{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T06:50:05Z","timestamp":1781333405146,"version":"3.54.1"},"reference-count":92,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T00:00:00Z","timestamp":1644883200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations (yGGA), are potentially efficient real-space semilocal methods that include significant non-local effects and can describe different important exact properties of the kinetic energy. In this work, we focus in particular on the linear response behavior for the homogeneous electron gas (HEG). We show that such functionals are able to reproduce the exact Lindhard function behavior with a very good accuracy, outperforming all other semilocal kinetic functionals. These theoretical advances allow us to perform a detailed analysis of a special class of yGGAs, namely the linear yGGA functionals. Thus, we show how the present approach can generalize the yGGA functionals improving the HEG linear behavior and leading to an extended formula for the kinetic functional. Moreover, testing on several jellium cluster model systems allows highlighting advantages and limitations of the linear yGGA functionals and future perspectives for the development of yGGA kinetic functionals.<\/jats:p>","DOI":"10.3390\/computation10020030","type":"journal-article","created":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T22:43:22Z","timestamp":1644965002000},"page":"30","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Kinetic Energy Density Functionals Based on a Generalized Screened Coulomb Potential: Linear Response and Future Perspectives"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3990-669X","authenticated-orcid":false,"given":"Eduardo","family":"Fabiano","sequence":"first","affiliation":[{"name":"Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy"},{"name":"Center for Biomolecular Nanotechnologies@UNILE, Istituto Italiano di Tecnologia, Via Barsanti 14, 73010 Arnesano, 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":"Center for Biomolecular Nanotechnologies@UNILE, Istituto Italiano di Tecnologia, Via Barsanti 14, 73010 Arnesano, Italy"},{"name":"Department of Mathematics and Physics \u201cE. De Giorgi\u201d, University of Salento, Via Arnesano, 73100 Lecce, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8923-3203","authenticated-orcid":false,"given":"Lucian","family":"Constantin","sequence":"additional","affiliation":[{"name":"Istituto di Nanoscienze, Consiglio Nazionale delle Ricerche (CNR-NANO), 41125 Modena, 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), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy"},{"name":"Center for Biomolecular Nanotechnologies@UNILE, Istituto Italiano di Tecnologia, Via Barsanti 14, 73010 Arnesano, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"B864","DOI":"10.1103\/PhysRev.136.B864","article-title":"Inhomogeneous Electron Gas","volume":"136","author":"Hohenberg","year":"1964","journal-title":"Phys. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Dreizler, R.M., and Gross, E.K.U. (1990). Density Functional Theory, Springer.","DOI":"10.1007\/978-3-642-86105-5"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6062","DOI":"10.1073\/pnas.76.12.6062","article-title":"Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem","volume":"76","author":"Levy","year":"1979","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"A1133","DOI":"10.1103\/PhysRev.140.A1133","article-title":"Self-Consistent Equations Including Exchange and Correlation Effects","volume":"140","author":"Kohn","year":"1965","journal-title":"Phys. Rev."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wang, Y.A., and Carter, E.A. (2002). Orbital-free kinetic-energy density functional theory. Theoretical Methods in Condensed Phase Chemistry, Springer.","DOI":"10.1007\/0-306-46949-9_5"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wesolowski, T.A., and Wang, Y.A. (2013). Recent Progress in Orbital-Free Density Functional Theory, World Scientific.","DOI":"10.1142\/8633"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1016\/j.jmps.2007.01.012","article-title":"Quasi-continuum orbital-free density-functional theory: A route to multi-million atom non-periodic DFT calculation","volume":"55","author":"Gavini","year":"2007","journal-title":"J. Mech. Phys. Sol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1557\/jmr.2017.462","article-title":"Orbital-free density functional theory for materials research","volume":"33","author":"Witt","year":"2018","journal-title":"J. Mater. