{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T14:01:49Z","timestamp":1790085709027,"version":"4.0.1"},"reference-count":44,"publisher":"American Chemical Society (ACS)","issue":"18","license":[{"start":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T00:00:00Z","timestamp":1788912000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T00:00:00Z","timestamp":1788912000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T00:00:00Z","timestamp":1788912000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"DOI":"10.13039\/501100002855","name":"Ministry of Science and Technology of the People's Republic of China","doi-asserted-by":"publisher","award":["2024YFA1209000"],"award-info":[{"award-number":["2024YFA1209000"]}],"id":[{"id":"10.13039\/501100002855","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/na","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22203018"],"award-info":[{"award-number":["22203018"]}],"id":[{"id":"10.13039\/na","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/na","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22303017"],"award-info":[{"award-number":["22303017"]}],"id":[{"id":"10.13039\/na","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/na","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22333002"],"award-info":[{"award-number":["22333002"]}],"id":[{"id":"10.13039\/na","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/na","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22673022"],"award-info":[{"award-number":["22673022"]}],"id":[{"id":"10.13039\/na","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/na","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52394272"],"award-info":[{"award-number":["52394272"]}],"id":[{"id":"10.13039\/na","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Theoretical simulation methods such as self-consistent field theory (SCFT) have enabled the discovery of numerous novel ordered structures, making space-group identification an important and challenging problem. Existing methods for space-group determination are primarily designed for discrete atomic coordinates or diffraction data. However, many structures obtained from theoretical calculations are represented as periodic scalar fields sampled on regular grids within a unit cell, i.e., volumetric data. Moreover, the origin of such data is generally unknown and may not coincide with the standard origin of a candidate space group. Consequently, existing methods cannot be straightforwardly applied to these data. To address this issue, we propose an automated space-group determination method that combines reciprocal-space analysis with real-space verification. Candidate space groups are initially prescreened using systematic absence rules. For each prescreened space group, the origin of the scalar field is recovered using Fourier components whose phase angles are constrained by symmetry. This recovery is achieved by minimizing the deviations of these phase angles from their symmetry-allowed values. All symmetry operations of each candidate space group are subsequently applied to the registered scalar field. The space group is then assigned by quantifying the agreement between the original and symmetry-transformed volumetric data. The method is validated on several representative structures, yielding the correct space groups. Without requiring atomic-coordinate models, the proposed method provides a general framework for determining space groups from periodic volumetric data. It enables subsequent structural classification, analysis of formation mechanisms, and property calculations using standardized primitive cells.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c01542","type":"journal-article","created":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T09:02:40Z","timestamp":1788944560000},"page":"9711-9723","source":"Crossref","is-referenced-by-count":0,"title":["Automated Space\nGroup Determination for Periodic Volumetric\nData"],"prefix":"10.1021","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2062-274X","authenticated-orcid":true,"given":"Qingshu","family":"Dong","sequence":"first","affiliation":[{"name":"Fudan University , , ,","place":["Shanghai, China, 200433"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2818-6025","authenticated-orcid":true,"given":"Qingliang","family":"Song","sequence":"additional","affiliation":[{"name":"Fudan University , , ,","place":["Shanghai, China, 200433"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xintong","family":"You","sequence":"additional","affiliation":[{"name":"Fudan University , , ,","place":["Shanghai, China, 