{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T10:17:26Z","timestamp":1760523446602,"version":"build-2065373602"},"reference-count":125,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2016,9,6]],"date-time":"2016-09-06T00:00:00Z","timestamp":1473120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001736","name":"German-Israeli Foundation for Scientific Research and Development","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001736","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>We investigate four diatomic molecules containing transition metals using two variants of hybrid functionals. We compare global hybrid functionals that only partially counteract self-interaction to local hybrid functionals that are designed to be formally free from one-electron self-interaction. As d-orbitals are prone to be particularly strongly influenced by self-interaction errors, one may have expected that self-interaction-free local hybrid functionals lead to a qualitatively different Kohn\u2013Sham density of states than global hybrid functionals. Yet, we find that both types of hybrids lead to a very similar density of states. For both global and local hybrids alike, the intrinsic amount of exact exchange plays the dominant role in counteracting electronic self-interaction, whereas being formally free from one-electron self-interaction seems to be of lesser importance.<\/jats:p>","DOI":"10.3390\/computation4030033","type":"journal-article","created":{"date-parts":[[2016,9,6]],"date-time":"2016-09-06T10:10:16Z","timestamp":1473156616000},"page":"33","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["The Influence of One-Electron Self-Interaction on d-Electrons"],"prefix":"10.3390","volume":"4","author":[{"given":"Tobias","family":"Schmidt","sequence":"first","affiliation":[{"name":"Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephan","family":"K\u00fcmmel","sequence":"additional","affiliation":[{"name":"Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,9,6]]},"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","unstructured":"Parr, R.G., and Yang, W. (1989). Density-Functional Theory of Atoms and Molecules, Oxford University Press."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"18A301","DOI":"10.1063\/1.4869598","article-title":"Perspective: Fifty years of density-functional theory in chemical physics","volume":"140","author":"Becke","year":"2014","journal-title":"J. Chem. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"10757","DOI":"10.1039\/b907148b","article-title":"Density functional theory for transition metals and transition metal chemistry","volume":"11","author":"Cramer","year":"2009","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4029","DOI":"10.1103\/PhysRevB.47.4029","article-title":"Application of the self-interaction correction to transition-metal oxides","volume":"47","author":"Szotek","year":"1993","journal-title":"Phys. Rev. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1038\/nmat1509","article-title":"Electronic structure and exchange coupling of Mn impurities in III\u2013V semiconductors","volume":"4","author":"Schulthess","year":"2005","journal-title":"Nat. Mater."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1038\/21595","article-title":"Understanding the valency of rare earths from first-principles theory","volume":"399","author":"Strange","year":"1999","journal-title":"Nature"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/0009-2614(79)87292-9","article-title":"Orbital functional for exchange and correlation: Self-interaction correction to the local density approximation","volume":"64","author":"Perdew","year":"1979","journal-title":"Chem. Phys. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5048","DOI":"10.1103\/PhysRevB.23.5048","article-title":"Self-interaction correction to density-functional approximations for many-electron systems","volume":"23","author":"Perdew","year":"1981","journal-title":"Phys. Rev. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1103\/RevModPhys.80.3","article-title":"Orbital-dependent density functionals: Theory and applications","volume":"80","author":"Kronik","year":"2008","journal-title":"Rev. Mod. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"18A513","DOI":"10.1063\/1.4866996","article-title":"Self-interaction corrections in density functional theory","volume":"140","author":"Tsuneda","year":"2014","journal-title":"J. Chem. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"201205(R)","DOI":"10.1103\/PhysRevB.79.201205","article-title":"When to trust photoelectron spectra from Kohn\u2013Sham eigenvalues: The case of organic semiconductors","volume":"79","author":"Marom","year":"2009","journal-title":"Phys. Rev. B"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"129903","DOI":"10.1103\/PhysRevB.82.129903","article-title":"Erratum: When to trust photoelectron spectra from Kohn\u2013Sham eigenvalues: The case of organic semiconductors [Phys. Rev. B 79, 201205 (2009)]","volume":"82","author":"Marom","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1080\/00268970010018431","article-title":"Left-right correlation energy","volume":"99","author":"Handy","year":"2001","journal-title":"Mol. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1899","DOI":"10.1080\/00268970110083564","article-title":"Density functional theory: Coverage of dynamic and non-dynamic electron correlation effects","volume":"99","author":"Cremer","year":"2001","journal-title":"Mol. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1080\/00268970110111788","article-title":"Electron correlation and the self-interaction error of density functional theory","volume":"100","author":"Polo","year":"2002","journal-title":"Mol. Phys."},{"key":"ref_18","unstructured":"Fermi, E., and Amaldi, E. (1934). Le Orbite [infinito] s Ddegli Elementi, R. Accademia d\u2019Italia."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1103\/PhysRevA.34.769","article-title":"New self-interaction-corrected local-density approximation to tzhe density-functional theory","volume":"34","author":"Cortona","year":"1986","journal-title":"Phys. Rev. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1002\/jcc.540120705","article-title":"An alternative self-interaction correction in the generalized exchange local-density functional theory","volume":"12","author":"Guo","year":"1991","journal-title":"J. Comput. Chem."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1002\/1097-461X(2001)81:4<247::AID-QUA1>3.0.CO;2-9","article-title":"Novel method of self-interaction corrections in density functional calculations","volume":"81","author":"Lundin","year":"2001","journal-title":"Int. J. Quantum Chem."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/S0375-9601(01)00283-3","article-title":"Self-interaction correction with an explicitly density-dependent functional","volume":"284","author":"Unger","year":"2001","journal-title":"Phys. Lett. A"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"191101","DOI":"10.1063\/1.2204599","article-title":"A simple method to selectively scale down the self-interaction correction","volume":"124","author":"Vydrov","year":"2006","journal-title":"J. Chem. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3319","DOI":"10.1021\/ct100352r","article-title":"Investigation of self-interaction corrections for an exactly solvable model system: Orbital dependence and electron localization","volume":"6","author":"Vieira","year":"2010","journal-title":"J. Chem. Theory Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"233103","DOI":"10.1103\/PhysRevB.84.233103","article-title":"Improving atomization energies of molecules and solids with a spin-dependent gradient correction from one-electron density analysis","volume":"84","author":"Constantin","year":"2011","journal-title":"Phys. Rev. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/bs.aamop.2015.06.007","article-title":"The two-set and average-density self-interaction corrections applied to small electronic systems","volume":"Volume 64","author":"Dinh","year":"2015","journal-title":"Advances in Atomic, Molecules, and Optical Physics"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"075135","DOI":"10.1103\/PhysRevB.90.075135","article-title":"Koopmans-compliant functionals and their performance against reference molecular data","volume":"90","author":"Borghi","year":"2014","journal-title":"Phys. Rev. B"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"166405","DOI":"10.1103\/PhysRevLett.114.166405","article-title":"First-principles photoemission spectroscopy and orbital tomography in molecules from koopmans-compliant functionals","volume":"114","author":"Nguyen","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1972","DOI":"10.1063\/1.446959","article-title":"Local-density Hartree-Fock theory of electronic states of molecules with self-interaction correction","volume":"80","author":"Pederson","year":"1984","journal-title":"J. Chem. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"8187","DOI":"10.1063\/1.1794633","article-title":"Effect of the Perdew-Zunger self-interaction correction on the thermochemical performance of approximate density functionals","volume":"121","author":"Vydrov","year":"2004","journal-title":"J. Chem. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/PhysRevLett.101.096404","article-title":"Time-dependent density-functional theory with a self-interaction correction","volume":"101","author":"Messud","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"060502","DOI":"10.1103\/PhysRevA.77.060502","article-title":"Understanding and correcting the self-interaction error in the electrical response of hydrogen chains","volume":"77","author":"Ruzsinszky","year":"2008","journal-title":"Phys. Rev. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"133004","DOI":"10.1103\/PhysRevLett.100.133004","article-title":"Electrical Response of Molecular Systems: The Power of Self-Interaction Corrected Kohn\u2013Sham Theory","volume":"100","author":"Mundt","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/bs.aamop.2015.06.006","article-title":"Self-interaction correction as a Kohn\u2013Sham scheme in ground-state and time-dependent density functional theory","volume":"Volume 64","year":"2015","journal-title":"Advances in Atomic, Molecular, and Optical Physics"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3939","DOI":"10.1103\/PhysRevA.54.3939","article-title":"Kohn\u2013Sham calculations with self-interaction-corrected local-spin-density exchange-correlation energy functional for atomic systems","volume":"54","author":"Chen","year":"1996","journal-title":"Phys. Rev. A"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"7880","DOI":"10.1063\/1.481421","article-title":"The optimized effective potential and the self-interaction correction in density functional theory: Application to molecules","volume":"112","author":"Garza","year":"2000","journal-title":"J. Chem. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1063\/1.1370527","article-title":"Curing difficult cases in magnetic properties prediction with self-interaction corrected density functional theory","volume":"115","author":"Patchkovskii","year":"2001","journal-title":"J. Chem. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1088\/0953-4075\/35\/4\/333","article-title":"Comparison of self-interaction-corrections for metal clusters","volume":"35","author":"Legrand","year":"2002","journal-title":"J. Phys. B Atomic Mol. Opt. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"4647","DOI":"10.1039\/b902613d","article-title":"Physical signatures of discontinuities of the time-dependent exchange-correlation potential","volume":"11","author":"Vieira","year":"2009","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"121204(R)","DOI":"10.1103\/PhysRevB.77.121204","article-title":"Polarizability of molecular chains: A self-interaction correction approach","volume":"77","author":"Pemmaraju","year":"2008","journal-title":"Phys. Rev. B"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"014110","DOI":"10.1063\/1.2944272","article-title":"Self-interaction correction and the optimized effective potential","volume":"129","author":"Mundt","year":"2008","journal-title":"J. Chem. Phys."},{"key":"ref_42","unstructured":"Roy, A.K. (2012). Theoretical Computational Developments in Modern Density Functional Theory, Nova Science Publishers."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1103\/PhysRevLett.65.1148","article-title":"Transition-metal oxides in the self-interaction-corrected density-functional formalism","volume":"65","author":"Svane","year":"1990","journal-title":"Phys. Rev. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"11533","DOI":"10.1103\/PhysRevB.47.11533","article-title":"Self-interaction-corrected electronic strucutre of La2CuO4","volume":"47","author":"Temmerman","year":"1993","journal-title":"Phys. Rev. B"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1765","DOI":"10.1103\/PhysRevA.55.1765","article-title":"Critical assessment of the self-interaction-corrected-local-density-functional method and its algorithmic implementation","volume":"55","author":"Goedecker","year":"1997","journal-title":"Phys. Rev. A"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2688","DOI":"10.1063\/1.448266","article-title":"Density-functional theory with self-interaction correction: Application to the lithium molecule","volume":"82","author":"Pederson","year":"1985","journal-title":"J. Chem. Phys."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1807","DOI":"10.1063\/1.454104","article-title":"Localized and canonical atomic orbitals in self-interaction corrected local density functional approximation","volume":"88","author":"Pederson","year":"1988","journal-title":"J. Chem. Phys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"050501","DOI":"10.1103\/PhysRevA.84.050501","article-title":"Importance of complex orbitals in calculating the self-interaction- corrected ground state of atoms","volume":"84","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"062514","DOI":"10.1103\/PhysRevA.85.062514","article-title":"Using complex degrees of freedom in the Kohn\u2013Sham self-interaction correction","volume":"85","author":"Hofmann","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"124102","DOI":"10.1063\/1.4752229","article-title":"The effect of the Perdew-Zunger self-interaction correction to density functionals on the energetics of small molecules","volume":"137","year":"2012","journal-title":"J. Chem. Phys."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"146401","DOI":"10.1103\/PhysRevLett.108.146401","article-title":"Kohn\u2013Sham Self-Interaction Correction in Real Time","volume":"108","author":"Hofmann","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"5324","DOI":"10.1021\/ct500637x","article-title":"Variational, self-consistent implementation of the Perdew-Zunger self-interaction correction with complex optimal orbitals","volume":"10","author":"Lehtola","year":"2014","journal-title":"J. Chem. Theory Comput."