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3161","DOI":"10.1021\/ct9001784","article-title":"Performance of Kinetic Energy Functionals for Interaction Energies in a Subsystem Formulation of Density Functional Theory","volume":"5","author":"Beyhan","year":"2009","journal-title":"J. Chem. Theory Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1002\/wcms.1175","article-title":"Subsystem density-functional theory","volume":"4","author":"Jacob","year":"2014","journal-title":"Wiley Interdiscip. Rev. Comput. Mol. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5891","DOI":"10.1021\/cr500502v","article-title":"Frozen-Density Embedding Strategy for Multilevel Simulations of Electronic Structure","volume":"115","author":"Wesolowski","year":"2015","journal-title":"Chem. Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2009.12.001","article-title":"Chromophore-specific theoretical spectroscopy: From subsystem density functional theory to mode-specific vibrational spectroscopy","volume":"489","author":"Neugebauer","year":"2010","journal-title":"Phys. Rep."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"183202","DOI":"10.1088\/0953-8984\/27\/18\/183202","article-title":"Subsystem density-functional theory as an effective tool for modeling ground and excited states, their dynamics and many-body interactions","volume":"27","author":"Krishtal","year":"2015","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"164111","DOI":"10.1063\/1.3494537","article-title":"Frozen density embedding with hybrid functionals","volume":"133","author":"Laricchia","year":"2010","journal-title":"J. Chem. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"154121","DOI":"10.1063\/1.4917257","article-title":"Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals","volume":"142","author":"Fabiano","year":"2015","journal-title":"J. Chem. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7132","DOI":"10.1038\/ncomms8132","article-title":"Resonance Shifts and Spill-out Effects in Self-Consistent Hydrodynamic Nanoplasmonics","volume":"6","author":"Toscano","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"205405","DOI":"10.1103\/PhysRevB.93.205405","article-title":"Quantum hydrodynamic theory for plasmonics: Impact of the electron density tail","volume":"93","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"031903","DOI":"10.1063\/1.5003910","article-title":"Theoretical Foundations of Quantum Hydrodynamics for Plasmas","volume":"25","author":"Moldabekov","year":"2018","journal-title":"Phys. Plasmas"},{"key":"ref_19","first-page":"011049","article-title":"Laplacian-Level Quantum Hydrodynamic Theory for Plasmonics","volume":"11","author":"Baghramyan","year":"2021","journal-title":"Phys. Rev. X"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"052512","DOI":"10.1103\/PhysRevA.96.052512","article-title":"Deorbitalization strategies for meta-generalized-gradient-approximation exchange-correlation functionals","volume":"96","author":"Trickey","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"115161","DOI":"10.1103\/PhysRevB.98.115161","article-title":"Deorbitalized meta-GGA exchange-correlation functionals in solids","volume":"98","author":"Trickey","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"121109","DOI":"10.1103\/PhysRevB.102.121109","article-title":"Meta-GGA performance in solids at almost GGA cost","volume":"102","author":"Trickey","year":"2020","journal-title":"Phys. Rev. B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"144105","DOI":"10.1063\/1.5048907","article-title":"Orbital-free approximations to the kinetic-energy density in exchange-correlation MGGA functionals: Tests on solids","volume":"149","author":"Tran","year":"2018","journal-title":"J. Chem. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"024407","DOI":"10.1103\/PhysRevB.102.024407","article-title":"Shortcomings of meta-GGA functionals when describing magnetism","volume":"102","author":"Tran","year":"2020","journal-title":"Phys. Rev. B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"6978","DOI":"10.1073\/pnas.77.12.6978","article-title":"An atomic kinetic energy functional with full Weizsacker correction","volume":"77","author":"Acharya","year":"1980","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"6920","DOI":"10.1103\/PhysRevA.46.6920","article-title":"Comparison of kinetic-energy density functionals","volume":"46","author":"Thakkar","year":"1992","journal-title":"Phys. Rev. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5328","DOI":"10.1103\/PhysRevA.50.5328","article-title":"Obtaining a gradient\u2013corrected kinetic\u2013energy functional from the Perdew\u2013Wang exchange functional","volume":"50","author":"Lembarki","year":"1994","journal-title":"Phys. Rev. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1002\/qua.10306","article-title":"Link between the kinetic-and exchange-energy functionals in the generalized gradient approximation","volume":"89","author":"Tran","year":"2002","journal-title":"Int. J. Quant. Chem."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"186406","DOI":"10.1103\/PhysRevLett.106.186406","article-title":"Semiclassical neutral atom as a reference system in density functional theory","volume":"106","author":"Constantin","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2439","DOI":"10.1021\/ct200382w","article-title":"Generalized Gradient Approximations of the Noninteracting Kinetic Energy from the Semiclassical Atom Theory: Rationalization of the Accuracy of the Frozen Density Embedding Theory for Nonbonded Interactions","volume":"7","author":"Laricchia","year":"2011","journal-title":"J. Chem. Theory Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"161108(R)","DOI":"10.1103\/PhysRevB.88.161108","article-title":"Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations","volume":"88","author":"Karasiev","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2250","DOI":"10.1021\/ct400129d","article-title":"Density scaling of noninteracting kinetic energy functionals","volume":"9","author":"Borgoo","year":"2013","journal-title":"J. Chem. Theory Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"117101","DOI":"10.1103\/PhysRevB.92.117101","article-title":"Comment on \u201cSingle-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation\u201d","volume":"92","author":"Trickey","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"117102","DOI":"10.1103\/PhysRevB.92.117102","article-title":"Reply to \u201cComment on \u2018Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation\u2019\u201d","volume":"92","author":"Xia","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"115153","DOI":"10.1103\/PhysRevB.95.115153","article-title":"Jellium-with-gap model applied to semilocal kinetic functionals","volume":"95","author":"Constantin","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"041111(R)","DOI":"10.1103\/PhysRevB.98.041111","article-title":"A simple generalized gradient approximation for the noninteracting kinetic energy density functional","volume":"98","author":"Luo","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"165111","DOI":"10.1103\/PhysRevB.100.165111","article-title":"Semilocal kinetic energy functionals with parameters from neutral atoms","volume":"100","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"155109","DOI":"10.1103\/PhysRevB.75.155109","article-title":"Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy","volume":"75","author":"Perdew","year":"2007","journal-title":"Phys. Rev. B"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"245120","DOI":"10.1103\/PhysRevB.80.245120","article-title":"Properties of constraint-based single-point approximate kinetic energy functionals","volume":"80","author":"Karasiev","year":"2009","journal-title":"Phys. Rev. B"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1021\/ct400836s","article-title":"Laplacian-Level kinetic energy approximations based on the fourth-order gradient expansion: Global assessment and application to the subsystem formulation of density functional theory","volume":"10","author":"Laricchia","year":"2013","journal-title":"J. Chem. Theory Comput."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"084107","DOI":"10.1063\/1.4942016","article-title":"Visualization and analysis of the Kohn-Sham kinetic energy density and its orbital-free description in molecules","volume":"144","author":"Cancio","year":"2016","journal-title":"J. Chem. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1080\/00268976.2016.1246757","article-title":"Visualisation and orbital-free parametrisation of the large-Z scaling of the kinetic energy density of atoms","volume":"115","author":"Cancio","year":"2017","journal-title":"Mol. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"4385","DOI":"10.1021\/acs.jpclett.8b01926","article-title":"Semilocal Pauli\u2013Gaussian Kinetic Functionals for Orbital-Free Density Functional Theory Calculations of Solids","volume":"9","author":"Constantin","year":"2018","journal-title":"J. Phys. Chem. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"3044","DOI":"10.1021\/acs.jctc.9b00183","article-title":"Performance of Semilocal Kinetic Energy Functionals for Orbital-Free Density Functional Theory","volume":"15","author":"Constantin","year":"2019","journal-title":"J. Chem. Theory Comput."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"\u015amiga, S., Constantin, L.A., Della Sala, F., and Fabiano, E. (2019). The Role of the Reduced Laplacian Renormalization in the Kinetic Energy Functional Development. Computation, 7.","DOI":"10.3390\/computation7040065"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"045124","DOI":"10.1103\/PhysRevB.91.045124","article-title":"Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation","volume":"91","author":"Xia","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"13196","DOI":"10.1103\/PhysRevB.45.13196","article-title":"Kinetic-energy functional of the electron density","volume":"45","author":"Wang","year":"1992","journal-title":"Phys. Rev. B"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1088\/0953-8984\/6\/2\/014","article-title":"Hydrogen-hydrogen interaction in an electron gas","volume":"6","author":"Perrot","year":"1994","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"5220","DOI":"10.1103\/PhysRevB.49.5220","article-title":"Orbital-free kinetic-energy functionals for first-principles molecular dynamics","volume":"49","author":"Smargiassi","year":"1994","journal-title":"Phys. Rev. B"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"9509","DOI":"10.1103\/PhysRevB.53.9509","article-title":"Nonlocal kinetic-energy-density functionals","volume":"53","author":"Alvarellos","year":"1996","journal-title":"Phys. Rev. B"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1897","DOI":"10.1103\/PhysRevA.54.1897","article-title":"Kinetic-energy density functional: Atoms and shell structure","volume":"54","author":"Alvarellos","year":"1996","journal-title":"Phys. Rev. A"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"4857","DOI":"10.1103\/PhysRevB.57.4857","article-title":"Nonlocal symmetrized kinetic-energy density functional: Application to simple surfaces","volume":"57","author":"Alvarellos","year":"1998","journal-title":"Phys. Rev. B"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"13465","DOI":"10.1103\/PhysRevB.58.13465","article-title":"Orbital-free kinetic-energy functionals for the nearly free electron gas","volume":"58","author":"Wang","year":"1998","journal-title":"Phys. Rev. B"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"16350","DOI":"10.1103\/PhysRevB.60.16350","article-title":"Orbital-free kinetic-energy density functionals with a density-dependent kernel","volume":"60","author":"Wang","year":"1999","journal-title":"Phys. Rev. B"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"044103","DOI":"10.1063\/1.1834563","article-title":"Improving the orbital-free density functional theory description of covalent materials","volume":"122","author":"Zhou","year":"2005","journal-title":"J. Chem. Phys."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"074103","DOI":"10.1063\/1.2968612","article-title":"Fully nonlocal kinetic energy density functionals: A proposal and a general assessment for atomic systems","volume":"129","author":"Alvarellos","year":"2008","journal-title":"J. Chem. Phys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"022502","DOI":"10.1103\/PhysRevA.77.022502","article-title":"Approach to kinetic energy density functionals: Nonlocal terms with the structure of the von Weizs\u00e4cker functional","volume":"77","author":"Alvarellos","year":"2008","journal-title":"Phys. Rev. A"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"045206","DOI":"10.1103\/PhysRevB.81.045206","article-title":"Nonlocal orbital-free kinetic energy density functional for semiconductors","volume":"81","author":"Huang","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"18A531","DOI":"10.1063\/1.4869867","article-title":"Enhanced von Weizs\u00e4cker Wang-Govind-Carter kinetic energy density functional for semiconductors","volume":"140","author":"Shin","year":"2014","journal-title":"J. Chem. Phys."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"205137","DOI":"10.1103\/PhysRevB.97.205137","article-title":"Nonlocal kinetic energy functional from the jellium-with-gap model: Applications to orbital-free density functional theory","volume":"97","author":"Constantin","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"184107","DOI":"10.1063\/1.5023926","article-title":"Nonlocal kinetic energy functionals by functional integration","volume":"148","author":"Mi","year":"2018","journal-title":"J. Chem. Phys."