{"id":"https://openalex.org/W2057902160","doi":"https://doi.org/10.1107/s0108767393008980","title":"Structure solution by minimal-function phase refinement and Fourier filtering. I. Theoretical basis","display_name":"Structure solution by minimal-function phase refinement and Fourier filtering. I. Theoretical basis","publication_year":1994,"publication_date":"1994-03-01","ids":{"openalex":"https://openalex.org/W2057902160","doi":"https://doi.org/10.1107/s0108767393008980","mag":"2057902160","pmid":"https://pubmed.ncbi.nlm.nih.gov/8166951"},"language":"en","primary_location":{"id":"doi:10.1107/s0108767393008980","doi":"https://doi.org/10.1107/s0108767393008980","is_oa":false,"landing_page_url":"https://doi.org/10.1107/s0108767393008980","pdf_url":null,"source":{"id":"https://openalex.org/S150871906","display_name":"Acta Crystallographica Section A Foundations of Crystallography","issn_l":"0108-7673","issn":["0108-7673","1600-5724"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Crystallographica Section A Foundations of Crystallography","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004281454","display_name":"George T. DeTitta","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. T. DeTitta","raw_affiliation_strings":["Medical Foundation of Buffalo, Inc., NY 14203"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Medical Foundation of Buffalo, Inc., NY 14203","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108739443","display_name":"Charles M. Weeks","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. M. Weeks","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063807045","display_name":"P. Thuman","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Thuman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109286228","display_name":"Russ Miller","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. Miller","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5084474101","display_name":"Herbert A. Hauptman","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. A. Hauptman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.7303,"has_fulltext":false,"cited_by_count":92,"citation_normalized_percentile":{"value":0.95866039,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"50","issue":"2","first_page":"203","last_page":"210"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12613","display_name":"X-ray Diffraction in Crystallography","score":0.8324999809265137,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12613","display_name":"X-ray Diffraction in Crystallography","score":0.8324999809265137,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11162","display_name":"Enzyme Structure and Function","score":0.14149999618530273,"subfield":{"id":"https://openalex.org/subfields/1315","display_name":"Structural Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10464","display_name":"Crystal structures of chemical compounds","score":0.012000000104308128,"subfield":{"id":"https://openalex.org/subfields/1604","display_name":"Inorganic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/phase-determination","display_name":"phase determination","score":0.7649999856948853},{"id":"https://openalex.org/keywords/structure-solution","display_name":"structure solution","score":0.6489999890327454},{"id":"https://openalex.org/keywords/fourier-filtering","display_name":"Fourier filtering","score":0.9129999876022339},{"id":"https://openalex.org/keywords/structure-factor","display_name":"structure factor","score":0.8029999732971191},{"id":"https://openalex.org/keywords/conditional-distributions","display_name":"conditional distributions","score":0.6779999732971191},{"id":"https://openalex.org/keywords/global-minimum","display_name":"global minimum","score":0.578000009059906},{"id":"https://openalex.org/keywords/reciprocal-lattice-vectors","display_name":"reciprocal lattice vectors","score":0.7089999914169312},{"id":"https://openalex.org/keywords/enantiomorphs","display_name":"enantiomorphs","score":0.5839999914169312},{"id":"https://openalex.org/keywords/space-groups","display_name":"space groups","score":0.5709999799728394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.624915599822998},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5530272722244263},{"id":"https://openalex.org/C89957378","wikidata":"https://www.wikidata.org/wiki/Q164129","display_name":"Reciprocal lattice","level":3,"score":0.4887702167034149},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.48493435978889465},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4757359027862549},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.47051945328712463},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4257567822933197},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4228770136833191},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4135187864303589},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.41168081760406494},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30082643032073975},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2259540855884552},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14520591497421265},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12010762095451355},{"id":"https://openalex.org/C207114421","wikidata":"https://www.wikidata.org/wiki/Q133900","display_name":"Diffraction","level":2,"score":0.09386160969734192},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D005583","descriptor_name":"Fourier Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008968","descriptor_name":"Molecular