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We show that the Q-path integral given by the homogeneous density scaling, n\u03bb(r) = \u03bbn(r), is related to the gauge of the semilocal functionals in the slowly-varying density regime. This fact makes the Q-path integral a useful method for developing density functionals for solid-state systems. To prove this statement, we construct generalized gradient approximation kinetic and exchange energy functionals, starting from simple model potentials and using the Q-path approach. We test these functionals for several equilibrium properties of bulk solids.<\/jats:p>","DOI":"10.1063\/5.0348651","type":"journal-article","created":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T11:11:40Z","timestamp":1790161900000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Kinetic and exchange energy semilocal functionals derived from model potentials by\n                    <i>Q<\/i>\n                    -path integration"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8923-3203","authenticated-orcid":false,"given":"Lucian A.","family":"Constantin","sequence":"first","affiliation":[{"name":"Institute for Microelectronics and Microsystems (CNR-IMM) 1 , Via Monteroni, Campus Unisalento, 73100 Lecce,","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7270-6043","authenticated-orcid":false,"given":"Fulvio","family":"Sarcinella","sequence":"additional","affiliation":[{"name":"Institute for Microelectronics and Microsystems (CNR-IMM) 1 , Via Monteroni, Campus Unisalento, 73100 Lecce,","place":["Italy"]},{"name":"Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia 2 , Via Barsanti 14, 73010 Arnesano, LE,","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0940-8830","authenticated-orcid":false,"given":"Fabio","family":"Della Sala","sequence":"additional","affiliation":[{"name":"Institute for Microelectronics and Microsystems (CNR-IMM) 1 , Via Monteroni, Campus Unisalento, 73100 Lecce,","place":["Italy"]},{"name":"Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia 2 , Via Barsanti 14, 73010 Arnesano, LE,","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,23]]},"reference":[{"key":"2026092307101382000_c1","doi-asserted-by":"publisher","first-page":"B864","DOI":"10.1103\/physrev.136.b864","volume":"136","year":"1964","journal-title":"Phys. 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