200433"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5133-0267","authenticated-orcid":true,"given":"Weihua","family":"Li","sequence":"additional","affiliation":[{"name":"Fudan University , , ,","place":["Shanghai, China, 200433"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,9]]},"reference":[{"key":"2026092209073793700_cit1","volume-title":"International Tables\nfor Crystallography, Vol. A: space-group symmetry","author":"Hahn","year":"2005","edition":"5th"},{"key":"2026092209073793700_cit2","volume-title":"International Tables\nfor Crystallography, Vol. B: reciprocal space","author":"Shmueli","year":"2001","edition":"2nd"},{"key":"2026092209073793700_cit3","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1016\/j.commatsci.2016.10.015","article-title":"Band Structure\nDiagram Paths Based on Crystallography","volume":"128","author":"Hinuma","year":"2017","journal-title":"Comput.\nMater. Sci."},{"key":"2026092209073793700_cit4","doi-asserted-by":"publisher","first-page":"664","DOI":"10.1038\/nmat979","article-title":"Exploring for 3D\nPhotonic Bandgap Structures in the 11 f.c.c. Space Groups","volume":"2","author":"Maldovan","year":"2003","journal-title":"Nat. Mater."},{"key":"2026092209073793700_cit5","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/j.commatsci.2010.05.010","article-title":"High-Throughput Electronic Band Structure Calculations:\nChallenges and Tools","volume":"49","author":"Setyawan","year":"2010","journal-title":"Comput. Mater. Sci."},{"key":"2026092209073793700_cit6","doi-asserted-by":"publisher","DOI":"10.2307\/j.ctvcm4gz9","volume-title":"Photonic\nCrystals: molding the Flow of Light -","author":"Joannopoulos","year":"2011","edition":"Second"},{"key":"2026092209073793700_cit7","doi-asserted-by":"publisher","DOI":"10.1002\/smll.202511158","article-title":"Deep Learning-Assisted\nFourier Analysis for High-Efficiency Structural Design: A Case Study\non Three-Dimensional Photonic Crystals Enumeration","volume":"22","author":"Cui","year":"2026","journal-title":"Small"},{"key":"2026092209073793700_cit8","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1107\/S0021889802022112","article-title":"Single-Crystal\nStructure Validation with the Program PLATON","volume":"36","author":"Spek","year":"2003","journal-title":"J. Appl. Crystallogr."},{"key":"2026092209073793700_cit9","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1107\/S090744490804362X","article-title":"Structure\nValidation in Chemical Crystallography","volume":"65","author":"Spek","year":"2009","journal-title":"Acta\nCrystallogr., Sect. D: Biol. Crystallogr."},{"key":"2026092209073793700_cit10","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1107\/S0021889804031528","article-title":"FINDSYM: Program\nfor Identifying the Space-Group Symmetry\nof a Crystal","volume":"38","author":"Stokes","year":"2005","journal-title":"J. Appl. Crystallogr."},{"key":"2026092209073793700_cit11","doi-asserted-by":"publisher","first-page":"2384822","DOI":"10.1080\/27660400.2024.2384822","article-title":"Spglib: A Software Library for Crystal\nSymmetry Search","volume":"4","author":"Togo","year":"2024","journal-title":"Sci. Technol. Adv. Mater.:\nMethods"},{"key":"2026092209073793700_cit12","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1107\/S2053273318003066","article-title":"AFLOW-SYM:\nPlatform for the Complete, Automatic and Self-Consistent Symmetry\nAnalysis of Crystals","volume":"74","author":"Hicks","year":"2018","journal-title":"Acta Crystallogr., Sect.\nA: Found. Adv."},{"key":"2026092209073793700_cit13","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1107\/S2053273314026370","article-title":"SHELXT\n\u2013 Integrated Space-Group and Crystal-Structure Determination","volume":"71","author":"Sheldrick","year":"2015","journal-title":"Acta Crystallogr., Sect. A: Found. Adv."},{"key":"2026092209073793700_cit14","doi-asserted-by":"publisher","first-page":"786","DOI":"10.1107\/S0021889807029238","article-title":"SUPERFLIP - a Computer\nProgram for the Solution of\nCrystal Structures by Charge Flipping in Arbitrary Dimensions","volume":"40","author":"Palatinus","year":"2007","journal-title":"J. Appl. Crystallogr."},{"key":"2026092209073793700_cit15","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1107\/S1600576715001132","article-title":"Crystal Structure\nDetermination and Refinement via\nSIR2014","volume":"48","author":"Burla","year":"2015","journal-title":"J. Appl. Crystallogr."