10.1016\/j.cpc.2026.110260_bib0035","doi-asserted-by":"crossref","DOI":"10.1016\/j.cpc.2023.108947","article-title":"The real-time TDDFT code \u201cQuantum Dissipative Dynamics\u201d on a GPU","volume":"295","author":"Dinh","year":"2024","journal-title":"Comput. Phys. Commun."},{"key":"10.1016\/j.cpc.2026.110260_bib0036","doi-asserted-by":"crossref","first-page":"3979","DOI":"10.1103\/PhysRevB.40.3979","article-title":"Ab initio multicenter tight-binding model for molecular-dynamics simulations and other applications in covalent systems","volume":"40","author":"Sankey","year":"1989","journal-title":"Phys. Rev. B"},{"issue":"1","key":"10.1016\/j.cpc.2026.110260_bib0037","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1063\/1.458452","article-title":"An all-electron numerical method for solving the local density functional for polyatomic molecules","volume":"92","author":"Delley","year":"1990","journal-title":"J. Chem. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0038","doi-asserted-by":"crossref","first-page":"4716","DOI":"10.1103\/PhysRevB.15.4716","article-title":"Self-consistent numerical-basis-set linear-combination-of-atomic-orbitals model for the study of solids in the local density formalism","volume":"15","author":"Zunger","year":"1977","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.cpc.2026.110260_bib0039","unstructured":"Hygon deep computing unit, 2025, Accessed: 2026-01-16. https:\/\/www.hygon.cn\/product\/accelerator."},{"key":"10.1016\/j.cpc.2026.110260_bib0040","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1007\/s42514-024-00200-3","article-title":"Optimizing depthwise separable convolution on DCU","volume":"6","author":"Liu","year":"2024","journal-title":"CCF Trans. High Perform. Comput."},{"issue":"12","key":"10.1016\/j.cpc.2026.110260_bib0041","doi-asserted-by":"crossref","first-page":"3202","DOI":"10.1016\/j.jpdc.2014.07.003","article-title":"Kokkos: enabling manycore performance portability through polymorphic memory access patterns","volume":"74","author":"Carter Edwards","year":"2014","journal-title":"J. Parallel Distributed Comput."},{"issue":"44","key":"10.1016\/j.cpc.2026.110260_bib0042","article-title":"Systematically improvable optimized atomic basis sets for ab initio calculations","volume":"22","author":"Chen","year":"2010","journal-title":"J. Phys.: Condens. Matter"},{"key":"10.1016\/j.cpc.2026.110260_bib0043","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1016\/j.commatsci.2015.07.004","article-title":"Large-scale ab initio simulations based on systematically improvable atomic basis","volume":"112","author":"Li","year":"2016","journal-title":"Comput. Mater. Sci."},{"issue":"19","key":"10.1016\/j.cpc.2026.110260_bib0044","doi-asserted-by":"crossref","DOI":"10.1063\/5.0297563","article-title":"ABACUS: An electronic structure analysis package for the AI era","volume":"163","author":"Zhou","year":"2025","journal-title":"J. Chem. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0045","unstructured":"ABACUS code repository, 2026, Accessed: 2026-01-24. https:\/\/github.com\/deepmodeling\/abacus-develop."},{"issue":"2","key":"10.1016\/j.cpc.2026.110260_bib0046","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1021\/acs.jpclett.1c03442","article-title":"Real-time, time-dependent density functional theory study on photoinduced isomerizations of azobenzene under a light field","volume":"13","author":"He","year":"2022","journal-title":"J. Phys. Chem. Lett."},{"key":"10.1016\/j.cpc.2026.110260_bib0047","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevResearch.6.013123","article-title":"Ultrafast shift current dynamics in WS2 monolayer","volume":"6","author":"He","year":"2024","journal-title":"Phys. Rev. Res."},{"issue":"7","key":"10.1016\/j.cpc.2026.110260_bib0048","doi-asserted-by":"crossref","first-page":"3335","DOI":"10.1021\/acs.jctc.5c00111","article-title":"Hybrid gauge approach for accurate real-time TDDFT simulations with numerical atomic orbitals","volume":"21","author":"Zhao","year":"2025","journal-title":"J. Chem. Theory Comput."