{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:19:35Z","timestamp":1760242775469,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2016,7,5]],"date-time":"2016-07-05T00:00:00Z","timestamp":1467676800000},"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>Based on a computational procedure for determining the functional derivative with respect to the density of any antisymmetric N-particle wave function for a non-interacting system that leads to the density, we devise a test as to whether or not a wave function known to lead to a given density corresponds to a solution of a Schr\u00f6dinger equation for some potential. We examine explicitly the case of non-interacting systems described by Slater determinants. Numerical examples for the cases of a one-dimensional square-well potential with infinite walls and the harmonic oscillator potential illustrate the formalism.<\/jats:p>","DOI":"10.3390\/computation4030024","type":"journal-article","created":{"date-parts":[[2016,7,5]],"date-time":"2016-07-05T10:06:19Z","timestamp":1467713179000},"page":"24","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["On the v-Representabilty Problem in Density Functional Theory: Application to Non-Interacting Systems"],"prefix":"10.3390","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9301-8469","authenticated-orcid":false,"given":"Markus","family":"D\u00e4ne","sequence":"first","affiliation":[{"name":"Lawrence Livermore National Laboratory, P.O. Box 808, L-372, Livermore, CA 94551, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonios","family":"Gonis","sequence":"additional","affiliation":[{"name":"Lawrence Livermore National Laboratory, P.O. Box 808, L-372, Livermore, CA 94551, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,7,5]]},"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","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_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. Natl. Acad. Sci. USA"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1103\/PhysRevA.26.1200","article-title":"Electron densities in search of Hamiltonians","volume":"26","author":"Levy","year":"1982","journal-title":"Phys. Rev. A"},{"key":"ref_5","unstructured":"Shimony, A., and Feshbach, H. (1982). Physics as Natural Philosophy: Essays in Honor of Laszlo Tisza on His 75th Birthday, MIT Press."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Dreizler, R., and Providencia, J. (1985). Density Functional Methods in Physics, Plenum Press.","DOI":"10.1007\/978-1-4757-0818-9"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1596","DOI":"10.1103\/PhysRevLett.51.1596","article-title":"v-representability and density functional theory","volume":"51","author":"Kohn","year":"1983","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/0378-4371(83)90254-6","article-title":"Hohenberg\u2013Kohn theorem and non-v-representable densities","volume":"121","author":"Englisch","year":"1983","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1103\/PhysRevA.47.153","article-title":"v-representability for noninteracting systems","volume":"47","author":"Chen","year":"1993","journal-title":"Phys. Rev. A"},{"key":"ref_10","unstructured":"Parr, R.G., and Yang, C.Y. (1989). Density Functional Theory of Atoms and Molecules, Oxford University Press."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Dreitzler, R.M., and Gross, E.K.U. (1990). Density Functional Theory, Springer Verlag.","DOI":"10.1007\/978-3-642-86105-5"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.jpcs.2015.10.006","article-title":"Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem","volume":"89","author":"Gonis","year":"2016","journal-title":"J. Phys. Chem. Solids"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1016\/j.ssc.2012.01.048","article-title":"Computationally simple, analytic, closed form solution of the Coulomb self-interaction problem in Kohn\u2013Sham density functional theory","volume":"152","author":"Gonis","year":"2012","journal-title":"Solid State Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1016\/j.jpcs.2014.05.014","article-title":"On a solution of the self-interaction problem in Kohn\u2013Sham density functional theory","volume":"75","author":"Gonis","year":"2014","journal-title":"J. Phys. Chem. Solids"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.jpcs.2014.09.013","article-title":"Solving the self-interaction problem in Kohn\u2013Sham density functional theory: Application to atoms","volume":"79","author":"Gonis","year":"2015","journal-title":"J. Phys. Chem. Solids"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2141","DOI":"10.1103\/PhysRevLett.60.2141","article-title":"Density functionals for the energy of electronic systems: Explicit variational construction","volume":"60","author":"Cioslowski","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1002\/qua.560360829","article-title":"Density driven self-consistent field method. II. Construction of all one-particle wavefunctions that are orthonormal and sum up to a given density","volume":"36","author":"Cioslowski","year":"1989","journal-title":"Int. J. Quantum Chem."},{"key":"ref_18","unstructured":"Shimony, A., and Feshbach, H. (1982). Physics as Natural Philosophy, Essays in Honor of Laszlo Tisza, MIT Press."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/andp.19554520102","article-title":"Zur wellenmechanischen Behandlung von Vielk\u00f6rperproblemen","volume":"452","author":"Macke","year":"1955","journal-title":"Ann. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1103\/PhysRevA.24.680","article-title":"Orthonormal orbitals for the representation of an arbitrary density","volume":"24","author":"Harriman","year":"1981","journal-title":"Phys. Rev. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1103\/PhysRevA.28.544","article-title":"New approach to the calculation of density functionals","volume":"28","author":"Zumbach","year":"1983","journal-title":"Phys. Rev. A"},{"key":"ref_22","unstructured":"(2016). Mathematica, Wolfram Research, Inc.. Version 10.4."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/4\/3\/24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:25:29Z","timestamp":1760210729000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/4\/3\/24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,5]]},"references-count":22,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,9]]}},"alternative-id":["computation4030024"],"URL":"https:\/\/doi.org\/10.3390\/computation4030024","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2016,7,5]]}}}