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Quantum fluctuations and kinetic correlation in the strongly Interacting Limit of

Density Functional Theory

Grossi, J.

2020

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Grossi, J. (2020). Quantum fluctuations and kinetic correlation in the strongly Interacting Limit of Density Functional Theory.

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[1] Dorothy L Sayers. Have his carcase. McClelland & Stewart, 1932. [2] Paul Adrien Maurice Dirac. “Quantum mechanics of many-electron systems.” In: Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Charac-ter 123.792 (1929), pp. 714–733.

[3] Llewellyn H Thomas. “The calculation of atomic fields.” In: Mathematical Proceedings of the Cambridge Philosophical Society. Vol. 23. 5. Cambridge University Press. 1927, pp. 542–548. [4] Enrico Fermi. “Un metodo statistico per la determinazione

di alcune priorieta dell’atome.” In: Rend. Accad. Naz. Lincei 6.602-607 (1927), p. 32.

[5] Pierre Hohenberg and Walter Kohn. “Inhomogeneous electron gas.” In: Physical review 136.3B (1964), B864.

[6] Walter Kohn and Lu Jeu Sham. “Self-consistent equations in-cluding exchange and correlation effects.” In: Physical review 140.4A (1965), A1133.

[7] Michael Seidl. “Strong-interaction limit of density functional theory.” In: Physical Review A 60.6 (1999), p. 4387.

[8] Michael Seidl, John P Perdew, and Mel Levy. “Strictly corre-lated electrons in density-functional theory.” In: Physical Review A 59.1 (1999), p. 51.

[9] John P Perdew and Karla Schmidt. “Jacob’s ladder of den-sity functional approximations for the exchange-correlation energy.” In: AIP Conference Proceedings. Vol. 577. 1. AIP. 2001, pp. 1–20.

[10] John P Perdew, Adrienn Ruzsinszky, Jianmin Tao, Viktor N Staroverov, Gustavo E Scuseria, and Gábor I Csonka. “Pre-scription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits.” In: J. Chem. Phys. 123.6 (2005), p. 062201.

[11] Axel D Becke. “Perspective: Fifty years of density-functional theory in chemical physics.” In: The Journal of chemical physics 140.18 (2014), 18A301.

[12] Michael G Medvedev, Ivan S Bushmarinov, Jianwei Sun, John P Perdew, and Konstantin A Lyssenko. “Density functional theory is straying from the path toward the exact functional.” In: Science 355.6320 (2017), pp. 49–52.

(3)

[13] Sharon Hammes-Schiffer. “A conundrum for density functional theory.” In: Science 355.6320 (2017), pp. 28–29.

[14] Paola Gori-Giorgi, Giovanni Vignale, and Michael Seidl. “Elec-tronic zero-point oscillations in the strong-interaction limit of density functional theory.” In: Journal of chemical theory and computation 5.4 (2009), pp. 743–753.

[15] Saeed H Abedinpour, Marco Polini, Gao Xianlong, and MP Tosi. “Density-functional theory of inhomogeneous electron systems in thin quantum wires.” In: The European Physical Journal B 56.2 (2007), pp. 127–134.

[16] Francesc Malet, André Mirtschink, Klaas J. H. Giesbertz, Lucas O. Wagner, and Paola Gori-Giorgi. “Exchange-correlation func-tionals from the strong interaction limit of DFT: applications to model chemical systems.” In: Phys. Chem. Chem. Phys. 16.28 (Apr. 2014), pp. 14551–14558. doi:10.1039/C4CP00407H. [17] Juri Grossi, Michael Seidl, Paola Gori-Giorgi, and Klaas JH

Giesbertz. “Functional derivative of the zero-point-energy func-tional from the strong-interaction limit of density-funcfunc-tional theory.” In: Physical Review A 99.5 (2019), p. 052504.

[18] WJ Carr Jr. “Energy, specific heat, and magnetic properties of the low-density electron gas.” In: Physical Review 122.5 (1961), p. 1437.

[19] ND Drummond, Z Radnai, JR Trail, MD Towler, and RJ Needs. “Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals.” In: Physical Review B 69.8 (2004), p. 085116. [20] Lucien Hardy and Robert Spekkens. “Why physics needs

quan-tum foundations.” In: arXiv preprint arXiv:1003.5008 (2010). [21] Trygve Helgaker, Poul Jørgensen, and Jeppe Olsen.

Density-functional Theory: A Convex Treatment. Wiley Blackwell, 2016. [22] Robert van Leeuwen. “Density functional approach to the

many-body problem: key concepts and exact functionals.” In: Adv. Quantum Chem. 43 (2003), pp. 24–94.

[23] Simen Kvaal, Ulf Ekström, Andrew M Teale, and Trygve Hel-gaker. “Differentiable but exact formulation of density-functional theory.” In: The Journal of chemical physics 140.18 (2014), 18A518. [24] Paul E Lammert. “Coarse-grained V representability.” In: The

Journal of chemical physics 125.7 (2006), p. 074114.

[25] C. J. Umrigar and X. Gonze. “Accurate exchange-correlation potentials and total-energy components for the helium isoelec-tronic series.” In: Phys. Rev. A 50.5 (1994), pp. 3827 –3837.

(4)

[26] C. Filippi, X. Gonze, and C. J. Umrigar. “Generalized gradient approximations to density functional theory: comparison with exact results.” In: Recent developments and applications in mod-ern DFT. Ed. by J. M. Seminario. Amsterdam: Elsevier, 1996, pp. 295–321.

