{"public_id":"cl_66208319e3542dac9d8596afa9b72b1f","status":"active","superseded_by_public_id":null,"corpus_id":32330648,"text":"At T=0, the inverse hardness 1/η equals the density of states at the Fermi energy g(εF), and the Fukui function f(r) equals the local density of states at the Fermi energy g(εF, r) divided by g(εF).","confidence":0.95,"paper":{"corpus_id":32330648,"title":"Hardness, softness, and the fukui function in the electronic theory of metals and catalysis.","url":"https://sah.borca.ai/papers/32330648"},"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"origin_summary":{"object_type":"claim","status":"active","confidence":0.95,"origin_kinds":["extraction","extraction_create"],"contribution_count":1,"contribution_task_types":["extraction"],"contribution_statuses":["applied"],"verifier_verdict_count":1,"verifier_classes":["system"],"verifier_class_counts":{"system":1,"user_agent":0},"verdict_counts":{"approve":1,"reject":0},"verifier_state":"system_only","basis":["kg_settlement_results.decision_payload.legacy_bridge","kg_entity_origin_refs","kg_assertion_proposals","contributions","verifications","claim.status","claim.confidence"],"limits":["ledger provenance is aggregated; raw contribution and verifier audit rows are not expanded","entity matching uses settlement bridge refs and edge commands"]},"concepts":[{"public_id":"co_7cdb4c733eb77014a35fb722c9d2e3bb","name":"density of states g(εF)","description":"The density of electronic states evaluated at the Fermi energy εF, used to express the inverse hardness at T=0.","types":["physical quantity"],"url":"https://sah.borca.ai/concepts/co_7cdb4c733eb77014a35fb722c9d2e3bb"},{"public_id":"co_a78dd17741f932fff372dfa49c4e08b6","name":"local density of states g(εF, r)","description":"The local density of states at the Fermi energy εF as a function of position r, used to express the Fukui function at T=0.","types":["physical quantity"],"url":"https://sah.borca.ai/concepts/co_a78dd17741f932fff372dfa49c4e08b6"},{"public_id":"co_b3688039e728391c2114da33e6576ca7","name":"hardness η","description":"A concept from chemical reactivity theory, defined as η = (∂²E/∂N²)ν, extended to metals where at T=0 its inverse equals the density of states at the Fermi energy.","types":["theoretical concept"],"url":"https://sah.borca.ai/concepts/co_b3688039e728391c2114da33e6576ca7"},{"public_id":"co_c5bf1fe3c1f3d21c1d03cdadb96b19e9","name":"Fukui function f(r)","description":"A function defined as f(r) = [∂ρ(r)/∂N]ν, extended to metals where at T=0 it equals the local density of states at the Fermi energy divided by the total density of states.","types":["theoretical concept"],"url":"https://sah.borca.ai/concepts/co_c5bf1fe3c1f3d21c1d03cdadb96b19e9"}],"related_claims":[],"url":"https://sah.borca.ai/claims/cl_66208319e3542dac9d8596afa9b72b1f"}