{"id":"W2081994518","doi":"10.1063/1.2006087","title":"Generalizations of the Hohenberg-Kohn theorem: I. Legendre Transform Constructions of Variational Principles for Density Matrices and Electron Distribution Functions","year":2006,"lang":"en","type":"article","venue":"The Journal of Chemical Physics","topic":"Advanced Chemical Physics Studies","field":"Physics and Astronomy","cited_by":92,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs","keywords":"Legendre transformation; Legendre polynomials; Ansatz; Mathematics; Hamiltonian (control theory); Maximization; Legendre function; Operator (biology); Formalism (music); Diagonal; Pure mathematics; Applied mathematics; Mathematical physics; Mathematical analysis; Quantum mechanics; Physics; Mathematical optimization; Chemistry","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002251619,0.0005227612,0.0005845908,0.0008578545,0.0006756677,0.001311713,0.001713742,0.001241357,0.003820351],"category_scores_gemma":[0.003055087,0.000310059,0.0009908275,0.0006869386,0.00303777,0.004126895,0.001353308,0.001799104,0.0004848978],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008879944,"about_ca_system_score_gemma":0.001006688,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001191438,"about_ca_topic_score_gemma":0.00100124,"domain_scores_codex":[0.9994429,0.0001794495,0.00002908286,0.00008185283,0.0001987701,0.00006806435],"domain_scores_gemma":[0.9992635,0.0003456938,0.00008429917,0.000175024,0.00008993579,0.00004156034],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000004220948,0.000005466934,0.00003026902,0.00002138343,0.000003253336,0.0000205915,0.00003358108,0.005079276,0.0007011641,0.9911816,0.0002245633,0.002694752],"study_design_scores_gemma":[0.000004952483,0.0000136536,0.00009243007,0.00001002443,0.000001703184,0.00006326242,0.00002148618,0.05688753,0.0005925001,0.9406902,0.001611177,0.00001104604],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03623683,0.0009620331,0.9228005,0.001257081,0.0001803636,0.00006056005,0.0001219146,0.0001104129,0.03827032],"genre_scores_gemma":[0.6784328,0.002168349,0.2975386,0.0009938834,0.0003390698,0.0002759238,0.0001916225,0.0002164945,0.01984332],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003820351,"threshold_uncertainty_score":0.01278037,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007429314557984753,"score_gpt":0.2249575659045683,"score_spread":0.2175282513465835,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}