[27] AI Al-Sharif, R Resta, and CJ Umrigar. “Evidence of physical reality in the Kohn-Sham potential: The case of atomic Ne.” In: Physical Review A 57.4 (1998), p. 2466.

[28] J Harris. “Adiabatic-connection approach to Kohn-Sham the-ory.” In: Physical Review A 29.4 (1984), p. 1648.

[29] Mel Levy. “Electron densities in search of Hamiltonians.” In: Physical Review A 26.3 (1982), p. 1200.

[30] Mel Levy and John P Perdew. “Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibil-ity for atoms.” In: Physical Review A 32.4 (1985), p. 2010. [31] R. M. Dreizler and E. K. U. Gross. Density Functional Theory.

Berlin: Springer-Verlag, 1990.

[32] Andreas Görling and Mel Levy. “Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion.” In: Physical Review B 47.20 (1993), p. 13105.

[33] Andreas Görling and Mel Levy. “Exact Kohn-Sham scheme based on perturbation theory.” In: Physical Review A 50.1 (1994), p. 196.

[34] Elliott H Lieb. “A lower bound for Coulomb energies.” In: Physics Letters A 70.5-6 (1979), pp. 444–446.

[35] Elliott H Lieb and Stephen Oxford. “Improved lower bound on the indirect Coulomb energy.” In: International Journal of Quantum Chemistry 19.3 (1981), pp. 427–439.

[36] Mathieu Lewin, Elliott H Lieb, and Robert Seiringer. “A float-ing Wigner crystal with no boundary charge fluctuations.” In: arXiv preprint arXiv:1905.09138 (2019).

[37] Garnet Kin-Lic Chan and Nicholas C Handy. “Optimized Lieb-Oxford bound for the exchange-correlation energy.” In: Physical Review A 59.4 (1999), p. 3075.

[38] Michael Seidl, Stefan Vuckovic, and Paola Gori-Giorgi. “Chal-lenging the Lieb–Oxford bound in a systematic way.” In: Mol. Phys. 114 (2016), pp. 1076–1085.

[39] Mel Levy. “Density-functional exchange correlation through co-ordinate scaling in adiabatic connection and correlation hole.” In: Physical Review A 43.9 (1991), p. 4637.

(5)

[40] Mel Levy and John P Perdew. “Tight bound and convexity constraint on the exchange-correlation-energy functional in the low-density limit, and other formal tests of generalized-gradient approximations.” In: Physical Review B 48.16 (1993), p. 11638.

[41] Michael Seidl, John P Perdew, and Stefan Kurth. “Density functionals for the strong-interaction limit.” In: Physical Review A 62.1 (2000), p. 012502.

[42] Michael Seidl, John P. Perdew, and Stefan Kurth. “Simula-tion of All-Order Density-Func“Simula-tional Perturba“Simula-tion Theory, Us-ing the Second Order and the Strong-Correlation Limit.” In: Phys. Rev. Lett. 84.22 (May 2000), pp. 5070–5073. doi:10.1103/ PhysRevLett.84.5070.

[43] Elliott H. Lieb. “Density Functionals for CouIomb Systems.” In: Int. J. Quantum. Chem. 24.3 (Sept. 1983), pp. 243–277. doi:

10.1002/qua.560240302.

[44] Mathieu Lewin. “Semi-classical limit of the Levy–Lieb func-tional in Density Funcfunc-tional Theory.” In: C. R. Math. 356.4 (Mar. 2018), pp. 449–455. doi:10.1016/j.crma.2018.03.002.

[45] Maria Colombo and Federico Stra. “Counterexamples in multi-marginal optimal transport with Coulomb cost and spherically symmetric data.” In: arXiv preprint arXiv:1507.08522 (2015). [46] Michael Seidl, Simone Di Marino, Augusto Gerolin, Luca Nenna,

Klaas JH Giesbertz, and Paola Gori-Giorgi. “The strictly-correlated electron functional for spherically symmetric systems revis-ited.” In: arXiv preprint arXiv:1702.05022 (2017).

[47] Maria Colombo, Luigi De Pascale, and Simone Di Marino. “Multimarginal Optimal Transport Maps for One-dimensional Repulsive Costs.” In: Canad. J. Math 67 (May 2015), pp. 350–368. doi:10.4153/CJM-2014-011-x.

[48] Codina Cotar, Gero Friesecke, and Claudia Klüppelberg. “Den-sity Functional Theory and Optimal Transportation with Coulomb Cost.” In: Comm. Pure Appl. Math. 66 (2013), pp. 548–99.

[49] Giuseppe Buttazzo, Luigi De Pascale, and Paola Gori-Giorgi. “Optimal-transport formulation of electronic density-functional theory.” In: Phys. Rev. A 85.6 (June 2012), p. 062502. doi: 10. 1103/PhysRevA.85.062502.

[50] Michael Seidl, Paola Gori-Giorgi, and Andreas Savin. “Strictly correlated electrons in density-functional theory: A general for-mulation with applications to spherical densities.” In: Physical Review A 75.4 (2007), p. 042511.

[51] Gaspard Monge. “Mémoire sur la théorie des déblais et des remblais.” In: Histoire de l’Académie Royale des Sciences de Paris (1781).

(6)

[52] LV Kantorovich. “On mass transference.” In: Dokl. Akad. Nauk. SSSR. Vol. 37. 1942, pp. 227–229.

[53] Bernard F Schutz. Geometrical methods of mathematical physics. Cambridge university press, 1980.