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"83006","DOI":"10.1088\/1367-2630\/17\/8\/083006","article-title":"Calculations of Al dopant in \u03b1-quartz using a variational implementation of the Perdew-Zunger self-interaction correction","volume":"17","year":"2015","journal-title":"New J. Phys."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Lehtola, S., J\u00f3nsson, E.\u00d6., and J\u00f3nsson, H. (2016). Effect of complex-valued optimal orbitals on atomization energies with the Perdew\u2013Zunger self-interaction correction to density functional theory. J. Chem. Theory Comput.","DOI":"10.1021\/acs.jctc.6b00622"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"3195","DOI":"10.1021\/acs.jctc.6b00347","article-title":"Complex orbitals, multiple local minima and symmetry breaking in Perdew-Zunger self-interaction corrected density-functional theory calculations","volume":"12","author":"Lehtola","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"121103","DOI":"10.1063\/1.4869581","article-title":"Communication: Self-interaction correction with unitary invariance in density functional theory","volume":"140","author":"Pederson","year":"2014","journal-title":"J. Chem. Phys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/bs.aamop.2015.06.005","article-title":"Self-interaction corrections within the fermi-orbital-based formalism","volume":"Volume 64","author":"Pederson","year":"2015","journal-title":"Advance in Atomic, Molecular, and Optical Physics"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"224104","DOI":"10.1063\/1.4936777","article-title":"Fermi orbital self-interaction corrected electronic structure of molecules beyond local density approximation","volume":"143","author":"Hahn","year":"2015","journal-title":"J. Chem. Phys."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"194112","DOI":"10.1063\/1.2387954","article-title":"Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals","volume":"125","author":"Ruzsinszky","year":"2006","journal-title":"J. Chem. Phys."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"201102","DOI":"10.1063\/1.2403848","article-title":"Many-electron self-interaction error in approximate density functionals","volume":"125","author":"Cohen","year":"2006","journal-title":"J. Chem. Phys."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1691","DOI":"10.1103\/PhysRevLett.49.1691","article-title":"Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy","volume":"49","author":"Perdew","year":"1982","journal-title":"Phys. Rev. Lett."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1126\/science.1158722","article-title":"Insights into current limitations of density functional theory","volume":"321","author":"Cohen","year":"2008","journal-title":"Science"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"226403","DOI":"10.1103\/PhysRevLett.106.226403","article-title":"Hole localization in molecular crystals from hybrid density functional theory","volume":"106","author":"Sai","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"3740","DOI":"10.1021\/jz3015937","article-title":"Curvature and frontier orbital energies in density functional theory","volume":"3","author":"Stein","year":"2012","journal-title":"J. Phys. Chem. Lett."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"053001","DOI":"10.1103\/PhysRevLett.114.053001","article-title":"Local scaling correction for reducing delocalization error in density functional approximations","volume":"114","author":"Li","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"121115","DOI":"10.1103\/PhysRevB.93.121115","article-title":"Piecewise linearity in the GW approximation for accurate quasiparticle energy predictions","volume":"93","author":"Dauth","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"165120","DOI":"10.1103\/PhysRevB.93.165120","article-title":"One- and many-electron self-interaction error in local and global hybrid functionals","volume":"93","author":"Schmidt","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"035140","DOI":"10.1103\/PhysRevB.94.035140","article-title":"Enforcing the linear behavior of the total energy with hybrid functionals: Implications for charge transfer, interaction energies, and the random-phase approximation","volume":"94","author":"Atalla","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.cplett.2004.06.011","article-title":"A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP)","volume":"393","author":"Yanai","year":"2004","journal-title":"Chem. Phys. Lett."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1039\/B511865D","article-title":"Assessment of a Coulomb-attenuated exchange-correlation energy functional","volume":"8","author":"Peach","year":"2006","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"3540","DOI":"10.1063\/1.1383587","article-title":"A long-range correction scheme for generalized-gradient- approximation exchange functionals","volume":"115","author":"Iikura","year":"2001","journal-title":"J. Chem. Phys."