Abstract
After a brief introduction to the use of the idempotent Dirac first-order density matrix (DM), its time-dependent generalization is considered. Special attention is focused on the equation of motion for the time-dependent DM, which is characterized by the one-body potential V(r, t) of time-dependent density functional theory. It is then shown how the force –∇ V(r, t) can be extracted explicitly from this equation of motion. Following a linear-response treatment in which a weak potential V(r, t) is switched on to an initially uniform electron gas, the non-linear example of the two-electron spin-compensated Moshinsky atom is a further focal point. We demonstrate explicitly how the correlated DM for this model can be constructed from the idempotent Dirac DM, in this time-dependent example.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dirac P.A.M.: Proc. Cam. Phil. Soc. 26, 70 (1930)
March N.H.: J. Phys. Chem. 86, 2262–2267 (1982)
Parr R.G., Yang W.: Density-functional theory of atoms and molecules. Oxford University Press, New York (1989)
Slater J.C.: Phys. Rev. 81, 385–390 (1951)
March N.H.: Self-consistent fields in atoms: hartree and Thomas-Fermi atoms. Pergamon Press, Oxford (1975)
Kohn W., Sham L.J.: Phys. Rev. 140, A1133 (1965)
March N.H.: Phys. Rev. A 36, 5077–5078 (1987)
March N.H., Murray A.M.: Phys. Rev. 120, 830–836 (1960)
March N.H., Murray A.M.: Proc. Roy. Soc. London A 261, 119–133 (1961)
Stoddart J.C., March N.H.: Proc. Roy. Soc. London A 299, 279–286 (1967)
Löwdin P.O.: Phys. Rev. 97, 1474–1489 (1955)
Sham L.J., Schlüter M.: Phys. Rev. Lett. 51, 1888–1891 (1983)
Leeuwen R.: Phys. Rev. Lett. 76, 3610–3613 (1996)
Görling A., Levy M.: Phys. Rev. A 50, 196–204 (1994)
Runge E., Gross E.K.U.: Phys. Rev. Lett. 52, 997–1000 (1984)
Zhao Q., Parr R.G.: Phys. Rev. A 46, 2337 (1992)
Zhao Q., Parr R.G.: J. Chem. Phys. 98, 543 (1993)
Zhao Q., Morrison R.C., Parr R.G.: Phys. Rev. A 50, 2138 (1994)
Umrigar C.J., Gonze X.: Phys. Rev. A 50, 3827–3837 (1994)
Amico I.D., Vignale G.: Phys. Rev. B 59, 7876–7887 (1999)
Lein M., Kümmel S.: Phys. Rev. Lett. 94, 143003 (2005)
Leeuwen R.: Phys. Rev. Lett. 82, 3863–3866 (1999)
March N., Young W.H.: Nucl. Phys. 12, 237–240 (1959)
Holas A., March N.H.: Phys. Rev. A 51, 2040–2048 (1995)
E.K.U. Gross, C.A. Ulrich, U.J. Gossmann, in Density functional theory, ed. by E.K.U. Gross, R.M. Dreizler (Plenum Press, New York, 1995).
Maitra N.T., Burke K.: Phys. Rev. A 63, 042501 (2001)
Maitra N.T., Burke K.: Phys. Rev. A 64, 039901 (2001)
Stoddart J.C., March N.H., Stott M.J.: Phys. Rev. 186, 683–696 (1969)
Sakurai J.J.: Modern quantum mechanics. Addison-Wesley, Reading, Massachusetts (1994)
Feynman R.P., Hibbs A.R.: Quantum mechanics and path integrals. McGraw-Hill, New York (1965)
March N.H., Tosi M.P.: Philos. Mag. 28, 91–102 (1973)
Lindhard J.: Kgl. Danske Videnskab. Selskab, Mat. Fys. Medd 28, 1 (1954)
Giuliani G.F., Vignale G.: Quantum theory of the electron liquid. Cambridge University Press, Cambridge (2005)
Moshinsky M.: Am. J. Phys. 36, 52 (1968)
March N.H., Howard I.A., Nagy I., Rubio A.: Phys. Lett. A 288, 101–104 (2001)
March N.H.: Phys. Lett. A 306, 63–65 (2002)
Niehaus T.A., Suhai S., March N.H.: J. Phys. A: Math. Theor. 41, 085304 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Niehaus, T.A., March, N.H. & Suhai, S. Correlated and idempotent Dirac first-order density matrices with identical diagonal Fermion density: a route to extract a one-body potential energy in TDDFT. J Math Chem 47, 505–519 (2010). https://doi.org/10.1007/s10910-009-9592-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-009-9592-7