[54] Albert John Coleman and Vyacheslav I Yukalov. Reduced density matrices: Coulson’s challenge. Vol. 72. Springer Science & Business Media, 2000.

[55] Codina Cotar, Gero Friesecke, and Claudia Klüppelberg. “Smooth-ing of transport plans with fixed marginals and rigorous semi-classical limit of the Hohenberg–Kohn functional.” In: Arch. Ration. Mech. An. 228.3 (June 2018), pp. 891–922. doi:10.1007/ s00205-017-1208-y.

[56] Christian B Mendl and Lin Lin. “Kantorovich dual solution for strictly correlated electrons in atoms and molecules.” In: Physical Review B 87.12 (2013), p. 125106.

[57] Stefan Vuckovic, Lucas O Wagner, André Mirtschink, and Paola Gori-Giorgi. “Hydrogen Molecule Dissociation Curve with Functionals Based on the Strictly Correlated Regime.” In: J. Chem. Theory Comput. 11.7 (2015), pp. 3153–3162.

[58] Michael Seidl, Simone Di Marino, Augusto Gerolin, Luca Nenna, Klaas JH Giesbertz, and Paola Gori-Giorgi. “The strictly-correlated electron functional for spherically symmetric systems revis-ited.” In: arXiv preprint arXiv:1702.05022 (2017).

[59] Mel Levy. “Universal variational functionals of electron densi-ties, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem.” In: Proceedings of the National Academy of Sciences 76.12 (1979), pp. 6062–6065. [60] Aron J Cohen and Paula Mori-Sánchez. “Landscape of an exact

energy functional.” In: Physical Review A 93.4 (2016), p. 042511. [61] Paula Mori-Sánchez and Aron J Cohen. “Exact density func-tional obtained via the Levy constrained search.” In: The journal of physical chemistry letters 9.17 (2018), pp. 4910–4914.

[62] Huajie Chen and Gero Friesecke. “Pair densities in density functional theory.” In: Multiscale Modeling & Simulation 13.4 (2015), pp. 1259–1289.

[63] Luis Cort, Daniel Karlsson, Giovanna Lani, and Robert van Leeuwen. “Time-dependent density-functional theory for strongly interacting electrons.” In: Physical Review A 95.4 (Apr. 2017), p. 042505. doi:10.1103/PhysRevA.95.042505.

[64] Paola Gori-Giorgi, Michael Seidl, and Giovanni Vignale. “Density-functional theory for strongly interacting electrons.” In: Physical review letters 103.16 (2009), p. 166402.

(7)

[65] John P Boyd. “The devil’s invention: asymptotic, superasymp-totic and hyperasympsuperasymp-totic series.” In: Acta Applicandae Mathe-matica 56.1 (1999), pp. 1–98.

[66] Lucas O Wagner and Paola Gori-Giorgi. “Electron avoidance: A nonlocal radius for strong correlation.” In: Physical Review A 90.5 (2014), p. 052512.

[67] Hilke Bahmann, Yongxi Zhou, and Matthias Ernzerhof. “The shell model for the exchange-correlation hole in the strong-correlation limit.” In: J. Chem. Phys. 145.12 (2016), p. 124104. [68] Stefan Vuckovic and Paola Gori-Giorgi. “Simple Fully Nonlocal

Density Functionals for Electronic Repulsion Energy.” In: The Journal of Physical Chemistry Letters 8.13 (June 2017). PMID: 28581751, pp. 2799–2805. doi:10.1021/acs.jpclett.7b01113.

[69] Alan L Mackay. A dictionary of scientific quotations. CRC Press, 1991.

[70] Egor Ospadov, Ilya G Ryabinkin, and Viktor N Staroverov. “Improved method for generating exchange-correlation poten-tials from electronic wave functions.” In: The Journal of Chemical Physics 146.8 (Feb. 2017), p. 084103. doi:10.1063/1.4975990. [71] Rogelio Cuevas-Saavedra, Paul W Ayers, and Viktor N Staroverov.

“Kohn–Sham exchange-correlation potentials from second-order reduced density matrices.” In: The Journal of chemical physics 143.24 (2015), p. 244116.

[72] Rogelio Cuevas-Saavedra and Viktor N Staroverov. “Exact ex-pressions for the Kohn–Sham exchange-correlation potential in terms of wave-function-based quantities.” In: Molecular Physics 114.7-8 (2016), pp. 1050–1058.

[73] Evert Jan Baerends and Oleg V Gritsenko. “A quantum chemi-cal view of density functional theory.” In: The Journal of Physichemi-cal Chemistry A 101.30 (1997), pp. 5383–5403.

[74] MJP Hodgson, JD Ramsden, and RW Godby. “Origin of static and dynamic steps in exact Kohn-Sham potentials.” In: Physical Review B 93.15 (2016), p. 155146.

[75] Robert Van Leeuwen, Oleg Gritsenko, and Evert Jan Baerends. “Step structure in the atomic Kohn-Sham potential.” In: Zeitschrift

für Physik D Atoms, Molecules and Clusters 33.4 (1995), pp. 229– 238.

[76] Francesc Malet and Paola Gori-Giorgi. “Strong correlation in Kohn-Sham density functional theory.” In: Phys. Rev. Lett. 109.24 (Dec. 2012), p. 246402. doi:10.1103/PhysRevLett.109. 246402.

(8)

[77] F. Malet, A. Mirtschink, J. C. Cremon, S. M. Reimann, and P. Gori-Giorgi. “Kohn-Sham density functional theory for quan-tum wires in arbitrary correlation regimes.” In: Phys. Rev. B 87.11 (Mar. 2013), p. 115146. doi: 10 . 1103 / PhysRevB . 87 . 115146.