},{"key":"2026092209073793700_cit16","volume-title":"The Equilibrium\nTheory of Inhomogeneous Polymers","author":"Fredrickson","year":"2006"},{"key":"2026092209073793700_cit17","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1140\/epje\/i2009-10534-3","article-title":"Fast and\nAccurate SCFT Calculations for Periodic Block-Copolymer Morphologies\nUsing the Spectral Method with Anderson Mixing","volume":"30","author":"Matsen","year":"2009","journal-title":"Eur. Phys. J. E"},{"key":"2026092209073793700_cit18","doi-asserted-by":"publisher","first-page":"5859","DOI":"10.1016\/j.jcp.2008.02.021","article-title":"An Efficient Numerical Method of\nLandau\u2013Brazovskii Model","volume":"227","author":"Zhang","year":"2008","journal-title":"J. Comput. Phys."},{"key":"2026092209073793700_cit19","doi-asserted-by":"publisher","first-page":"B1350","DOI":"10.1137\/20M1321176","article-title":"Efficient Numerical Methods for Computing\nthe Stationary States of Phase Field Crystal Models","volume":"42","author":"Jiang","year":"2020","journal-title":"SIAM J. Sci. Comput."},{"key":"2026092209073793700_cit20","doi-asserted-by":"publisher","first-page":"13196","DOI":"10.1103\/q4gq-dkkp","article-title":"Exploring\nTransition Pathways in the Landau-Brazovskii Model","volume":"8","author":"Zhang","year":"2026","journal-title":"Phys. Rev. Res."},{"key":"2026092209073793700_cit21","doi-asserted-by":"publisher","first-page":"67801","DOI":"10.1103\/PhysRevLett.118.067801","article-title":"Process-Accessible\nStates of Block Copolymers","volume":"118","author":"Sun","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"2026092209073793700_cit22","doi-asserted-by":"publisher","first-page":"8865","DOI":"10.1021\/acs.macromol.6c01738","article-title":"Accelerated\nPseudospectral Method of Wormlike-Chain Self-Consistent Field Theory","volume":"59","author":"Song","year":"2026","journal-title":"Macromolecules"},{"key":"2026092209073793700_cit23","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1063\/1.882522","article-title":"Block Copolymers - Designer Soft Materials","volume":"52","author":"Bates","year":"1999","journal-title":"Phys. Today"},{"key":"2026092209073793700_cit24","doi-asserted-by":"publisher","first-page":"R21","DOI":"10.1088\/0953-8984\/14\/2\/201","article-title":"The Standard\nGaussian Model for Block Copolymer Melts","volume":"14","author":"Matsen","year":"2002","journal-title":"J.\nPhys.: Condens. Matter"},{"key":"2026092209073793700_cit25","doi-asserted-by":"publisher","first-page":"2161","DOI":"10.1021\/ma202782s","article-title":"Effect\nof Architecture on the Phase Behavior of AB-type Block Copolymer Melts","volume":"45","author":"Matsen","year":"2012","journal-title":"Macromolecules"},{"key":"2026092209073793700_cit26","doi-asserted-by":"publisher","first-page":"434","DOI":"10.1126\/science.1215368","article-title":"Multiblock Polymers: Panacea or Pandora\u2019s Box?","volume":"336","author":"Bates","year":"2012","journal-title":"Science"},{"key":"2026092209073793700_cit27","doi-asserted-by":"publisher","first-page":"2974","DOI":"10.1021\/ja412760k","article-title":"Macromolecular Metallurgy of Binary Mesocrystals via\nDesigned Multiblock Terpolymers","volume":"136","author":"Xie","year":"2014","journal-title":"J. Am. Chem.\nSoc."},{"key":"2026092209073793700_cit28","doi-asserted-by":"publisher","first-page":"4675","DOI":"10.1021\/acs.macromol.6b00107","article-title":"Broadly\nAccessible Self-Consistent\nField Theory for Block Polymer Materials Discovery","volume":"49","author":"Arora","year":"2016","journal-title":"Macromolecules"},{"key":"2026092209073793700_cit29","doi-asserted-by":"publisher","first-page":"9943","DOI":"10.1021\/acs.macromol.0c01974","article-title":"Accelerated Pseudo-Spectral Method\nof Self-Consistent Field Theory\nvia Crystallographic Fast Fourier Transform","volume":"53","author":"Qiang","year":"2020","journal-title":"Macromolecules"},{"key":"2026092209073793700_cit30","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1021\/acs.macromol.0c02442","article-title":"Effect of Molecular Asymmetry on\nthe Formation of Asymmetric Nanostructures\nin ABC-type Block Copolymers","volume":"54","author":"Dong","year":"2021","journal-title":"Macromolecules"},{"key":"2026092209073793700_cit31","doi-asserted-by":"publisher","first-page":"6558","DOI":"10.1021\/acs.macromol.6b01323","article-title":"Genetic\nAlgorithm for Discovery of\nGlobally Stable Phases in Block Copolymers","volume":"49","author":"Tsai","year":"2016","journal-title":"Macromolecules"},{"key":"2026092209073793700_cit32","doi-asserted-by":"publisher","first-page":"5249","DOI":"10.1021\/acs.macromol.2c00042","article-title":"Using Particle Swarm Optimization\nand Self-Consistent\nField Theory to Discover Globally Stable Morphologies of Block Copolymers","volume":"55","author":"Tsai","year":"2022","journal-title":"Macromolecules"},{"key":"2026092209073793700_cit33","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2308698120","article-title":"Gaming Self-Consistent Field Theory:\nGenerative Block\nPolymer Phase Discovery","volume":"120","author":"Chen","year":"2023","journal-title":"Proc. Natl. Acad. Sci.