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"041105","DOI":"10.1103\/PhysRevB.100.041105","article-title":"Orbital-free density functional theory correctly models quantum dots when asymptotics, nonlocality, and nonhomogeneity are accounted for","volume":"100","author":"Mi","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"045110","DOI":"10.1103\/PhysRevB.101.045110","article-title":"Nonlocal kinetic energy density functionals for isolated systems obtained via local density approximation kernels","volume":"101","author":"Xu","year":"2020","journal-title":"Phys. Rev. B"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1007\/s00214-015-1711-x","article-title":"Shell-structure-based functionals for the kinetic energy","volume":"134","author":"Finzel","year":"2015","journal-title":"Theor. Chem. Acc."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"034108","DOI":"10.1063\/1.4940035","article-title":"Local conditions for the Pauli potential in order to yield self-consistent electron densities exhibiting proper atomic shell structure","volume":"144","author":"Finzel","year":"2016","journal-title":"J. Chem. Phys."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"e25601","DOI":"10.1002\/qua.25601","article-title":"The Liu-Parr power series expansion of the Pauli kinetic energy functional with the incorporation of shell-inducing traits: Atoms","volume":"118","author":"Salazar","year":"2018","journal-title":"Int. J. Quantum Chem."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"1313","DOI":"10.1002\/qua.25179","article-title":"Study of some simple approximations to the non-interacting kinetic energy functional","volume":"116","author":"Salazar","year":"2016","journal-title":"Int. J. Quantum Chem."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1021\/acs.jctc.5b01011","article-title":"Kinetic Energy of Hydrocarbons as a Function of Electron Density and Convolutional Neural Networks","volume":"12","author":"Yao","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"3735","DOI":"10.1103\/PhysRevB.17.3735","article-title":"Nonlocal approximation to the exchange potential and kinetic energy of an inhomogeneous electron gas","volume":"17","author":"Alonso","year":"1978","journal-title":"Phys. Rev. B"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"7868","DOI":"10.1103\/PhysRevB.32.7868","article-title":"Nonlocal kinetic energy functional for nonhomogeneous electron systems","volume":"32","author":"Alvarellos","year":"1985","journal-title":"Phys. Rev. B"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"155127","DOI":"10.1103\/PhysRevB.103.155127","article-title":"Nonlocal kinetic energy functionals in real space using a Yukawa-potential kernel: Properties, linear response, and model functionals","volume":"103","author":"Sarcinella","year":"2021","journal-title":"Phys. Rev. B"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"024110","DOI":"10.1063\/5.0063629","article-title":"Accurate parameterization of the kinetic energy functional","volume":"156","author":"Kumar","year":"2022","journal-title":"J. Chem. Phys."},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Bach, V., and Delle Site, L. (2014). Progress on New Approaches to Old Ideas: Orbital-Free Density Functionals. Many-Electron Approaches in Physics, Chemistry and Mathematics, Springer.","DOI":"10.1007\/978-3-319-06379-9"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1002\/qua.560390405","article-title":"Non-local relation between kinetic and exchange energy densities in Hartree\u2013Fock theory","volume":"39","author":"March","year":"1991","journal-title":"Int. J. Quantum Chem."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"035126","DOI":"10.1103\/PhysRevB.91.035126","article-title":"Kohn-Sham kinetic energy density in the nuclear and asymptotic regions: Deviations from the von Weizs\u00e4cker behavior and applications to density functionals","volume":"91","author":"Fabiano","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"062501","DOI":"10.1103\/PhysRevA.63.062501","article-title":"r- and p-space electron densities and related kinetic and exchange energies in terms of s states alone for the leading term in the 1\/Z expansion for nonrelativistic closed-shell atomic ions","volume":"63","author":"Howard","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_77","doi-asserted-by":"crossref","unstructured":"Constantin, L.A., Fabiano, E., and Della Sala, F. (2016). Kinetic and Exchange Energy Densities near the Nucleus. Computation, 