},{"issue":"11","key":"10.1016\/j.cpc.2026.110260_bib0049","first-page":"2745","article-title":"The SIESTA method for ab initio order-N materials simulation","volume":"14","author":"Soler","year":"2002","journal-title":"J. Phys.: Condens. Matter"},{"issue":"7","key":"10.1016\/j.cpc.2026.110260_bib0050","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1007\/BF01339455","article-title":"\u00dcber die Quantenmechanik der Elektronen in Kristallgittern","volume":"52","author":"Bloch","year":"1929","journal-title":"Zeitschrift f\u00fcr Physik"},{"key":"10.1016\/j.cpc.2026.110260_bib0051","doi-asserted-by":"crossref","first-page":"3863","DOI":"10.1103\/PhysRevLett.82.3863","article-title":"Mapping from densities to potentials in time-dependent density-functional theory","volume":"82","author":"van Leeuwen","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"10.1016\/j.cpc.2026.110260_bib0052","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1103\/PhysRev.75.486","article-title":"The radiation theories of Tomonaga, Schwinger, and Feynman","volume":"75","author":"Dyson","year":"1949","journal-title":"Phys. Rev."},{"issue":"20","key":"10.1016\/j.cpc.2026.110260_bib0053","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1002\/andp.19273892002","article-title":"Zur Quantentheorie der Molekeln","volume":"389","author":"Born","year":"1927","journal-title":"Annalen der Physik"},{"key":"10.1016\/j.cpc.2026.110260_bib0054","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.87.205117","article-title":"Nonadiabatic molecular dynamics simulation for carrier transport in a pentathiophene butyric acid monolayer","volume":"87","author":"Ren","year":"2013","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.cpc.2026.110260_bib0055","article-title":"Efficient real-time time-dependent density functional theory method and its application to a collision of an ion with a 2D material","volume":"114","author":"Wang","year":"2015","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"10.1016\/j.cpc.2026.110260_bib0056","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1017\/S0305004100023197","article-title":"A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type","volume":"43","author":"Crank","year":"1947","journal-title":"Math. Proc. Camb. Philos. Soc."},{"issue":"8","key":"10.1016\/j.cpc.2026.110260_bib0057","doi-asserted-by":"crossref","first-page":"3425","DOI":"10.1063\/1.1774980","article-title":"Propagators for the time-dependent Kohn-Sham equations","volume":"121","author":"Castro","year":"2004","journal-title":"J. Chem. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0058","doi-asserted-by":"crossref","first-page":"7998","DOI":"10.1103\/PhysRevB.62.7998","article-title":"Real-space, real-time method for the dielectric function","volume":"62","author":"Bertsch","year":"2000","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.cpc.2026.110260_bib0059","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.87.087402","article-title":"Coupling of nonlocal potentials to electromagnetic fields","volume":"87","author":"Ismail-Beigi","year":"2001","journal-title":"Phys. Rev. Lett."},{"issue":"7","key":"10.1016\/j.cpc.2026.110260_bib0060","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/BF01329203","article-title":"Bemerkung \u00fcber die angen\u00e4herte G\u00fcltigkeit der klassischen Mechanik innerhalb der Quantenmechanik","volume":"45","author":"Ehrenfest","year":"1927","journal-title":"Zeitschrift f\u00fcr Physik"},{"issue":"14","key":"10.1016\/j.cpc.2026.110260_bib0061","doi-asserted-by":"crossref","DOI":"10.1063\/1.3700800","article-title":"Nonadiabatic Ehrenfest molecular dynamics within the projector augmented-wave method","volume":"136","author":"Ojanper\u00e4","year":"2012","journal-title":"J. Chem. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0062","series-title":"Einf\u00fchrung in die Quantenchemie","author":"Hellmann","year":"1937"},{"key":"10.1016\/j.cpc.2026.110260_bib0063","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1103\/PhysRev.56.340","article-title":"Forces in molecules","volume":"56","author":"Feynman","year":"1939","journal-title":"Phys. Rev."},{"key":"10.1016\/j.cpc.2026.110260_bib0064","doi-asserted-by":"crossref","first-page":"1494","DOI":"10.1103\/PhysRevLett.43.1494","article-title":"Norm-conserving pseudopotentials","volume":"43","author":"Hamann","year":"1979","journal-title":"Phys. Rev. Lett."},{"key":"10.1016\/j.cpc.2026.110260_bib0065","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1103\/PhysRevLett.48.1425","article-title":"Efficacious form for model pseudopotentials","volume":"48","author":"Kleinman","year":"1982","journal-title":"Phys. Rev. Lett."},{"issue":"3","key":"10.1016\/j.cpc.2026.110260_bib0066","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1002\/andp.19213690304","article-title":"Die Berechnung optischer und elektrostatischer Gitterpotentiale","volume":"369","author":"Ewald","year":"1921","journal-title":"Ann. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0067","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.83.195102","article-title":"Accurate ionic forces and geometry optimization in linear-scaling density-functional theory with local orbitals","volume":"83","author":"Hine","year":"2011","journal-title":"Phys. Rev. B"},{"issue":"90","key":"10.1016\/j.cpc.2026.110260_bib0068","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1090\/S0025-5718-1965-0178586-1","article-title":"An algorithm for the machine calculation of complex Fourier series","volume":"19","author":"Cooley","year":"1965","journal-title":"Math. Comput."},{"issue":"2","key":"10.1016\/j.cpc.2026.110260_bib0069","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1080\/00268976900100941","article-title":"Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules","volume":"17","author":"Pulay","year":"1969","journal-title":"Mol. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0070","doi-asserted-by":"crossref","first-page":"1456","DOI":"10.1103\/PhysRevB.51.1456","article-title":"Linear system-size scaling methods for electronic-structure calculations","volume":"51","author":"Ordej\u00f3n","year":"1995","journal-title":"Phys. Rev. B"},{"issue":"4","key":"10.1016\/j.cpc.2026.110260_bib0071","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1080\/00268978800101471","article-title":"An algorithm for the simulation of condensed matter which grows as the 3\/2 power of the number of particles","volume":"65","author":"Perram","year":"1988","journal-title":"Mol. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0072","unstructured":"The FHI-aims Team, Real-time and imaginary-time TDDFT \u2013 FHI-aims manual, 2026, Accessed: 2026-05-27. https:\/\/fhi-aims.org\/uploads\/manual\/Ch3\/S30.html."},{"key":"10.1016\/j.cpc.2026.110260_bib0073","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1103\/PhysRev.159.98","article-title":"Computer \u201cexperiments\u201d on classical fluids. i. thermodynamical properties of Lennard-Jones molecules","volume":"159","author":"Verlet","year":"1967","journal-title":"Phys. Rev."},{"issue":"1","key":"10.1016\/j.cpc.2026.110260_bib0074","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1063\/1.442716","article-title":"A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: application to small water clusters","volume":"76","author":"Swope","year":"1982","journal-title":"J. Chem. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0075","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.94.184310","article-title":"Ab initio evidence for nonthermal characteristics in ultrafast laser melting","volume":"94","author":"Lian","year":"2016","journal-title":"Phys. Rev. B"},{"issue":"2","key":"10.1016\/j.cpc.2026.110260_bib0076","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1063\/1.1675788","article-title":"Trajectory surface hopping approach to nonadiabatic molecular collisions: the reaction of H+ with D2","volume":"55","author":"Tully","year":"1971","journal-title":"J. Chem. Phys."},{"issue":"2","key":"10.1016\/j.cpc.2026.110260_bib0077","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1063\/1.459170","article-title":"Molecular dynamics with electronic transitions","volume":"93","author":"Tully","year":"1990","journal-title":"J. Chem. Phys."},{"issue":"2","key":"10.1016\/j.cpc.2026.110260_bib0078","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1145\/567806.567807","article-title":"An updated set of basic linear algebra subprograms (BLAS)","volume":"28","author":"Blackford","year":"2002","journal-title":"ACM Trans. Math. Softw."},{"key":"10.1016\/j.cpc.2026.110260_bib0079","series-title":"LAPACK Users\u2019 Guide","author":"Anderson","year":"1999"},{"key":"10.1016\/j.cpc.2026.110260_bib0080","doi-asserted-by":"crossref","first-page":"A796","DOI":"10.1103\/PhysRev.139.A796","article-title":"New method for calculating the one-particle Green\u2019s function with application to the electron-gas problem","volume":"139","author":"Hedin","year":"1965","journal-title":"Phys. Rev."},{"key":"10.1016\/j.cpc.2026.110260_bib0081","doi-asserted-by":"crossref","first-page":"5390","DOI":"10.1103\/PhysRevB.34.5390","article-title":"Electron correlation in semiconductors and insulators: band gaps and quasiparticle energies","volume":"34","author":"Hybertsen","year":"1986","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.cpc.2026.110260_bib0082","unstructured":"H. Zhang, Z. Deng, Y. Liu, T. Liu, M. Chen, S. Yin, L. He, GPU acceleration of numerical atomic orbitals-based density functional theory algorithms within the ABACUS package, 2024. arXiv: 2409.09399 [cond-mat.mtrl-sci]."