[78] C. B. Mendl, F. Malet, and P. Gori-Giorgi. “Wigner localiza-tion in quantum dots from Kohn-Sham density funclocaliza-tional the-ory without symmetry breaking.” In: Phys. Rev. B 89 (2014), p. 125106. doi:10.1103/PhysRevB.89.125106.

[79] Eduardo Fabiano, S ´Smiga, Sara Giarrusso, Timothy J Daas, Fabio Della Sala, Ireneusz Grabowski, and Paola Gori-Giorgi. “Investigation of the exchange-correlation potential of function-als based on the adiabatic connection interpolation.” In: arXiv preprint arXiv:1810.08458 (2018).

[80] D. G. Tempel, T. J. Martínez, and N. T. Maitra. “Revisiting Molecular Dissociation in Density Functional Theory: A Simple Model.” In: J. Chem. Theory. Comput. 5.4 (Mar. 2009), pp. 770– 780. doi:10.1021/ct800535c.

[81] A. Benítex and C. R. Proetto. “Kohn-Sham potential for a strongly correlated finite system with fractional occupancy.” In: Phys. Rev. A 94.4 (Nov. 2016), p. 052506. doi:10.1103/PhysRevA. 94.052506.

[82] R. J. Magyar and Kieron Burke. “Density-functional theory in one dimension for contact-interacting fermions.” In: Phys. Rev. A 70.3 (Sept. 2004), p. 032508. doi:10.1103/PhysRevA.70. 032508.

[83] N. Helbig, I. V. Tokatly, and A. Rubio. “Exact Kohn–Sham potential of strongly correlated finite systems.” In: J. Chem. Phys. 131.22 (Dec. 2009), p. 224105. doi:10.1063/1.3271392. [84] Giovanna Lani, Simone Di Marino, Augusto Gerolin, Robert

van Leeuwen, and Paola Gori-Giorgi. “The adiabatic strictly-correlated-electrons functional: kernel and exact properties.” In: Phys. Chem. Chem. Phys. 18.31 (Mar. 2016), pp. 21092–21101. doi:10.1039/c6cp00339g.

[85] Thomas E. Baker, E. Miles Stoudenmire, Lucas O. Wagner, Kieron Burke, and Steven R. White. “One-dimensional mimick-ing of electronic structure: The case for exponentials.” In: Phys. Rev. B 91.23 (June 2015). Err. 93 119912 (2016), p. 235141. doi:

10.1103/PhysRevB.91.235141.

[86] M. A. Buijse, E. J. Baerends, and J. G. Snijders. “Analysis of cor-relation in terms of exact local potentials: Applications to two-electron systems.” In: Phys. Rev. A 40.8 (Oct. 1989), pp. 4190– 4202. doi:10.1103/PhysRevA.40.4190.

(9)

[87] Oleg V. Gritsenko and Evert Jan Baerends. “Effect of molecular dissociation on the exchange-correlation Kohn-Sham poten-tial.” In: Phys. Rev. A 54.3 (Sept. 1996), pp. 1957–1972. doi:

10.1103/PhysRevA.54.1957.

[88] R. van Leeuwen and E. J. Baerends. “An Analysis of Non-local Density Functionals in Chemical Bonding.” In: Int. J. Quant. Chem. 52.4 (Nov. 1994), pp. 711–730. doi: 10 . 1002 / qua.560520405.

[89] Zu-Jian Ying, Valentina Brosco, Giorgia Maria Lopez, Daniele Varsano, Paola Gori-Giorgi, and José Lorenzana. “Anomalous scaling and breakdown of conventional density functional theory methods for the description of Mott phenomena and stretched bonds.” In: Phys. Rev. B 94.7 (Aug. 2016), p. 075154. doi:10.1103/PhysRevB.94.075154.

[90] Sara Giarrusso, Stefan Vuckovic, and Paola Gori-Giorgi. “Re-sponse potential in the strong-interaction limit of DFT: Anal-ysis and comparison with the coupling-constant average.” In: J. Chem. Theory Comput. 14.8 (June 2018), pp. 4151–4167. doi:

10.1021/acs.jctc.8b00386.

[91] P. Gori-Giorgi and M. Seidl. “Density functional theory for strongly-interacting electrons: perspectives for physics and chemistry.” In: JPhys. Chem. Chem. Phys 12.43 (Nov. 2010), pp. 14405–14419. doi:10.1039/c0cp01061h.

[92] Sara Giarrusso, Paola Gori-Giorgi, Fabio Della Sala, and Ed-uardo Fabiano. “Assessment of interaction-strength interpola-tion formulas for gold and silver clusters.” In: J. Chem. Phys. 148.13 (Apr. 2018), p. 134106. doi:10.1063/1.5022669.

[93] Stefan Vuckovic, Paola Gori-Giorgi, Fabio Della Sala, and Ed-uardo Fabiano. “Restoring size consistency of approximate functionals constructed from the adiabatic connection.” In: J. Phys. Chem. Lett. 9.11 (May 2018), pp. 3137–3142. doi:10.1021/ acs.jpclett.8b01054.

[94] Dirk Ter-Haar. Elements of statistical mechanics. Rinehart, 1958. [95] Christian B. Mendl, Francesc Malet, and Paola Gori-Giorgi.

“Wigner localization in quantum dots from Kohn-Sham density functional theory without symmetry breaking.” In: Phys. Rev. B 89 (12 2014), p. 125106. doi:10.1103/PhysRevB.89.125106. url:

http://link.aps.org/doi/10.1103/PhysRevB.89.125106.

