On derivatives of the energy with respect to total electron number and orbital occupation numbers. A critique of Janak's theorem

References

• J.C. Slater, J.B. Mann, T.M. Wilson and J.H. Wood, Phys. Rev. 184, 672 (1969). doi: https://doi.org/10.1103/PhysRev.184.672
   Web of Science ®Google Scholar
• J.C. Slater, The Self-Consistent Field for Molecules and Solids: Quantum Theory of Molecules and Solids, Vol. 4. (McGraw-Hill Inc., New York, 1974).
   Google Scholar
• E.J. Baerends, J. Chem. Phys. 149, 054105 (2018). doi: https://doi.org/10.1063/1.5026951
   PubMed Web of Science ®Google Scholar
• J.F. Janak, Phys. Rev. B 18, 7165 (1978). doi: https://doi.org/10.1103/PhysRevB.18.7165
   Web of Science ®Google Scholar
• A. Görling, Phys. Rev. B 91, 245120 (2015). doi: https://doi.org/10.1103/PhysRevB.91.245120
   Web of Science ®Google Scholar
• J.P. Perdew, R.G. Parr, M. Levy and J.L. Balduz, Phys. Rev. Lett. 49, 1691 (1982). doi: https://doi.org/10.1103/PhysRevLett.49.1691
   Web of Science ®Google Scholar
• J.P. Perdew, in Density Functional Methods in Physics, edited by R. M. Dreizler and J. da Providencia (Plenum, New York, 1985), vol. 123 of NATO Advanced Study Institute Series B: Physics, pp. 265–308.
   Google Scholar
• E.H. Lieb, Int. J. Quant. Chem. 24, 243 (1983). doi: https://doi.org/10.1002/qua.560240302
   Web of Science ®Google Scholar
• R. van Leeuwen, Adv. Quantum Chem. 43, 25 (2003). doi: https://doi.org/10.1016/S0065-3276(03)43002-5
   Web of Science ®Google Scholar
• P.E. Lammert, Int. J. Quantum Chem. 107, 1943 (2007). doi: https://doi.org/10.1002/qua.21342
   Web of Science ®Google Scholar
• S. Kvaal, U. Ekström, A.M. Teale and T. Helgaker, J. Chem. Phys. 140, 18A518 (2014). doi: https://doi.org/10.1063/1.4867005
   PubMed Web of Science ®Google Scholar
• N.D. Mermin, Phys. Rev. A 137, 1441 (1965). doi: https://doi.org/10.1103/PhysRev.137.A1441
   Web of Science ®Google Scholar
• N.W. Ashcroft and N.D. Mermin, Solid State Physics (Holt, Rinehart and Winston, London – New York, 1976).
   Google Scholar
• E. Kraisler and L. Kronik, Phys. Rev. A 91, 032504 (2015). doi: https://doi.org/10.1103/PhysRevA.91.032504
   Web of Science ®Google Scholar
• V. Atalla, I.Y. Zhang, O.T. Hofmann, X. Ren, P. Rinke and M. Scheffler, Phys. Rev. B 94, 035140 (2016). doi: https://doi.org/10.1103/PhysRevB.94.035140
   Web of Science ®Google Scholar
• C. Li, J. Lu and W.T. Yang, J. Chem. Phys. 146, 214109 (2017).
   PubMed Web of Science ®Google Scholar
• R. Fletcher, Practical Methods of Optimization, vol. 2: Constrained Optimization (John Wiley & Sons, Ltd., New York, 1981), ISBN 0-471-27828-9.
   Google Scholar
• J. Nocedal and S.J. Wright, Numerical Optimization (Springer-Verlag, New York, 1999), ISBN 0-387-98793-2 (hardcover).
   Google Scholar
• R.G. Parr and L.J. Bartolotti, J. Phys. Chem. 87, 2810 (1983). doi: https://doi.org/10.1021/j100238a023
   Web of Science ®Google Scholar
• T. Gál, Phys. Rev. A 63, 022506 (2001).
   Web of Science ®Google Scholar
• R.M. Dreizler and E.K.U. Gross, Density Functional Theory: An Approach to the Quantum Many-Body Problem (Springer-Verlag, Berlin Heidelberg, 1990), ISBN 3-540-51993-9.
   Google Scholar
• M. Levy, Proc. Natl. Acad. Sci. USA 76, 6062 (1979). doi: https://doi.org/10.1073/pnas.76.12.6062
   PubMed Web of Science ®Google Scholar
• S.M. Valone, J. Chem. Phys. 73, 1344 (1980). doi: https://doi.org/10.1063/1.440249
   Web of Science ®Google Scholar
• H. Eschrig, The Fundamentals of Density Functional Theory, no. 32 in Teubner-Texte zur Physik (B. G. Teubner Verlagsgesellschaft, Stuttgart – Leipzig, 1996), ISBN 3-8154-3030-5.
   Google Scholar
• K.J.H. Giesbertz and M. Ruggenthaler, to be published (2018).
   Google Scholar
• R.G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, 200 Madison Avenue, New York, NY 10016, USA, 1989), ISBN 0-19-504279-4.
