Abstract
In statistical mechanics the integration of Liouville’s equation over N-q particle variables leads to a well known hierarchy of equations for reduced statistical distributions. In essence, the same pattern of thought is behind the Contracted Schrödinger Equation (CSE), which has been obtained independently by Cho [1] in 1962 as well as by Nakatsuji [2], and Cohen and Frishberg [3] in 1976. Nakatsuji named his integro-differential equation density equation, whereas Cohen and Frishberg called theirs hierarchy equations because the p-electron equation was coupled to its (p+1)- and (p+2)- counterparts. The initial interest raised by these results [4–9] subsided after some time because, due to their hierarchical structure, these equations were undetermined [10].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Cho, Sei. Rep. Gumma Univ. 11, 1 (1962).
H. Nakatsuji, Phys. Rev. A 14, 41 (1976).
L. Cohen and C. Prishberg, Phys. Rev. A13, 927 (1976).
L. Cohen and C. Frishberg, J. Chem. Phys. 65, 4234 (1976).
H. Schlosser, Phys. Rev. A 15, 1349 (1977).
L. Cohen, P. Santhanam, and C. Frishberg, Int. J. Quant. Chem. S14, 143 (1980).
L. Cohen, C. Prishberg, and P. Blumenau, Int. J. Quant. Chem. S14,160 (1980).
L. Cohen and L. Massa, Int. J. Quant. Chem. S14, 168 (1980).
L. Cohen, Int. J. Quant. Chem., 29, 249 (1986).
J. E. Harriman, Phys. Rev. A 19, 1893 (1979).
C. Valdemoro, An. R. Soc. Esp. Fis. 79, 106 (1983).
C. Valdemoro, Phys. Rev. A 31, 2114 (1985).
C. Valdemoro, in Density Matrices and Density Functionals, Proceedings of the A.J. Coleman Symposium, Kingston, Ontario, 1985, R. Erdahl and V. Smith (eds.), Reidel, Dordrecht (1987), p. 275.
P. Hohenberg, W. Kohn, Phys. Rev. B 136, 864 (1964).
C. Valdemoro, Phys. Rev. A45, 4462 (1992).
F. Colmenero, C. Pérez del Valle, and C. Valdemoro, Phys. Rev. A. 47, 971 (1993).
C. Valdemoro, L. M. Tel, and E. Pérez-Romero, Adv. Quant Chem. 28, 33 (1997).
F. Colmenero and C. Valdemoro, Int. J. Quant Chem. 51, 369 (1994).
H. Nakatsuji and K. Yasuda, Phys. Rev. Letts. 76, 1039 (1996).
K. Yasuda and H. Nakatsuji, Phys. Rev.A 56, 2648 (1997).
D. Mazziotti, Phys. Rev.A 57, 4219 (1998).
D. Mazziotti, Int. J. Quant Chem. 70, 557 (1998).
D. Mazziotti, Phys. Rev. A 60, 3618 (1999).
P. O. Löwdin, Phys. Rev. 97, 1474 (1955).
R. McWeeny, Rev. Mod. Phys. 32, 335 (1960).
A. J. Coleman, Rev. Mod. Phys. 35, 668 (1963).
J. A. Coleman in Density Matrices and Density Functional, Proceedings of the A. J. Coleman Symposium, Kingston, Ontario, 1985, R. Erdahl and V. Smith (eds.). Reidel, Dordrecht (1987), p. 5 and the references cited therein.
C. Valdemoro, L. M. Tel, and E. Pérez-Romero, Phys. Rev.,A (in press).
C. Garrod and J. K. Percus, J. Math. Phys. 5, 1756 (1964).
W. Kutzelnigg, J. Chem. Phys. 110, 2800 (1999).
C. Valdemoro, M. P. de Lara-Castells, E. Pérez-Romero, and L. M. Tel, Adv. Quant. Chem. 31, 37 (1999).
C. Valdemoro, Top. Curr. Chem., Correlation and Localization, P. Surjan (ed.), Springer-Verlag (1999).
C. Valdemoro, L. M. Tel, and E. Pérez-Romero, in Quantum Systems in Chemistry and Physics I. A. Hernandez-Laguna, J. Maruani, R. McWeeny, S. Wilson (eds.), Kluwer, Dordrecht (in press).
M. Rosina, B. Golli, and R. M. Erdahl Density Matrices and Density Functionals, Proceedings of the A.J. Coleman Symposium, Kingston, Ontario, 1985, R. Erdahl and V. Smith (eds.), Reidel, Dordrecht (1987), p. 231.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
Valdemoro, C., Tel, L.M., Pérez-Romero, E. (2000). Critical Questions Concerning Iterative Solution of the Contracted Schrödinger Equation. In: Cioslowski, J. (eds) Many-Electron Densities and Reduced Density Matrices. Mathematical and Computational Chemistry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4211-7_6
Download citation
DOI: https://doi.org/10.1007/978-1-4615-4211-7_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6890-8
Online ISBN: 978-1-4615-4211-7
eBook Packages: Springer Book Archive