[96] A. Mirtschink, M. Seidl, and P. Gori-Giorgi. “The derivative dis-continuity in the strong-interaction limit of density functional theory.” In: Phys. Rev. Lett. 111 (2013), p. 126402.

[97] Amit Ghosal, AD Güçlü, CJ Umrigar, Denis Ullmo, and Harold U Baranger. “Correlation-induced inhomogeneity in circular quantum dots.” In: Nature Physics 2.5 (2006), p. 336.

(10)

[98] Massimo Rontani, Carlo Cavazzoni, Devis Bellucci, and Guido Goldoni. “Full configuration interaction approach to the few-electron problem in artificial atoms.” In: The Journal of chemical physics 124.12 (2006), p. 124102.

[99] Amit Ghosal, AD Güçlü, CJ Umrigar, Denis Ullmo, and Harold U Baranger. “Incipient Wigner localization in circular quantum dots.” In: Physical Review B 76.8 (2007), p. 085341.

[100] Stefan Vuckovic. “Density functionals from the multiple-radii approach: analysis and recovery of the kinetic correlation en-ergy.” In: Journal of chemical theory and computation (2019). [101] Tim Gould and Stefan Vuckovic. “Range-separation and the

multiple radii functional approximation inspired by the strongly interacting limit of density functional theory.” In: The Journal of Chemical Physics 151.18 (2019), p. 184101.

[102] Yongxi Zhou, Hilke Bahmann, and Matthias Ernzerhof. “Con-struction of exchange-correlation functionals through interpo-lation between the non-interacting and the strong-correinterpo-lation limit.” In: J. Chem. Phys. 143.12 (Sept. 2015), p. 124103. doi:

10.1063/1.4931160.

[103] S. Vuckovic, T. J. P. Irons, A. Savin, A. M. Teale, and P. Gori-Giorgi. “Exchange–correlation functionals via local interpola-tion along the adiabatic connecinterpola-tion.” In: J. Chem. Theory Comput. 12.6 (2016), pp. 2598–2610.

[104] Stefan Vuckovic, Tom J. P. Irons, Lucas O. Wagner, Andrew M. Teale, and Paola Gori-Giorgi. “Interpolated energy densities, correlation indicators and lower bounds from approximations to the strong coupling limit of DFT.” In: Phys. Chem. Chem. Phys. 19 (8 2017), pp. 6169–6183. doi: 10 . 1039 / C6CP08704C.

url:http://dx.doi.org/10.1039/C6CP08704C.

[105] M Zarenia, D Neilson, B Partoens, and FM Peeters. “Wigner crystallization in transition metal dichalcogenides: A new ap-proach to correlation energy.” In: Phys. Rev. B 95.11 (2017), p. 115438.

[106] Eduardo Fabiano, Paola Gori-Giorgi, Michael Seidl, and Fabio Della Sala. “Interaction-Strength Interpolation Method for Main-Group Chemistry: Benchmarking, Limitations, and Perspec-tives.” In: J. Chem. Theory. Comput. 12.10 (2016), pp. 4885–4896. [107] Lucian A Constantin. “Correlation energy functionals from adiabatic connection formalism.” In: Phys. Rev. B 99.8 (2019), p. 085117.

(11)

[108] Eduardo Fabiano, Szymon Smiga, Sara Giarrusso, Timothy J Daas, Fabio Della Sala, Ireneusz Grabowski, and Paola Gori-Giorgi. “Investigation of the exchange-correlation potentials of functionals based on the adiabatic connection interpolation.” In: Journal of chemical theory and computation 15.2 (2019), pp. 1006– 1015.

[109] Oleg V Gritsenko, Robert van Leeuwen, and Evert Jan Baerends. “Molecular exchange-correlation Kohn–Sham potential and energy density from ab initio first-and second-order density matrices: Examples for XH (X= Li, B, F).” In: The Journal of chemical physics 104.21 (1996), pp. 8535–8545.

[110] M. J. P. Hodgson, E. Kraisler, A. Schild, and E. K. U. Gross. “How Interatomic Steps in the Exact Kohn-Sham Potential Relate to Derivative Discontinuities of the Energy.” In: J. Phys. Chem. Lett. 8.(24) (2017), pp. 5974–5980.

[111] Juri Grossi, Derk P. Kooi, Klaas J. H. Giesbertz, Michael Seidl, Aron J. Cohen, Paula Mori-Sánchez, and Paola Gori-Giorgi. “Fermionic statistics in the strongly correlated limit of Density Functional Theory.” In: J. Chem. Theory Comput. 13.12 (Nov. 2017), pp. 6089–6100. doi:10.1021/acs.jctc.7b00998.

[112] Luis Cort, Soeren Ersbak Bang Nielsen, and Robert van Leeuwen. “Strictly-correlated-electron approach to excitation energies

of dissociating molecules.” In: Physical Review A 99.2 (2019), p. 022501.

[113] Alfred Galichon and Bernard Salanié. “Matching with trade-offs: Revealed preferences over competing characteristics.” In: (2010).

[114] Marco Cuturi. “Sinkhorn distances: Lightspeed computation of optimal transport.” In: Advances in neural information processing systems. 2013, pp. 2292–2300.

[115] Alfred Galichon. Optimal transport methods in economics. Prince-ton University Press, 2018.

[116] Gabriel Peyré, Marco Cuturi, et al. “Computational optimal transport.” In: Foundations and Trends® in Machine Learning 11.5-6 (2019), pp. 355–607.