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"234109","DOI":"10.1063\/1.2409292","article-title":"Assessment of a long-range corrected hybrid functional","volume":"125","author":"Vydrov","year":"2006","journal-title":"J. Chem. Phys."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"084106","DOI":"10.1063\/1.2834918","article-title":"Systematic optimization of long-range corrected hybrid density functionals","volume":"128","author":"Chai","year":"2008","journal-title":"J. Chem. Phys."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"034101","DOI":"10.1063\/1.4926468","article-title":"Tuned range separated hybrid functionals for solvated low bandgap oligomers","volume":"143","year":"2015","journal-title":"J. Chem. Phys."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"204115","DOI":"10.1063\/1.4807325","article-title":"Using optimally tuned range separated hybrid functionals in ground-state calculations: Consequences and caveats","volume":"138","author":"Karolewski","year":"2013","journal-title":"J. Chem. Phys."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"1372","DOI":"10.1063\/1.464304","article-title":"A new mixing of Hartree-Fock and local density-functional theories","volume":"98","author":"Becke","year":"1993","journal-title":"J. Chem. Phys."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"5648","DOI":"10.1063\/1.464913","article-title":"Density-functional thermochemistry. III. The role of exact exchange","volume":"98","author":"Becke","year":"1993","journal-title":"J. Chem. Phys."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"9982","DOI":"10.1063\/1.472933","article-title":"Rationale for mixing exact exchange with density functional approximations","volume":"105","author":"Perdew","year":"1996","journal-title":"J. Chem. Phys."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"4911","DOI":"10.1021\/jp980950v","article-title":"Exchange-correlation energy density from virial theorem","volume":"102","author":"Cruz","year":"1998","journal-title":"J. Phys. Chem. A"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1063\/1.1528936","article-title":"Local hybrid functionals","volume":"118","author":"Jaramillo","year":"2003","journal-title":"J. Chem. Phys."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"204102","DOI":"10.1063\/1.2196883","article-title":"From local hybrid functionals to \u201clocalized local hybrid\u201d potentials: Formalism and thermochemical tests","volume":"124","author":"Arbuznikov","year":"2006","journal-title":"J. Chem. Phys."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"164117","DOI":"10.1063\/1.2784406","article-title":"Local hybrid functionals based on density matrix products","volume":"127","author":"Janesko","year":"2007","journal-title":"J. Chem. Phys."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"011103","DOI":"10.1063\/1.2429058","article-title":"A thermochemically competitive local hybrid functional without gradient corrections","volume":"126","author":"Bahmann","year":"2007","journal-title":"J. Chem. Phys."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"194102","DOI":"10.1063\/1.2795700","article-title":"Local hybrid functionals: An assessment for thermochemical kinetics","volume":"127","author":"Kaupp","year":"2007","journal-title":"J. Chem. Phys."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"052513","DOI":"10.1103\/PhysRevA.78.052513","article-title":"Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction","volume":"78","author":"Perdew","year":"2008","journal-title":"Phys. Rev. A"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"18A510","DOI":"10.1063\/1.4865942","article-title":"A self-interaction-free local hybrid functional: Accurate binding energies vis-\u00e0-vis accurate ionization potentials from Kohn\u2013Sham eigenvalues","volume":"140","author":"Schmidt","year":"2014","journal-title":"J. Chem. Phys."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"074112","DOI":"10.1063\/1.4908148","article-title":"Local hybrid functionals with orbital-free mixing functions and balanced elimination of self-interaction error","volume":"142","author":"Corminboeuf","year":"2015","journal-title":"J. Chem. Phys."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.1080\/0026897031000094506","article-title":"Two avenues to self-interaction correction within Kohn\u2013Sham theory: Unitary invariance is the shortcut","volume":"101","author":"Perdew","year":"2003","journal-title":"Mol. Phys."