Conformation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D018360","descriptor_name":"Crystallography, X-Ray","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1107/s0108767393008980","doi":"https://doi.org/10.1107/s0108767393008980","is_oa":false,"landing_page_url":"https://doi.org/10.1107/s0108767393008980","pdf_url":null,"source":{"id":"https://openalex.org/S150871906","display_name":"Acta Crystallographica Section A Foundations of Crystallography","issn_l":"0108-7673","issn":["0108-7673","1600-5724"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Crystallographica Section A Foundations of Crystallography","raw_type":"journal-article"},{"id":"pmid:8166951","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/8166951","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta crystallographica. Section A, Foundations of crystallography","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4915256299","display_name":"NEW METHODS OF BIOMOLECULAR STRUCTURE DETERMINATION","funder_award_id":"P01GM046733","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"},{"id":"https://openalex.org/G7074119801","display_name":"DIFFRACTION STUDIES OF THE BIOTIN VITAMERS","funder_award_id":"R01DK019856","funder_id":"https://openalex.org/F4320337357","funder_display_name":"National Institute of Diabetes and Digestive and Kidney Diseases"}],"funders":[{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"},{"id":"https://openalex.org/F4320337357","display_name":"National Institute of Diabetes and Digestive and Kidney Diseases","ror":"https://ror.org/00adh9b73"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2015335500"],"related_works":["https://openalex.org/W2506266366","https://openalex.org/W2008307266","https://openalex.org/W2015335500","https://openalex.org/W2017987515","https://openalex.org/W1988823689","https://openalex.org/W2731370656","https://openalex.org/W104384644","https://openalex.org/W2002143420","https://openalex.org/W1993351260","https://openalex.org/W2143624038"],"abstract_inverted_index":{"Eliminating":[0],"the":[1,14,19,30,36,58,71,94,109,117,139,159,170,175,186,195,200,212,218,236,254,263,267,272,275,284,287,294,299,304,307,316],"N":[2,46,82,292],"atomic":[3],"position":[4],"vectors":[5,65],"rj,":[6],"j":[7],"=":[8],"1,":[9],"2,":[10],"...,":[11],"N,":[12],"from":[13],"system":[15,26,52,103,311],"of":[16,27,38,53,62,70,81,104,125,134,141,150,172,188,197,215,256,261,266,286,291,306,312],"equations":[17,313],"defining":[18],"normalized":[20],"structure":[21],"factors":[22],"EH":[23],"yields":[24],"a":[25,90,102,147],"identities":[28,54,105,225,273],"that":[29,35,101,161,228,260,274],"EH's":[31,39],"must":[32,124,277],"satisfy,":[33],"provided":[34],"set":[37,59],"is":[40,68,75,106,169,194,209,233,245],"sufficiently":[41],"large.":[42],"Clearly,":[43],"for":[44,77,89,282],"fixed":[45,91],"and":[47,67,122,136,157,190,192,244,279,293],"specified":[48],"space":[49],"group,":[50],"this":[51],"depends":[55,115],"only":[56],"on":[57,116],"{H},":[60],"consisting":[61],"n":[63],"reciprocal-lattice":[64],"H,":[66],"independent":[69],"crystal":[72,92],"structure,":[73,93],"which":[74,114,123],"assumed":[76],"simplicity":[78],"to":[79,146,179,222,231,240,248,303],"consist":[80],"identical":[83],"atoms":[84],"per":[85],"unit":[86],"cell.":[87],"However,":[88],"magnitudes":[95,120,143,155,296],"|EH|":[96,121],"are":[97,177,202,220,229,238],"uniquely":[98,152],"determined":[99,153],"so":[100],"obtained":[107],"among":[108,226],"corresponding":[110],"phases":[111,176,201,219,237,276,288,317],"\u03d5H":[112],"alone,":[113],"presumed":[118],"known":[119,130,230,295],"necessity":[126],"be":[127],"satisfied.":[128],"The":[129,206],"conditional":[131],"probability":[132],"distributions":[133],"triplets":[135],"quartets,":[137],"given":[138],"values":[140,243,285],"certain":[142],"|E|,":[144],"lead":[145],"function":[148,268],"R(\u03d5)":[149,173,198,269],"phases,":[151],"by":[154,259,271,315],"|E|":[156],"having":[158],"property":[160],"RT":[162,168],"<":[163,165],"\u00bd":[164],"RR,":[166],"where":[167,217],"value":[171,196],"when":[174,199,235],"equal":[178,239,247],"their":[180,241],"true":[181,242],"values,":[182],"no":[183],"matter":[184],"what":[185],"choice":[187],"origin":[189],"enantiomorph,":[191],"RR":[193],"chosen":[203],"at":[204],"random.":[205],"following":[207],"conjecture":[208],"therefore":[210],"plausible:":[211],"global":[213,264],"minimum":[214,265],"R(\u03d5),":[216],"constrained":[221,270],"satisfy":[223,278],"all":[224],"them":[227],"exist,":[232],"attained":[234],"thus":[246],"RT.":[249],"This":[250],"`minimal":[251],"principle'":[252],"replaces":[253],"problem":[255],"phase":[257],"determination":[258],"finding":[262],"suggests":[280],"strategies":[281],"determining":[283],"in":[289],"terms":[290],"|E|.":[297],"Equivalently,":[298],"minimal":[300],"principle":[301],"leads":[302],"solution":[305],"(in":[308],"general":[309],"redundant)":[310],"satisfied":[314],"\u03d5H.":[318]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2016-06-24T00:00:00"}