   Google Scholar
• J.P. Perdew and M. Levy, Phys. Rev. Lett. 51, 1884 (1983). doi: https://doi.org/10.1103/PhysRevLett.51.1884
   Web of Science ®Google Scholar
• R.G. Parr and S. Liu, Chem. Phys. Lett. 280, 159 (1997). doi: https://doi.org/10.1016/S0009-2614(97)01115-9
   Web of Science ®Google Scholar
• W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965). doi: https://doi.org/10.1103/PhysRev.140.A1133
   Web of Science ®Google Scholar
• M.M. Valiev and G.W. Fernando, Phys. Rev. B 52, 10697 (1995). doi: https://doi.org/10.1103/PhysRevB.52.10697
   PubMed Web of Science ®Google Scholar
• H. Englisch and R. Englisch, Phys. Stat. Sol. (b) 124, 373 (1984). doi: https://doi.org/10.1002/pssb.2221240140
   Web of Science ®Google Scholar
• M. Levy, Phys. Rev. A 26, 1200 (1982). doi: https://doi.org/10.1103/PhysRevA.26.1200
   Web of Science ®Google Scholar
• P.R.T. Schipper, O.V. Gritsenko and E.J. Baerends, Theor. Chem. Acc. 99, 329 (1998). doi: https://doi.org/10.1007/s002140050343
   Web of Science ®Google Scholar
• C.A. Ullrich and W. Kohn, Phys. Rev. Lett. 87, 093001 (2001).
   PubMed Web of Science ®Google Scholar
• K.J.H. Giesbertz and E.J. Baerends, J. Chem. Phys. 132, 194108 (2010). doi: https://doi.org/10.1063/1.3426319
   PubMed Web of Science ®Google Scholar
• T.L. Gilbert, Phys. Rev. B 12, 2111 (1975). doi: https://doi.org/10.1103/PhysRevB.12.2111
   Web of Science ®Google Scholar
• W.T. Yang, Y. Zhang and P.W. Ayers, Phys. Rev. Lett. 84, 5172 (2000). doi: https://doi.org/10.1103/PhysRevLett.84.5172
   PubMed Web of Science ®Google Scholar
• P.W. Ayers, J. Math. Chem. 43, 285 (2008). doi: https://doi.org/10.1007/s10910-006-9195-5
   Web of Science ®Google Scholar
• S.M. Valone, J. Chem. Phys. 73, 1344 (1980). doi: https://doi.org/10.1063/1.440249
   Web of Science ®Google Scholar
• J. Katriel and E.R. Davidson, Proc. Natl. Acad. Sci. USA 77, 4403 (1980). doi: https://doi.org/10.1073/pnas.77.8.4403
   PubMed Web of Science ®Google Scholar
• C.-O. Almbladh and U. von Barth, Phys. Rev. B 31, 3231 (1985). doi: https://doi.org/10.1103/PhysRevB.31.3231
   PubMed Web of Science ®Google Scholar
• M. Levy, J.P. Perdew and V. Sahni, Phys. Rev. A 30, 2745 (1984). doi: https://doi.org/10.1103/PhysRevA.30.2745
   Web of Science ®Google Scholar
• C.O. Almbladh and U. von Barth, in Density Functional Methods in Physics, edited by R. M. Dreizler and J. da Providencia (Plenum, New York, 1985), vol. 123 of NATO Advanced Study Institute Series B: Physics.
   Google Scholar
• O.V. Gritsenko, R.V. Leeuwen and E.J. Baerends, J. Chem. Phys. 104, 8535 (1996). doi: https://doi.org/10.1063/1.471602
   Web of Science ®Google Scholar
• O.V. Gritsenko and E.J. Baerends, Phys. Rev. A 54, 1957 (1996). doi: https://doi.org/10.1103/PhysRevA.54.1957
   PubMed Web of Science ®Google Scholar
• N.T. Maitra, J. Chem. Phys. 122, 234104 (2005). doi: https://doi.org/10.1063/1.1924599
   PubMed Web of Science ®Google Scholar
• N.T. Maitra and M. van Faassen, J. Chem. Phys. 126, 191106 (2007). doi: https://doi.org/10.1063/1.2741243
   PubMed Web of Science ®Google Scholar
• N. Helbig, I.V. Tokatly and A. Rubio, J. Chem. Phys. 131, 224105 (2009). doi: https://doi.org/10.1063/1.3271392
   PubMed Web of Science ®Google Scholar
• D.G. Tempel, T.J. Martínez and N.T. Maitra, J. Chem. Theor. Comp. 5, 770 (2009). doi: https://doi.org/10.1021/ct800535c
   PubMed Web of Science ®Google Scholar
• P. Elliott, J.I. Fuks, A. Rubio and N.T. Maitra, Phys. Rev. Lett. 109, 266404 (2012). doi: https://doi.org/10.1103/PhysRevLett.109.266404
   PubMed Web of Science ®Google Scholar
• S.V. Kohut, A.M. Polgar and V.N. Staroverov, Phys. Chem. Chem. Phys. 18, 20938 (2016). doi: https://doi.org/10.1039/C6CP00878J
   PubMed Web of Science ®Google Scholar
• A. Savin, in Recent Developments and Applications of Modern Density Functional Theory, edited by J. M. Seminario (Elsevier, Amsterdam, The Netherlands, 1996), vol. 4 of Theoretical and Computational Chemistry, pp. 327–357.