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"4707","DOI":"10.1103\/PhysRevA.50.4707","article-title":"Kohn\u2013Sham density-functional orbitals as approximate Dyson orbitals scattering for the calculation","volume":"50","author":"Duffy","year":"1994","journal-title":"Phys. Rev. A"},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"1760","DOI":"10.1063\/1.1430255","article-title":"Interpretation of the Kohn\u2013Sham orbital energies as approximate vertical ionization potentials","volume":"116","author":"Chong","year":"2002","journal-title":"J. Chem. Phys."},{"key":"ref_91","doi-asserted-by":"crossref","unstructured":"di Valentin, C., Botti, S., and Coccoccioni, M. (2014). First Principles Approaches to Spectroscopic Properties of Complex Materials, Springer. Topics in Current Chemistry.","DOI":"10.1007\/978-3-642-55068-3"},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"13216","DOI":"10.1103\/PhysRevB.62.13216","article-title":"Aluminum cluster anions: Photoelectron spectroscopy and ab initio simulations","volume":"62","author":"Akola","year":"2000","journal-title":"Phys. Rev. B"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"235419","DOI":"10.1103\/PhysRevB.64.235419","article-title":"Relationship between photoelectron spectroscopy and the magnetic moment of Ni7 clusters","volume":"64","author":"Khanna","year":"2001","journal-title":"Phys. Rev. B"},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1038\/nmat704","article-title":"Highest electron affinity as a predictor of cluster anion structures","volume":"1","author":"Kronik","year":"2002","journal-title":"Nat. Mater."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"165413","DOI":"10.1103\/PhysRevB.68.165413","article-title":"Thermal effects in the photoelectron spectra of Na-N clustres (N = 4\u201319)","volume":"68","author":"Moseler","year":"2003","journal-title":"Phys. Rev. B"},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"093401","DOI":"10.1103\/PhysRevLett.93.093401","article-title":"Symmetry and electronic structure of noble-metal nanoparticles and the role of relativity","volume":"93","author":"Moseler","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"205407","DOI":"10.1103\/PhysRevB.73.205407","article-title":"Photoelectron spectra of sodium clusters: The problem of interpreting Kohn\u2013Sham eigenvalues","volume":"73","author":"Mundt","year":"2006","journal-title":"Phys. Rev. B"},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"6694","DOI":"10.1021\/jp112224t","article-title":"The electronic structure of gold-platinum nanoparticles: Collecting clues for why they are special","volume":"115","author":"Leppert","year":"2011","journal-title":"J. Phys. Chem. C"},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"17268","DOI":"10.1021\/jp404341v","article-title":"Interplay of electronic structure and atomic mobility in nanoalloys of Au and Pt","volume":"117","author":"Leppert","year":"2013","journal-title":"J. Phys. Chem. C"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"115425","DOI":"10.1103\/PhysRevB.88.115425","article-title":"Coordination-driven magnetic-to-nonmagnetic transition in manganese-doped silicon clusters","volume":"88","author":"Leppert","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"21647","DOI":"10.1021\/jp5058258","article-title":"The concept of localized atomic mobility: Unraveling properties of nanoparticles","volume":"118","author":"Capelo","year":"2014","journal-title":"J. Phys. Chem. C"},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"26140","DOI":"10.1039\/C5CP04174K","article-title":"Hydrogen binding energies and electronic structure of Ni\u2013Pd particles: A clue to their special catalytic properties","volume":"17","author":"Leppert","year":"2015","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"2745","DOI":"10.1039\/C5GC00047E","article-title":"The use of ultrasonic cavitation for near-surface structuring of robust and low-cost AlNi catalysts for hydrogen production","volume":"17","author":"Cherepanov","year":"2015","journal-title":"Green Chem."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"6676","DOI":"10.1039\/C6CP00342G","article-title":"Global optimization of small bimetallic Pd\u2013Co binary nanoalloy clusters: A genetic algorithm approach at the DFT level","volume":"18","author":"Aslan","year":"2016","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1023\/A:1008218128189","article-title":"Optimized effective potential for atoms and molecules","volume":"7","author":"Grabo","year":"1997","journal-title":"Mol. Eng."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"043004","DOI":"10.1103\/PhysRevLett.90.043004","article-title":"Simple Iterative Construction of the Optimized Effective Potential for Orbital Functionals, Including Exact Exchange","volume":"90","author":"Perdew","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"1731","DOI":"10.1021\/ct800485v","article-title":"Fully Numerical All-Electron Solutions of the Optimized Effective Potential Equation for Diatomic Molecules","volume":"5","author":"Makmal","year":"2009","journal-title":"J. Chem. Theory Comput."