},{"issue":"3","key":"10.1016\/j.cpc.2026.110260_bib0083","first-page":"477","article-title":"A quadrature formula for the sphere of the 131st algebraic order of accuracy","volume":"59","author":"Lebedev","year":"1999","journal-title":"Dokl. Math."},{"key":"10.1016\/j.cpc.2026.110260_bib0084","series-title":"NVIDIA Developer Technology","first-page":"1","article-title":"Optimizing parallel reduction in CUDA","author":"Harris","year":"2007"},{"issue":"11","key":"10.1016\/j.cpc.2026.110260_bib0085","doi-asserted-by":"crossref","first-page":"5645","DOI":"10.1021\/acs.jctc.8b00580","article-title":"Fast real-time time-dependent density functional theory calculations with the parallel transport gauge","volume":"14","author":"Jia","year":"2018","journal-title":"J. Chem. Theory Comput."},{"key":"10.1016\/j.cpc.2026.110260_bib0086","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.88.085117","article-title":"Optimized norm-conserving Vanderbilt pseudopotentials","volume":"88","author":"Hamann","year":"2013","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.cpc.2026.110260_bib0087","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.cpc.2015.05.011","article-title":"Optimization algorithm for the generation of ONCV pseudopotentials","volume":"196","author":"Schlipf","year":"2015","journal-title":"Comput. Phys. Commun."},{"issue":"32","key":"10.1016\/j.cpc.2026.110260_bib0088","article-title":"Electronic structure interpolation via atomic orbitals","volume":"23","author":"Chen","year":"2011","journal-title":"J. Phys.: Condens. Matter"},{"key":"10.1016\/j.cpc.2026.110260_bib0089","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.103.235131","article-title":"Strategy for constructing compact numerical atomic orbital basis sets by incorporating the gradients of reference wavefunctions","volume":"103","author":"Lin","year":"2021","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.cpc.2026.110260_bib0090","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.softx.2017.11.002","article-title":"Recent developments in Libxc - a comprehensive library of functionals for density functional theory","volume":"7","author":"Lehtola","year":"2018","journal-title":"SoftwareX"},{"key":"10.1016\/j.cpc.2026.110260_bib0091","doi-asserted-by":"crossref","first-page":"3865","DOI":"10.1103\/PhysRevLett.77.3865","article-title":"Generalized gradient approximation made simple","volume":"77","author":"Perdew","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"10.1016\/j.cpc.2026.110260_bib0092","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.78.1396","article-title":"Generalized gradient approximation made simple [Phys. Rev. Lett. 77, 3865 (1996)]","volume":"78","author":"Perdew","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"10.1016\/j.cpc.2026.110260_bib0093","unstructured":"The SIESTA Group, Optical properties from real-time TD-DFT \u2013 SIESTA documentation, 2021, Accessed: 2026-02-02. https:\/\/docs.siesta-project.org\/projects\/siesta\/en\/school-2021\/tutorials\/td-dft\/optical-properties\/index.html."},{"issue":"4","key":"10.1016\/j.cpc.2026.110260_bib0094","doi-asserted-by":"crossref","first-page":"2140","DOI":"10.1016\/j.jcp.2011.11.032","article-title":"Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: total energy calculation","volume":"231","author":"Lin","year":"2012","journal-title":"J. Comput. Phys."},{"issue":"12","key":"10.1016\/j.cpc.2026.110260_bib0095","doi-asserted-by":"crossref","DOI":"10.1063\/1.4931732","article-title":"DGDFT: a massively parallel method for large scale density functional theory calculations","volume":"143","author":"Hu","year":"2015","journal-title":"J. Chem. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0096","doi-asserted-by":"crossref","first-page":"1342","DOI":"10.1007\/s00214-013-1342-z","article-title":"Simulating the optical properties of CdSe clusters using the RT-TDDFT approach","volume":"132","author":"Nadler","year":"2013","journal-title":"Theor. Chem. Acc."},{"issue":"2","key":"10.1016\/j.cpc.2026.110260_bib0097","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1038\/nmat1056","article-title":"Ultra-stable nanoparticles of CdSe revealed from mass spectrometry","volume":"3","author":"Kasuya","year":"2004","journal-title":"Nat. Mater."},{"issue":"10","key":"10.1016\/j.cpc.2026.110260_bib0098","doi-asserted-by":"crossref","first-page":"2354","DOI":"10.1021\/ja003598j","article-title":"Size-dependent optical spectroscopy of a homologous series of CdSe cluster molecules","volume":"123","author":"Soloviev","year":"2001","journal-title":"J. Am. Chem. Soc."