   Google Scholar
• A. Savin, Chem. Phys. 356, 91 (2009). doi: https://doi.org/10.1016/j.chemphys.2008.10.023
   Web of Science ®Google Scholar
• P. Gori-Giorgi and A. Savin, J. Phys. Conf. Series 117, 012017 (2008). doi: https://doi.org/10.1088/1742-6596/117/1/012017
   Google Scholar
• E.J. Baerends, Phys. Rev. Lett. 87, 133004 (2001). doi: https://doi.org/10.1103/PhysRevLett.87.133004
   PubMed Web of Science ®Google Scholar
• M. Grüning, O.V. Gritsenko and E.J. Baerends, J. Chem. Phys. 118, 7183 (2003). doi: https://doi.org/10.1063/1.1562197
   Web of Science ®Google Scholar
• J.D. Chai, J. Chem. Phys. 136, 154104 (2012). doi: https://doi.org/10.1063/1.3703894
   PubMed Web of Science ®Google Scholar
• J.D. Chai, J. Chem. Phys. 140, 18A521 (2014). doi: https://doi.org/10.1063/1.4867532
   PubMed Web of Science ®Google Scholar
• M. Buijse and E.J. Baerends, Mol. Phys. 100, 401 (2002). doi: https://doi.org/10.1080/00268970110070243
   Web of Science ®Google Scholar
• O.V. Gritsenko, K. Pernal and E.J. Baerends, J. Chem. Phys. 122, 204102 (2005). doi: https://doi.org/10.1063/1.1906203
   PubMed Web of Science ®Google Scholar
• M. Piris, J.M. Matxain and X. Lopez, J. Chem. Phys. 139, 234109 (2013).
   PubMed Web of Science ®Google Scholar
• N.N. Lathiotakis, N. Helbig, A. Rubio and N.I. Gidopoulos, Phys. Rev. A 90, 032511 (2014). doi: https://doi.org/10.1103/PhysRevA.90.032511
   Web of Science ®Google Scholar
• I. Theophilou, N.N. Lathiotakis, N.I. Gidopoulos, A. Rubio and N. Helbig, J. Chem. Phys. 143, 054106 (2015). doi: https://doi.org/10.1063/1.4927784
   PubMed Web of Science ®Google Scholar
• K. Pernal and K.J.H. Giesbertz, Top. Curr. Chem. 368, 125 (2016). doi: https://doi.org/10.1007/128_2015_624
   PubMed Web of Science ®Google Scholar
• M. Seidl, Phys. Rev. A. 60, 4387 (1999). doi: https://doi.org/10.1103/PhysRevA.60.4387
   Web of Science ®Google Scholar
• M. Seidl, P. Gori-Giorgi and A. Savin, Phys. Rev. A 75, 042511 (2007).
   Web of Science ®Google Scholar
• S. Vuckovic, L.O. Wagner, A. Mirtschink and P. Gori-Giorgi, J. Chem. Theor. Comp. 11, 3153 (2015). doi: https://doi.org/10.1021/acs.jctc.5b00387
   PubMed Web of Science ®Google Scholar
• S. Vuckovic, T. Irons, A. Savin, A.M. Teale and P. Gori-Giorgi, J. Chem. Theor. Comp. 12, 2598 (2016). doi: https://doi.org/10.1021/acs.jctc.6b00177
   PubMed Web of Science ®Google Scholar
• J.C. Slater, Adv. Quantum Chem. 6, 1 (1972). doi: https://doi.org/10.1016/S0065-3276(08)60541-9
   Google Scholar
• A. Seidl, A. Görling, P. Vogl, J.A. Majewski and M. Levy, Phys. Rev. B 53, 3764 (1996). doi: https://doi.org/10.1103/PhysRevB.53.3764
   PubMed Web of Science ®Google Scholar
• W.T. Yang, A.J. Cohen and P. Mori-Sánchez, J. Chem. Phys. 136, 204111 (2012).
   PubMed Web of Science ®Google Scholar
• J.P. Perdew, W.T. Yang, K. Burke, Z. Yang, E.K.U. Gross, M. Scheffler, G.E. Scuseria, T.M. Henderson, I.Y. Zhang, A. Ruzsinszky and H. Peng, Proc. Natl. Acad. Sci. USA 114, 2801 (2017). doi: https://doi.org/10.1073/pnas.1621352114
   PubMed Web of Science ®Google Scholar
• P. Mori-Sánchez, A.J. Cohen and W.T. Yang, Phys. Rev. Lett. 100, 146401 (2008). doi: https://doi.org/10.1103/PhysRevLett.100.146401
   PubMed Web of Science ®Google Scholar
• T. Gál, J. Math. Phys. 48, 053520 (2007); err. 49, 029901 (2008).
   Google Scholar
• T. Gál, J. Math. Chem. 42, 661 (2007). doi: https://doi.org/10.1007/s10910-006-9216-4
   Web of Science ®Google Scholar