{"id":"https://openalex.org/W2801391568","doi":"https://doi.org/10.3390/computation6020036","title":"Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory","display_name":"Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory","publication_year":2018,"publication_date":"2018-05-03","ids":{"openalex":"https://openalex.org/W2801391568","doi":"https://doi.org/10.3390/computation6020036","mag":"2801391568"},"language":"en","primary_location":{"id":"doi:10.3390/computation6020036","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation6020036","pdf_url":"https://www.mdpi.com/2079-3197/6/2/36/pdf?version=1525778171","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-3197/6/2/36/pdf?version=1525778171","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005250292","display_name":"C. Amovilli","orcid":"https://orcid.org/0000-0001-8024-6972"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Claudio Amovilli","raw_affiliation_strings":["Dipartimento di Chimica e Chimica Industriale, University of Pisa, Via Giuseppe Moruzzi 13, 56124 Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Chimica e Chimica Industriale, University of Pisa, Via Giuseppe Moruzzi 13, 56124 Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057495807","display_name":"Franca Maria Floris","orcid":"https://orcid.org/0000-0001-7838-8031"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Franca Floris","raw_affiliation_strings":["Dipartimento di Chimica e Chimica Industriale, University of Pisa, Via Giuseppe Moruzzi 13, 56124 Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Chimica e Chimica Industriale, University of Pisa, Via Giuseppe Moruzzi 13, 56124 Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005250292"],"corresponding_institution_ids":["https://openalex.org/I108290504"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.5994,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.67643545,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"6","issue":"2","first_page":"36","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.9962999820709229,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/density-functional-theory","display_name":"Density functional theory","score":0.5711359977722168},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5568740367889404},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5318213105201721},{"id":"https://openalex.org/keywords/von-neumann-entropy","display_name":"Von Neumann entropy","score":0.529891312122345},{"id":"https://openalex.org/keywords/kohn\u2013sham-equations","display_name":"Kohn\u2013Sham equations","score":0.4754997193813324},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4734862744808197},{"id":"https://openalex.org/keywords/r\u00e9nyi-entropy","display_name":"R\u00e9nyi entropy","score":0.4281523823738098},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4078252613544464},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3933411240577698},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.39149022102355957},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.3423084616661072},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.2093711793422699},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.13890182971954346},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1279725730419159},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07951027154922485}],"concepts":[{"id":"https://openalex.org/C152365726","wikidata":"https://www.wikidata.org/wiki/Q1048589","display_name":"Density functional theory","level":2,"score":0.5711359977722168},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5568740367889404},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5318213105201721},{"id":"https://openalex.org/C101973423","wikidata":"https://www.wikidata.org/wiki/Q6961323","display_name":"Von Neumann entropy","level":4,"score":0.529891312122345},{"id":"https://openalex.org/C9059619","wikidata":"https://www.wikidata.org/wiki/Q3272140","display_name":"Kohn\u2013Sham equations","level":3,"score":0.4754997193813324},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4734862744808197},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.4281523823738098},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4078252613544464},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3933411240577698},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.39149022102355957},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3423084616661072},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.2093711793422699},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.13890182971954346},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1279725730419159},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07951027154922485}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/computation6020036","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation6020036","pdf_url":"https://www.mdpi.com/2079-3197/6/2/36/pdf?version=1525778171","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:arpi.unipi.it:11568/940029","is_oa":true,"landing_page_url":"https://www.mdpi.com/2079-3197/6/2/36","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:6d6be582580d4ec6ad8d94ffe9cdd782","is_oa":true,"landing_page_url":"https://doaj.org/article/6d6be582580d4ec6ad8d94ffe9cdd782","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computation, Vol 6, Iss 2, p 36 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2079-3197/6/2/36/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/computation6020036","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computation; Volume 6; Issue 2; Pages: 36","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/computation6020036","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation6020036","pdf_url":"https://www.mdpi.com/2079-3197/6/2/36/pdf?version=1525778171","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8999999761581421}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321015","display_name":"University of Twente","ror":"https://ror.org/006hf6230"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2801391568.pdf","grobid_xml":"https://content.openalex.org/works/W2801391568.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1538936441","https://openalex.org/W1614843501","https://openalex.org/W1965555277","https://openalex.org/W1975123852","https://openalex.org/W1978575119","https://openalex.org/W1983656816","https://openalex.org/W1987973194","https://openalex.org/W1988695792","https://openalex.org/W1989954305","https://openalex.org/W1995734340","https://openalex.org/W1998807253","https://openalex.org/W2008423326","https://openalex.org/W2022950330","https://openalex.org/W2023271753","https://openalex.org/W2023390323","https://openalex.org/W2032719166","https://openalex.org/W2035764067","https://openalex.org/W2038533471","https://openalex.org/W2052200330","https://openalex.org/W2061300072","https://openalex.org/W2061762703","https://openalex.org/W2062852634","https://openalex.org/W2071919153","https://openalex.org/W2075835929","https://openalex.org/W2076468224","https://openalex.org/W2081450391","https://openalex.org/W2086957099","https://openalex.org/W2099796414","https://openalex.org/W2112850441","https://openalex.org/W2138673728","https://openalex.org/W2556594845","https://openalex.org/W2606642590","https://openalex.org/W3125506358","https://openalex.org/W4254050667"],"related_works":["https://openalex.org/W2242992884","https://openalex.org/W2001290700","https://openalex.org/W1980286301","https://openalex.org/W3101369475","https://openalex.org/W3126762636","https://openalex.org/W3123254516","https://openalex.org/W2014583985","https://openalex.org/W2214322677","https://openalex.org/W2949606031","https://openalex.org/W4223924708"],"abstract_inverted_index":{"Electron":[0],"density":[1,43,98],"is":[2,29],"used":[3],"to":[4,20,23,36],"compute":[5],"Shannon":[6,27,106],"entropy.":[7,107],"The":[8],"deviation":[9],"from":[10,53,67,104],"the":[11,38,84,87,91,101],"Hartree\u2013Fock":[12],"(HF)":[13],"of":[14,40,58,77],"this":[15,50],"quantity":[16,35],"has":[17],"been":[18],"observed":[19],"be":[21],"related":[22],"correlation":[24],"energy.":[25],"Thus,":[26],"entropy":[28],"here":[30],"proposed":[31],"as":[32],"a":[33],"valid":[34],"assess":[37],"quality":[39],"an":[41],"energy":[42],"functional":[44],"developed":[45],"within":[46],"Kohn\u2013Sham":[47],"theory.":[48],"To":[49],"purpose,":[51],"results":[52,65,81],"eight":[54],"different":[55],"functionals,":[56],"representative":[57],"Jacob\u2019s":[59],"ladder,":[60],"are":[61,90],"compared":[62],"with":[63],"accurate":[64],"obtained":[66],"diffusion":[68],"quantum":[69],"Monte":[70],"Carlo":[71],"(DMC)":[72],"computations.":[73],"For":[74],"three":[75],"series":[76],"atomic":[78],"ions,":[79],"our":[80],"show":[82],"that":[83],"revTPSS":[85],"and":[86],"PBE0":[88],"functionals":[89],"best,":[92],"whereas":[93],"those":[94],"based":[95],"on":[96],"local":[97],"approximation":[99],"give":[100],"largest":[102],"discrepancy":[103],"DMC":[105]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}