4.","DOI":"10.3390\/computation4020019"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"165144","DOI":"10.1103\/PhysRevB.101.165144","article-title":"Methods to generate reference total and Pauli kinetic potentials","volume":"101","author":"Fabiano","year":"2020","journal-title":"Phys. Rev. B"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"253002","DOI":"10.1103\/PhysRevLett.108.253002","article-title":"Finding density functionals with machine learning","volume":"108","author":"Snyder","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1002\/qua.25040","article-title":"Understanding machine-learned density functionals","volume":"116","author":"Li","year":"2016","journal-title":"Int. J. Quant. Chem."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"e25373","DOI":"10.1002\/qua.25373","article-title":"Kinetic energy density for orbital-free density functional calculations by axiomatic approach","volume":"117","author":"Alharbi","year":"2017","journal-title":"Int. J. Quantum Chem."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"241705","DOI":"10.1063\/1.5007230","article-title":"Semi-local machine-learned kinetic energy density functional with third-order gradients of electron density","volume":"148","author":"Seino","year":"2018","journal-title":"J. Chem. Phys."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1039\/C8CP06433D","article-title":"Kinetic energy densities based on the fourth order gradient expansion: Performance in different classes of materials and improvement via machine learning","volume":"21","author":"Golub","year":"2019","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"074104","DOI":"10.1063\/5.0015042","article-title":"Data-driven kinetic energy density fitting for orbital-free DFT: Linear vs Gaussian process regression","volume":"153","author":"Manzhos","year":"2020","journal-title":"J. Chem. Phys."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"5685","DOI":"10.1021\/acs.jctc.0c00580","article-title":"Machine Learning Approaches toward Orbital-free Density Functional Theory: Simultaneous Training on the Kinetic Energy Density Functional and Its Functional Derivative","volume":"16","author":"Meyer","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"033198","DOI":"10.1103\/PhysRevResearch.3.033198","article-title":"Order-N orbital-free density-functional calculations with machine learning of functional derivatives for semiconductors and metals","volume":"3","author":"Imoto","year":"2021","journal-title":"Phys. Rev. Res."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"1122","DOI":"10.1021\/acs.jctc.1c00812","article-title":"Toward Orbital-Free Density Functional Theory with Small Data Sets and Deep Learning","volume":"18","author":"Ryczko","year":"2022","journal-title":"J. Chem. Theory Comput."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"11635","DOI":"10.1073\/pnas.0505436102","article-title":"Nearsightedness of electronic matter","volume":"102","author":"Prodan","year":"2005","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"4228","DOI":"10.1021\/acs.jctc.7b00705","article-title":"Modified Fourth-Order Kinetic Energy Gradient Expansion with Hartree Potential-Dependent Coefficients","volume":"13","author":"Constantin","year":"2017","journal-title":"J. Chem. Theory Comput."},{"key":"ref_90","first-page":"8","article-title":"On the properties of a gas of charged particles","volume":"28","author":"Lindhard","year":"1954","journal-title":"Dan. Vid. Selsk Mat.-Fys. Medd."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"245107","DOI":"10.1103\/PhysRevB.77.245107","article-title":"Nonempirical density functionals investigated for jellium: Spin-polarized surfaces, spherical clusters, and bulk linear response","volume":"77","author":"Tao","year":"2008","journal-title":"Phys. Rev. B"},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1103\/PhysRevA.38.625","article-title":"Exact properties of the Pauli potential for the square root of the electron density and the kinetic energy functional","volume":"38","author":"Levy","year":"1988","journal-title":"Phys. Rev. A"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/10\/2\/30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:19:58Z","timestamp":1760134798000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/10\/2\/30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,15]]},"references-count":92,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["computation10020030"],"URL":"https:\/\/doi.org\/10.3390\/computation10020030","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,15]]}}}