},{"issue":"2","key":"10.1016\/j.cpc.2026.110260_bib0099","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.cpc.2004.12.014","article-title":"Quickstep: fast and accurate density functional calculations using a mixed Gaussian and plane waves approach","volume":"167","author":"VandeVondele","year":"2005","journal-title":"Comput. Phys. Commun."},{"issue":"2","key":"10.1016\/j.cpc.2026.110260_bib0100","doi-asserted-by":"crossref","DOI":"10.1063\/5.0211238","article-title":"Efficient exact exchange using Wannier functions and other related developments in planewave-pseudopotential implementation of RT-TDDFT","volume":"161","author":"Shepard","year":"2024","journal-title":"J. Chem. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0101","series-title":"Quantum Theory of Solids","author":"Peierls","year":"1955"},{"key":"10.1016\/j.cpc.2026.110260_bib0102","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1103\/RevModPhys.60.1129","article-title":"The dynamics of charge-density waves","volume":"60","author":"Gr\u00fcner","year":"1988","journal-title":"Rev. Mod. Phys."},{"issue":"3","key":"10.1016\/j.cpc.2026.110260_bib0103","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1017\/S0305004100016108","article-title":"Note on exchange phenomena in the Thomas atom","volume":"26","author":"Dirac","year":"1930","journal-title":"Math. Proc. Camb. Philos. Soc."},{"key":"10.1016\/j.cpc.2026.110260_bib0104","doi-asserted-by":"crossref","first-page":"5048","DOI":"10.1103\/PhysRevB.23.5048","article-title":"Self-interaction correction to density-functional approximations for many-electron systems","volume":"23","author":"Perdew","year":"1981","journal-title":"Phys. Rev. B"},{"issue":"10","key":"10.1016\/j.cpc.2026.110260_bib0105","doi-asserted-by":"crossref","DOI":"10.1063\/5.0057587","article-title":"Simulating electronic excitation and dynamics with real-time propagation approach to TDDFT within plane-wave pseudopotential formulation","volume":"155","author":"Shepard","year":"2021","journal-title":"J. Chem. Phys."},{"issue":"22","key":"10.1016\/j.cpc.2026.110260_bib0106","doi-asserted-by":"crossref","DOI":"10.1063\/1.4758792","article-title":"Plane-wave pseudopotential implementation of explicit integrators for time-dependent Kohn-Sham equations in large-scale simulations","volume":"137","author":"Schleife","year":"2012","journal-title":"J. Chem. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0107","doi-asserted-by":"crossref","first-page":"12847","DOI":"10.1103\/PhysRevB.56.12847","article-title":"Maximally localized generalized Wannier functions for composite energy bands","volume":"56","author":"Marzari","year":"1997","journal-title":"Phys. Rev. B"},{"issue":"3","key":"10.1016\/j.cpc.2026.110260_bib0108","doi-asserted-by":"crossref","DOI":"10.1088\/2516-1075\/ac0c26","article-title":"All-electron full-potential implementation of real-time TDDFT in exciting","volume":"3","author":"Rodrigues Pela","year":"2021","journal-title":"Electron. Struct."},{"issue":"10","key":"10.1016\/j.cpc.2026.110260_bib0109","doi-asserted-by":"crossref","DOI":"10.3390\/app8101777","article-title":"Ab initio simulation of attosecond transient absorption spectroscopy in two-dimensional materials","volume":"8","author":"Sato","year":"2018","journal-title":"Appl. Sci."},{"issue":"9","key":"10.1016\/j.cpc.2026.110260_bib0110","doi-asserted-by":"crossref","first-page":"980","DOI":"10.1002\/jcc.27058","article-title":"Implementation of real-time TDDFT for periodic systems in the open-source PySCF software package","volume":"44","author":"Hanasaki","year":"2023","journal-title":"J. Comput. Chem."},{"key":"10.1016\/j.cpc.2026.110260_bib0111","doi-asserted-by":"crossref","first-page":"31371","DOI":"10.1039\/C5CP00351B","article-title":"Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems","volume":"17","author":"Andrade","year":"2015","journal-title":"Phys. Chem. Chem. Phys."},{"issue":"2","key":"10.1016\/j.cpc.2026.110260_bib0112","doi-asserted-by":"crossref","DOI":"10.1063\/5.0006074","article-title":"Recent developments in the PySCF program package","volume":"153","author":"Sun","year":"2020","journal-title":"J. Chem. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0113","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.cpc.2018.01.013","article-title":"Velocity-gauge real-time TDDFT within a numerical atomic orbital basis set","volume":"226","author":"Pemmaraju","year":"2018","journal-title":"Comput. Phys. Commun."