[117] Maria Colombo and Simone Di Marino. “Equality between Monge and Kantorovich multimarginal problems with Coulomb cost.” In: Annali di Matematica Pura ad Applicata. Berlin Heidel-berg: Springer, 2013, pp. 1–14.

[118] Luca Nenna. “Numerical methods for multi-marginal optimal transportation.” PhD thesis. 2016.

(12)

[119] Gero. Friesecke and Daniela. Vögler. “Breaking the Curse of Dimension in Multi-Marginal Kantorovich Optimal Transport on Finite State Spaces.” In: SIAM Journal on Mathematical Analy-sis 50.4 (2018), pp. 3996–4019. doi:10.1137/17M1150025. eprint: https://doi.org/10.1137/17M1150025. url: https://doi. org/10.1137/17M1150025.

[120] Yuehaw Khoo, Lin Lin, Michael Lindsey, and Lexing Ying. “Semidefinite relaxation of multi-marginal optimal transport for strictly correlated electrons in second quantization.” In: arXiv preprint arXiv:1905.08322 (2019).

[121] Yuehaw. Khoo and Lexing. Ying. “Convex Relaxation Ap-proaches for Strictly Correlated Density Functional Theory.” In: SIAM Journal on Scientific Computing 41.4 (2019), B773–B795. doi:10.1137/18M1207478. eprint:https://doi.org/10.1137/ 18M1207478. url:https://doi.org/10.1137/18M1207478.

[122] Augusto Gerolin, Anna Kausamo, and Tapio Rajala. “Multi-marginal Entropy-Transport with repulsive cost.” In: arXiv preprint arXiv:1907.07900 (2019).

[123] Stephen B Sears, Robert G Parr, and Uri Dinur. “On the Quantum-Mechanical Kinetic Energy as a Measure of the Infor-mation in a Distribution.” In: Israel Journal of Chemistry 19.1-4 (1980), pp. 165–173.

[124] Zhen Tao, Yang Yang, and Sharon Hammes-Schiffer. “Multi-component density functional theory: Including the density gradient in the electron-proton correlation functional for hydro-gen and deuterium.” In: The Journal of Chemical Physics 151.12 (2019), p. 124102.

[125] Christian Léonard. “A survey of the Schrödinger problem and some of its connections with optimal transport.” In: Discrete & Continuous Dynamical Systems-A 34.4 (2014), pp. 1533–1574. [126] Simone Di Marino and Augusto Gerolin. “An Optimal

Trans-port Approach for the Schrödinger Bridges problem and conver-gence of the Sinkhorn algorithm.” In: arXiv:1911.06850 (2019). [127] Jean-David Benamou, Guillaume Carlier, and Luca Nenna. “A numerical method to solve optimal transport problems with coulomb cost.” In: arXiv preprint arXiv:1505.01136 (2015). [128] Patrice Koehl, Marc Delarue, and Henri Orland. “Statistical

Physics Approach to the Optimal Transport Problem.” In: Phys-ical review letters 123.4 (2019), p. 040603.

[129] Patrice Koehl, Marc Delarue, and Henri Orland. “Optimal transport at finite temperature.” In: Physical Review E 100.1 (2019), p. 013310.

(13)

[130] Jonathan M Borwein, Adrian Stephen Lewis, and Roger D Nussbaum. “Entropy minimization, DAD problems, and dou-bly stochastic kernels.” In: Journal of Functional Analysis 123.2 (1994), pp. 264–307.

[131] D. C. Langreth and J. P. Perdew. “The exchange-correlation energy of a metallic surface.” In: Solid. State Commun. 17 (1975), pp. 1425–1429.

[132] Stefan Vuckovic, Mel Levy, and Paola Gori-Giorgi. “Augmented potential, energy densities, and virial relations in the weak-and strong-interaction limits of DFT.” In: J. Chem. Phys. 147.21 (2017), p. 214107.

[133] Mel Levy and Federico Zahariev. “Ground-state energy as a simple sum of orbital energies in Kohn-Sham theory: A shift in perspective through a shift in potential.” In: Physical review letters 113.11 (2014), p. 113002.

[134] N David Mermin. “Thermal properties of the inhomogeneous electron gas.” In: Physical Review 137.5A (1965), A1441.

[135] Aurora Pribram-Jones, Paul E Grabowski, and Kieron Burke. “Thermal density functional theory: Time-dependent linear response and approximate functionals from the fluctuation-dissipation theorem.” In: Physical review letters 116.23 (2016), p. 233001.

[136] Kieron Burke, Justin C Smith, Paul E Grabowski, and Aurora Pribram-Jones. “Exact conditions on the temperature depen-dence of density functionals.” In: Physical Review B 93.19 (2016), p. 195132.

[137] Aurora Pribram-Jones, Stefano Pittalis, EKU Gross, and Kieron Burke. “Thermal density functional theory in context.” In: Fron-tiers and Challenges in Warm Dense Matter. Springer, 2014, pp. 25– 60.

[138] Luigi Delle Site. “Shannon entropy and many-electron cor-relations: Theoretical concepts, numerical results, and Collins conjecture.” In: International Journal of Quantum Chemistry 115.19 (2015), pp. 1396–1404.

[139] Derk P Kooi and Paola Gori-Giorgi. “A variational approach to London dispersion interactions without density distortion.” In: The journal of physical chemistry letters 10.7 (2019), pp. 1537–1541. [140] WL Bade. “Drude-Model Calculation of Dispersion Forces. I. General Theory.” In: The Journal of Chemical Physics 27.6 (1957), pp. 1280–1284.

