Abstract
Nonrigorous character of the density-functional theory for inhomogeneous electron gas based on the hypothesis assuming the existence of a universal density functional is demonstrated. A single-particle density matrix must be determined to calculate the ground-state energy of a finite system with a finite number of electrons. A single-particle Green function can be used to unambiguously determine the ground-state energy of an inhomogeneous electron system that satisfies the thermodynamic limit.
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References
E. H. Lieb and R. Seiringer, The Stability of Matter in Quantum Mechanics (Cambridge Univ. Press, New York, 2010).
E. G. Maksimov and A. E. Karakozov, Phys.-Usp. 51, 535 (2008).
P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
Theory of the Inhomogeneous Electron Gas, Ed. by S. Lundqvist and N. H. March (Plenum, New York, 1983).
H. Eschrig, The Fundamentals of Density Functional Theory (Tueubner, Stuttgart, 1996).
A. D. Becke, J. Chem. Phys. 140, 18A301 (2014).
V. B. Bobrov, S. A. Trigger, and Yu. P. Vlasov, Europhys. Lett. 98, 53002 (2012).
R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford Univ. Press, New York, 1989).
V. B. Bobrov and S. A. Trigger, Bull. Lebedev Phys. Inst. 45, 127 (2018).
L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Nauka, Moscow, 1974).
V. B. Bobrov and S. A. Trigger, J. Exp. Theor. Phys. 116, 635 (2013).
V. B. Bobrov, S. A. Trigger, and Yu. P. Vlasov, Phys. Rev. A 83, 034501 (2011).
D. A. Kirzhnits, Field Methods of Many-Particle Theory (Nauka, Moscow, 1963).
W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
M. Ya. Amusia, A. Z. Msezane, V. R. Shaginyan, and D. Sokolovski, Phys. Lett. A 330, 10 (2004).
A. M. Sarry and M. F. Sarry, Phys. Solid State 54, 1315 (2012).
D. N. Zubarev, Nonequilibrium Statistical Thermodynamics (Nauka, Moscow, 1971).
A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinskii, The Methods of Quantum Field Theory in Statistical Physics (Gos. Izd. Fiz.-Mat. Lit., Moscow, 1962).
V. B. Bobrov, S. A. Trigger, and A. Zagorodny, Phys. Rev. A 82, 044105 (2010).
V. B. Bobrov, S. A. Trigger, G. J. F. van Heijst, and P. P. J. M. Schram, Phys. Rev. E 82, 010102(R) (2010).
N. D. Mermin, Phys. Rev. 137, A1441 (1965).
A. Fetter and J. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971).
G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, Rev. Mod. Phys. 78, 865 (2006).
P. E. Blöchl, T. Pruschke, and M. Potthoff, Phys. Rev. B 88, 205139 (2013).
V. M. Galitskii and A. B. Migdal, J. Exp. Theor. Phys. 7, 96 (1958).
E. Z. Kuchinskii, I. A. Nekrasov, and M. V. Sadovskii, Phys.-Usp. 55, 325 (2012).
R. W. Godby and P. Garsia-Gonzalez, in A Primer in Density Functional Theory, Ed. by C. Fiolhais, F. Nogueira, and M. A. L. Marques (Springer, Heidelberg, 2003), p. 185.
S. Sharma, J. K. Dewhurst, N. N. Lathiotakis, and E. K. U. Gross, Phys. Rev. B 78, 201103(R) (2008).
K. Pernal, Phys. Rev. A 81, 052511 (2010).
N. N. Lathiotakis, N. I. Gidopoulos, and N. Helbig, J. Chem. Phys. 132, 084105 (2010).
A. R. Welden, A. A. Rusakov, and D. Zgid, J. Chem. Phys. 145, 204106 (2016).
T. N. Lan, A. A. Kananenka, and D. Zgid, J. Chem. Theory Comput. 12, 4856 (2016).
E. Gull and D. Zgid, New J. Phys. 19, 023047 (2017).
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Original Russian Text © V.B. Bobrov, S.A. Trigger, 2018, published in Zhurnal Tekhnicheskoi Fiziki, 2018, Vol. 88, No. 8, pp. 1128–1136.
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Bobrov, V.B., Trigger, S.A. To the Theory of Inhomogeneous Electron Gas. Tech. Phys. 63, 1092–1100 (2018). https://doi.org/10.1134/S1063784218080030
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DOI: https://doi.org/10.1134/S1063784218080030