},{"key":"10.1016\/j.cpc.2026.110260_bib0114","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1103\/RevModPhys.74.601","article-title":"Electronic excitations: density-functional versus many-body Green\u2019s-function approaches","volume":"74","author":"Onida","year":"2002","journal-title":"Rev. Mod. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0115","doi-asserted-by":"crossref","first-page":"2312","DOI":"10.1103\/PhysRevLett.81.2312","article-title":"Electron-hole excitations in semiconductors and insulators","volume":"81","author":"Rohlfing","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"10.1016\/j.cpc.2026.110260_bib0116","doi-asserted-by":"crossref","first-page":"4927","DOI":"10.1103\/PhysRevB.62.4927","article-title":"Electron-hole excitations and optical spectra from first principles","volume":"62","author":"Rohlfing","year":"2000","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.cpc.2026.110260_bib0117","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.78.121201","article-title":"Dielectric properties and excitons for extended systems from hybrid functionals","volume":"78","author":"Paier","year":"2008","journal-title":"Phys. Rev. B"},{"issue":"22","key":"10.1016\/j.cpc.2026.110260_bib0118","doi-asserted-by":"crossref","DOI":"10.1063\/1.4937379","article-title":"Nonlinear electronic excitations in crystalline solids using meta-generalized gradient approximation and hybrid functional in time-dependent density functional theory","volume":"143","author":"Sato","year":"2015","journal-title":"J. Chem. Phys."},{"key":"10.1016\/j.cpc.2026.110260_bib0119","series-title":"Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis","first-page":"1","article-title":"Parallel transport time-dependent density functional theory calculations with hybrid functional on summit","author":"Jia","year":"2019"},{"key":"10.1016\/j.cpc.2026.110260_bib0120","unstructured":"Y. Ji, H. Zhao, P. Lin, X. Ren, L. He, Real-time time-dependent density functional theory simulations with range-separated hybrid functionals for periodic systems, 2025. arXiv: 2512.18754 [cond-mat.mtrl-sci]."},{"issue":"8","key":"10.1016\/j.cpc.2026.110260_bib0121","doi-asserted-by":"crossref","DOI":"10.1063\/1.2008258","article-title":"Ab initio Ehrenfest dynamics","volume":"123","author":"Li","year":"2005","journal-title":"J. Chem. Phys."},{"issue":"25","key":"10.1016\/j.cpc.2026.110260_bib0122","article-title":"Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method","volume":"22","author":"Enkovaara","year":"2010","journal-title":"J. Phys.: Condens. Matter"},{"issue":"9","key":"10.1016\/j.cpc.2026.110260_bib0123","doi-asserted-by":"crossref","DOI":"10.1063\/5.0182685","article-title":"GPAW: an open python package for electronic structure calculations","volume":"160","author":"Mortensen","year":"2024","journal-title":"J. Chem. Phys."},{"issue":"1","key":"10.1016\/j.cpc.2026.110260_bib0124","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0010-4655(96)00017-3","article-title":"ScaLAPACK: a portable linear algebra library for distributed memory computers - design issues and performance","volume":"97","author":"Choi","year":"1996","journal-title":"Comput. Phys. Commun."},{"key":"10.1016\/j.cpc.2026.110260_bib0125","series-title":"Proceedings of the April 18\u201320, 1967, Spring Joint Computer Conference","first-page":"483","article-title":"Validity of the single processor approach to achieving large scale computing capabilities","author":"Amdahl","year":"1967"},{"key":"10.1016\/j.cpc.2026.110260_bib0126","unstructured":"cuSOLVERMp: a high-performance CUDA library for distributed dense linear algebra, 2025, Accessed: 2026-01-16. https:\/\/docs.nvidia.com\/cuda\/cusolvermp\/index.html."}],"container-title":["Computer Physics Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0010465526002420?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0010465526002420?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T20:00:18Z","timestamp":1783627218000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0010465526002420"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":126,"alternative-id":["S0010465526002420"],"URL":"https:\/\/doi.org\/10.1016\/j.cpc.2026.110260","relation":{},"ISSN":["0010-4655"],"issn-type":[{"value":"0010-4655","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A unified heterogeneous implementation of numerical atomic orbitals-based real-time TDDFT within the ABACUS package","name":"articletitle","label":"Article Title"},{"value":"Computer Physics Communications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cpc.2026.110260","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"110260"}}