Abstract
A generalised Hohenberg–Kohn theorem is described in terms of the sign of the second‐order energy variation. Independently, it is also corroborated within the perturbation theoretical framework. An alternative formulation of the Hohenberg–Kohn theorem, based on the relationships involving the matrix representations of density functions and the Hamiltonian operator variations, is shown to extend the validity of the theorem to the excited states of the Hamiltonian operators possessing non‐degenerate spectra. Finally, a connection with Brillouin's theorem when energy variation becomes stationary is also outlined.
Similar content being viewed by others
References
L. Amat, R. CarbÉ-Dorca and R. Ponec, J. Comput. Chem. 19 (1998) 1575–1583.
L. Brillouin, J. Phys. Radium 7 (1932) 373–389.
R. CarbÉ and E. Besalú, J. Math. Chem. 18 (1994) 117–126.
R. CarbÉ and E. Besalú, in: Strategies and Applications in Quantum Chemistry, eds. Y. Ellinger and M. Defranceschi (Kluwer, Amsterdam, 1996) pp. 229–248.
R. CarbÉ, E. Besalú, L. Amat and X. Fradera, J. Math. Chem. 18 (1996) 237–246.
R. CarbÉ-Dorca, E. Besalú, L. Amat and X. Fradera, in: Advances in Molecular Similarity, Vol. 1, eds. R. CarbÉ-Dorca and P.G. Mezey (JAI Press, Greenwich, 1996) pp. 1–42.
H. Eyring, J. Walter and G.E. Kimball, Quantum Chemistry (Wiley, New York, 1940).
P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864–B871.
P.O. Loewdin, Phys. Rev. 97 (1955) 1474–1489.
R. McWeeny, Rev. Mod. Phys. 32 (1960) 335–369.
P.G. Mezey, J. Math. Chem. 23 (1998) 65–84.
L. Pauling and E.B. Wilson, Jr., Introduction to Quantum Mechanics (Dover, New York, 1985).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sen, K., Besalú, E. & Carbó‐Dorca, R. A naive look on the Hohenberg–Kohn theorem. Journal of Mathematical Chemistry 25, 253–257 (1999). https://doi.org/10.1023/A:1019148903821
Issue Date:
DOI: https://doi.org/10.1023/A:1019148903821