(14)

[141] Nicola Ferri, Robert A DiStasio Jr, Alberto Ambrosetti, Roberto Car, and Alexandre Tkatchenko. “Electronic properties of molecules and surfaces with a self-consistent interatomic van der Waals density functional.” In: Physical review letters 114.17 (2015), p. 176802.

[142] Rémi Flamary and Nicolas Courty. Pot python optimal transport library. 2017.

[143] Nathael Gozlan and Christian Léonard. “A large deviation ap-proach to some transportation cost inequalities.” In: Probability Theory and Related Fields 139.1-2 (2007), pp. 235–283.

[144] A Nagy. “Shannon entropy density as a descriptor of Coulomb systems.” In: Chemical Physics Letters 556 (2013), pp. 355–358. [145] A Nagy and Shubin Liu. “Local wave-vector, Shannon and

Fisher information.” In: Physics Letters A 372.10 (2008), pp. 1654– 1656.

[146] Robin P Sagar, Humberto G Laguna, and Nicolais L Guevara. “Statistical correlation between atomic electron pairs.” In:

Chem-ical Physics Letters 514.4-6 (2011), pp. 352–356.

[147] R González-Férez and JS Dehesa. “Shannon entropy as an indicator of atomic avoided crossings in strong parallel mag-netic and electric fields.” In: Physical review letters 91.11 (2003), p. 113001.

[148] Moyocoyani Molina-Espíritu, Rodolfo O Esquivel, Juan Car-los Angulo, Juan Antolín, and Jesús S Dehesa. “Information-theoretical complexity for the hydrogenic identity S N 2 ex-change reaction.” In: Journal of Mathematical Chemistry 50.7 (2012), pp. 1882–1900.

[149] Alex Borgoo, Pablo Jaque, Alejandro Toro-Labbé, Christian Van Alsenoy, and Paul Geerlings. “Analyzing Kullback–Leibler information profiles: an indication of their chemical relevance.” In: Physical Chemistry Chemical Physics 11.3 (2009), pp. 476–482. [150] Meressa A Welearegay, Robert Balawender, and Andrzej Holas. “Information and complexity measures in molecular reactivity studies.” In: Physical Chemistry Chemical Physics 16.28 (2014), pp. 14928–14946.

[151] Alex D Gottlieb and Norbert J Mauser. “New measure of electron correlation.” In: Physical review letters 95.12 (2005), p. 123003.

[152] Tianyi Lin, Nhat Ho, Marco Cuturi, and Michael I Jordan. “On the Complexity of Approximating Multimarginal Optimal

(15)

[153] Yale University. The Yale Literary Magazine. v. 47. Herrick & Noyes, 1882. url: https : / / books . google . nl / books ? id = iJ9MAAAAMAAJ.

[154] F Malet, A Mirtschink, CB Mendl, Johannes Bjerlin, EÖ Karab-ulut, SM Reimann, and Paola Gori-Giorgi. “Density-functional theory for strongly correlated bosonic and fermionic ultracold dipolar and ionic gases.” In: Physical review letters 115.3 (2015), p. 033006.

[155] Tim Gould and Stefan Vuckovic. “Range-separation and the multiple radii functional approximation inspired by the strongly interacting limit of density functional theory.” In: The Journal of Chemical Physics 151.18 (2019), p. 184101.

[156] Jean-David Benamou, Guillaume Carlier, Marco Cuturi, Luca Nenna, and Gabriel Peyré. “Iterative bregman projections for regularized transportation problems.” In: SIAM J. on Sci. Com-put. 37.2 (2015), A1111–A1138.

[157] A. Alfonsi, R. Coyaud, V. Ehrlacher, and D. Lombardi. “Ap-proximation of Optimal Transport problems with marginal mo-ments constraints.” In: arXiv preprint arXiv:1905.05663 (2019). [158] Lucas O. Wagner, Thomas E. Baker, E. M. Stoudenmire, Kieron

Burke, and Steven R. White. “Kohn-Sham calculations with the exact functional.” In: Phys. Rev. B 90 (4 2014), p. 045109. doi:

10.1103/PhysRevB.90.045109. url:https://link.aps.org/ doi/10.1103/PhysRevB.90.045109.

[159] Mark J Ablowitz and Ziad H Musslimani. “Spectral renor-malization method for computing self-localized solutions to nonlinear systems.” In: Optics letters 30.16 (2005), pp. 2140– 2142.

[160] Ziad H Musslimani and Jianke Yang. “Self-trapping of light in a two-dimensional photonic lattice.” In: JOSA B 21.5 (2004), pp. 973–981.

[161] MJ Ablowitz and TP Horikis. “Solitons and spectral renormal-ization methods in nonlinear optics.” In: The European Physical Journal Special Topics 173.1 (2009), pp. 147–166.

[162] MJ Ablowitz, AS Fokas, and ZH Musslimani. “On a new non-local formulation of water waves.” In: Journal of Fluid Mechanics 562 (2006), pp. 313–343.

[163] Mark J Ablowitz, Nalan Antar, ˙Ilkay Bakırta¸s, and Boaz Ilan. “Vortex and dipole solitons in complex two-dimensional

(16)

[164] Eric Akkermans, Sankalpa Ghosh, and Ziad H Musslimani. “Numerical study of one-dimensional and interacting Bose– Einstein condensates in a random potential.” In: Journal of Physics B: Atomic, Molecular and Optical Physics 41.4 (2008), p. 045302.