\nU. S. A."},{"key":"2026092209073793700_cit34","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2318123120","article-title":"Desperately\nSeeking Soft Structures","volume":"120","author":"Fredrickson","year":"2023","journal-title":"Proc. Natl. Acad. Sci.\nU. S. A."},{"key":"2026092209073793700_cit35","doi-asserted-by":"publisher","first-page":"987","DOI":"10.1021\/acsmacrolett.4c00384","article-title":"Automated Search Strategy for Novel Ordered Structures of Block Copolymers","volume":"13","author":"Dong","year":"2024","journal-title":"ACS Macro Lett."},{"key":"2026092209073793700_cit36","doi-asserted-by":"publisher","first-page":"1612","DOI":"10.1021\/acsmacrolett.4c00661","article-title":"Computational\nPhase Discovery in Block Polymers","volume":"13","author":"Dorfman","year":"2024","journal-title":"ACS Macro\nLett."},{"key":"2026092209073793700_cit37","doi-asserted-by":"publisher","first-page":"1730","DOI":"10.1007\/s10118-025-3396-5","article-title":"AI-driven Automated\nConstruction of Block Copolymer Phase Diagrams","volume":"43","author":"Dong","year":"2025","journal-title":"Chin. J. Polym. Sci."},{"key":"2026092209073793700_cit38","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2519094123","article-title":"Learning Nature\u2019s\nAssembly Language with Polymers","volume":"123","author":"Xie","year":"2026","journal-title":"Proc. Natl.\nAcad. Sci. U. S. A."},{"key":"2026092209073793700_cit39","doi-asserted-by":"publisher","first-page":"2237","DOI":"10.1093\/bioinformatics\/btz904","article-title":"Point-Group Symmetry\nDetection in Three-Dimensional Charge Density of Biomolecules","volume":"36","author":"Reboul","year":"2020","journal-title":"Bioinformatics"},{"key":"2026092209073793700_cit40","doi-asserted-by":"publisher","first-page":"110161","DOI":"10.1016\/j.cpc.2026.110161","article-title":"Algorithmic detection\nof crystal\nstructures from computer simulation data","volume":"325","author":"Kundu","year":"2025","journal-title":"Comput.\nPhys. Commun."},{"key":"2026092209073793700_cit41","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1107\/S0021889800000157","article-title":"Solving Crystal Structures\nin P1: An Automated Procedure\nfor Finding an Allowed Origin in the Correct Space Group","volume":"33","author":"Burla","year":"2000","journal-title":"J. Appl. Crystallogr."},{"key":"2026092209073793700_cit42","doi-asserted-by":"publisher","first-page":"975","DOI":"10.1107\/S0021889808028185","article-title":"Symmetry Determination Following\nStructure Solution\nin P1","volume":"41","author":"Palatinus","year":"2008","journal-title":"J. Appl. Crystallogr."},{"key":"2026092209073793700_cit43","doi-asserted-by":"publisher","first-page":"2430","DOI":"10.1107\/S1399004714014795","article-title":"Space-Group and\nOrigin Ambiguity in Macromolecular\nStructures with Pseudo-Symmetry and Its Treatment with the Program\nZanuda","volume":"70","author":"Lebedev","year":"2014","journal-title":"Acta Crystallogr. D"},{"key":"2026092209073793700_cit44","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1021\/acs.macromol.3c02103","article-title":"Stabilize Various\nNovel Network Structures\nvia the Alternate Arrangement of A\/C Domains in Close Contact by Tailoring\nABC Miktoarm Star Architectures","volume":"57","author":"Li","year":"2024","journal-title":"Macromolecules"}],"container-title":["Journal of Chemical Theory\nand Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acs.jctc.6c01542","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/jctcce\/article-pdf\/22\/18\/9711\/68455372\/acs.jctc.6c01542.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.acs.org\/jctcce\/article-pdf\/22\/18\/9711\/68455372\/acs.jctc.6c01542.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T13:16:32Z","timestamp":1790082992000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/jctcce\/article\/22\/18\/9711\/5426767\/Automated-Space-Group-Determination-for-Periodic"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,9]]},"references-count":44,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2026,9,9]]},"published-print":{"date-parts":[[2026,9,22]]}},"URL":"https:\/\/doi.org\/10.1021\/acs.jctc.6c01542","relation":{},"ISSN":["1549-9618","1549-9626"],"issn-type":[{"value":"1549-9618","type":"print"},{"value":"1549-9626","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,9]]}}}