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"062512","DOI":"10.1103\/PhysRevA.83.062512","article-title":"Dissociation of diatomic molecules and the exact-exchange Kohn\u2013Sham potential: The case of LiF","volume":"83","author":"Makmal","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"8161","DOI":"10.1063\/1.477479","article-title":"Unambiguous exchange-correlation energy density","volume":"109","author":"Burke","year":"1998","journal-title":"J. Chem. Phys."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"204101","DOI":"10.1063\/1.4901238","article-title":"Towards improved local hybrid functionals by calibration of exchange-energy densities","volume":"141","author":"Arbuznikov","year":"2014","journal-title":"J. Chem. Phys."},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"6158","DOI":"10.1063\/1.478522","article-title":"Toward reliable density functional methods without adjustable parameters: The PBE0 model","volume":"110","author":"Adamo","year":"1999","journal-title":"J. Chem. Phys."},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"5029","DOI":"10.1063\/1.478401","article-title":"Assessment of the Perdew-Burke-Ernzerhof exchange-correlation functional","volume":"110","author":"Ernzerhof","year":"1999","journal-title":"J. Chem. Phys."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"3865","DOI":"10.1103\/PhysRevLett.77.3865","article-title":"Generalized gradient approximation made simple","volume":"77","author":"Perdew","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"1396","DOI":"10.1103\/PhysRevLett.78.1396","article-title":"Erratum: Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]","volume":"78","author":"Perdew","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"155206","DOI":"10.1103\/PhysRevB.82.155206","article-title":"Single-particle and quasiparticle interpretation of Kohn\u2013Sham and generalized Kohn\u2013Sham eigenvalues for hybrid functionals","volume":"82","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.cplett.2011.07.061","article-title":"Linearity condition for orbital energies in density functional theory (II): Application to global hybrid functionals","volume":"513","author":"Imamura","year":"2011","journal-title":"Chem. Phys. Lett."},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"165122","DOI":"10.1103\/PhysRevB.88.165122","article-title":"Hybrid density functional theory meets quasiparticle calculations: A consistent electronic structure approach","volume":"88","author":"Atalla","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1103\/PhysRevLett.45.566","article-title":"Ground state of the electron gas by a stochastic method","volume":"45","author":"Ceperley","year":"1980","journal-title":"Phys. Rev. Lett."},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1139\/p80-159","article-title":"Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis","volume":"58","author":"Vosko","year":"1980","journal-title":"Can. J. Phys."},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"13244","DOI":"10.1103\/PhysRevB.45.13244","article-title":"Accurate and simple analytic representation of the electron-gas correlation energy","volume":"45","author":"Wang","year":"1992","journal-title":"Phys. Rev. B"},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"14357","DOI":"10.1039\/C3CP55433C","article-title":"One-electron self-interaction and the asymptotics of the Kohn\u2013Sham potential: An impaired relation","volume":"16","author":"Schmidt","year":"2014","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1002\/(SICI)1097-461X(1999)75:4\/5<889::AID-QUA54>3.0.CO;2-8","article-title":"Molecular and solid-state tests of density functional approximations: LSD, GGAs, and meta-GGAs","volume":"75","author":"Kurth","year":"1999","journal-title":"Int. J. Quantum Chem."},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1103\/PhysRevA.45.101","article-title":"Construction and application of an accurate local spin-polarized Kohn\u2013Sham potential with integer discontinuity: Exchange-only theory","volume":"45","author":"Krieger","year":"1992","journal-title":"Phys. Rev. A"},{"key":"ref_124","unstructured":"Lide, D.R. (2011). CRC Handbook of Chemistry and Physics, CRC. [92nd ed.]."},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"204114","DOI":"10.1063\/1.4950877","article-title":"On the errors of local density (LDA) and generalized gradient (GGA) approximations to the Kohn\u2013Sham potential and orbital energies","volume":"144","author":"Gritsenko","year":"2016","journal-title":"J. Chem. Phys."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/4\/3\/33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:30:12Z","timestamp":1760211012000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/4\/3\/33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,6]]},"references-count":125,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,9]]}},"alternative-id":["computation4030033"],"URL":"https:\/\/doi.org\/10.3390\/computation4030033","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2016,9,6]]}}}