[165] S Bednarek, B Szafran, T Chwiej, and J Adamowski. “Effective interaction for charge carriers confined in quasi-one-dimensional nanostructures.” In: Physical Review B 68.4 (2003), p. 045328. [166] G. F. Giuliani and G. Vignale. Quantum Theory of the Electron

Liquid. New York: Cambridge University Press, 2005.

[167] Michele Casula, Sandro Sorella, and Gaetano Senatore. “Ground state properties of the one-dimensional Coulomb gas using the lattice regularized diffusion Monte Carlo method.” In: Physical Review B 74.24 (2006), p. 245427.

[168] D. M. Ceperley and B. J. Alder. In: Phys. Rev. Lett. 45 (1980), p. 566.

[169] J. P. Perdew and A. Zunger. In: Phys. Rev. B 23 (1981), p. 5048. [170] S. J. Vosko, L. Wilk, and M. Nusair. In: Can. J. Phys. 58 (1980),

p. 1200.

[171] John P Perdew and Yue Wang. “Accurate and simple analytic representation of the electron-gas correlation energy.” In: Physi-cal Review B 45.23 (1992), p. 13244.

[172] Ping Nang Ma, Sebastiano Pilati, Matthias Troyer, and Xi Dai. “Density functional theory for atomic Fermi gases.” In: Nature

Physics 8.8 (2012), p. 601.

[173] Lorenzo Zecca, Paola Gori-Giorgi, Saverio Moroni, and Gio-vanni B. Bachelet. “Local density functional for the short-range part of the electron-electron interaction.” In: Phys. Rev. B 70.20 (2004), p. 205127.

[174] J. Toulouse, A. Savin, and H.-J. Flad. “Short-range exchange-correlation energy of a uniform electron gas with modified electron-electron interaction.” In: Int. J. Quantum. Chem. 100 (2004), p. 1047.

[175] S. Paziani, S. Moroni, P. Gori-Giorgi, and G. B. Bachelet. In: Phys. Rev. B 73 (2006), p. 155111.

[176] C. Attaccalite, S. Moroni, P. Gori-Giorgi, and G. B. Bachelet. In: Phys. Rev. Lett. 88 (2002), p. 256601.

[177] Stefania De Palo, Sergio Conti, and Saverio Moroni. “Monte Carlo simulations of two-dimensional charged bosons.” In: Physical Review B 69.3 (2004), p. 035109.

[178] K Kärkkäinen, M Koskinen, SM Reimann, and M Manninen. “Exchange-correlation energy of a multicomponent two-dimensional

(17)

[179] N Helbig, Johanna I Fuks, M Casula, Matthieu J Verstraete, Miguel AL Marques, IV Tokatly, and Angel Rubio. “Density functional theory beyond the linear regime: Validating an adia-batic local density approximation.” In: Physical Review A 83.3 (2011), p. 032503.

[180] J Andre Weideman and Satish C Reddy. “A MATLAB differ-entiation matrix suite.” In: ACM Transactions on Mathematical Software (TOMS) 26.4 (2000), pp. 465–519.

[181] Abraham H Maslow. “The psychology of science a reconnais-sance.” In: (1966).

[182] A. D. Becke. “Density-functional thermochemistry. III. The role of exact exchange.” In: The Journal of chemical physics 98 (1993), p. 5648.

[183] Axel D Becke. “A new mixing of Hartree–Fock and local density-functional theories.” In: The Journal of chemical physics 98.2 (1993), pp. 1372–1377.

[184] John P Perdew, Matthias Ernzerhof, and Kieron Burke. “Ra-tionale for mixing exact exchange with density functional ap-proximations.” In: The Journal of chemical physics 105.22 (1996), pp. 9982–9985.

[185] Jochen Heyd, Gustavo E Scuseria, and Matthias Ernzerhof. “Hybrid functionals based on a screened Coulomb potential.” In: The Journal of chemical physics 118.18 (2003), pp. 8207–8215. [186] Yan Zhao and Donald G Truhlar. “Density functionals with

broad applicability in chemistry.” In: Accounts of chemical re-search 41.2 (2008), pp. 157–167.

[187] Alexei V Arbuznikov and Martin Kaupp. “Local hybrid exchange-correlation functionals based on the dimensionless density gra-dient.” In: Chemical physics letters 440.1-3 (2007), pp. 160–168. [188] Michael Seidl, Sara Giarrusso, Stefan Vuckovic, Eduardo

Fabi-ano, and Paola Gori-Giorgi. “Communication: Strong-interaction limit of an adiabatic connection in Hartree-Fock theory.” In: The Journal of chemical physics 149.24 (2018), p. 241101.

[189] Eugene Wigner. “On the interaction of electrons in metals.” In: Physical Review 46.11 (1934), p. 1002.

[190] R. G. Parr and W. Yang. Density-Functional Theory of Atoms and Molecules. New York: Oxford University Press, 1989.

[191] John P Perdew, Kieron Burke, and Matthias Ernzerhof. “Gen-eralized gradient approximation made simple.” In: Physical review letters 77.18 (1996), p. 3865.

[192] Codina Cotar and Mircea Petrache. “Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Riesz potentials.” In: arXiv preprint arXiv:1707.07664 (2019).

(18)

[193] Eugene Wigner. “Effects of the electron interaction on the en-ergy levels of electrons in metals.” In: Transactions of the Faraday Society 34 (1938), pp. 678–685.

[194] Karim M Abadir and Jan R Magnus. Matrix algebra. Vol. 1. Cambridge University Press, 2005.

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