Density Matrices and Density Functionals pp 327-337 | Cite as
Inter-Relationships Between Various Representations of One-Matrices and Related Densities: A Road Map and An Example
Conference paper
Abstract
A brief, pedagogical survey is presented of the interrelationships between the position, momentum, Wigner, and Moyal representations of the spin traced first-order reduced density operator, and charge densities, momentum densities, form factors and internally folded densities. These somewhat abstract considerations are made concrete by explicit calculations for the “harmonium” atom, i.e. the harmonic model of two-electron atoms.
Preview
Unable to display preview. Download preview PDF.
REFERENCES
- 1.For reviews, see e.g., A.S. Bamzai and B.M. Deb, Rev. Mod. Phys. 53, 95 (1981); P. Coppens and M.B. Hall (Editors), Electron Distributions and the Chemical Bond (Plenum Press, New York 1982) and references cited therein; R.F.W. Bader, Acc. Chem. Res. 18, 9 (1985).Google Scholar
- 2.V.H. Smith, Jr., Phys. Scrip. 15, 147 (1977); P. Coppens and E.D. Stevens, Adv. Quantum Chem. 10, 1 (1977); P. Becker (Editor), Electron and Magnetization Densities in Molecules and Crystals, (Plenum Press, New York, 1980) and references cited therein.Google Scholar
- 3.B.G. Williams (Editor), Compton Scattering: The Investigation of Electron Momentum Distributions (McGraw Hill, New York, 1977) and references cited therein.Google Scholar
- 4.P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); G.A. Henderson, Phys. Rev. A 23, 19 (1981); V.H. Smith, Jr., unpublished paper presented at the Workshop on Density Functional Theory, Mexico City, October 1980; V.H. Smith, Jr. in Local Density Approximations in Quantum Chemistry and Solid State Physics, edited by J.P. Dahl and J. Avery (Plenum Press, New York, 1984 ), pp. 1 - 19.Google Scholar
- 5.P.O. Löwdin, Phys. Rev. 97, 1474 (1955).CrossRefGoogle Scholar
- 6.E. Wigner, Phys. Rev. 40, 749 (1932).CrossRefGoogle Scholar
- 7.For a very fine review, see: M. Hillery, R.F. Of Connell, M.O. Scully and E.P. Wigner, Phys. Reports 106, 122 (1984).Google Scholar
- 8.P. Claverie and S. Diner, Israel J. Chem. 19, 54 (1980); see especially p. 71.Google Scholar
- 9.J.P. Dahl, Phys. Scrip. 25, 499 (1982); Physica A 114, 439 (1982); in Energy Storage and Redistribution in Molecules, edited by J. Hinze (Plenum Press, New York, 1983), pp. 557-571; M. Springborg and J.P. Dahl in Local Density Approximations in Quantum Chemistry and Solid State Physics, edited by J.P. Dahl and J. Avery ( Plenum Press, New York, 1984 ), pp. 381 - 412.Google Scholar
- 10.J.P. Dahl and M. Springborg, Mol. Phys. 47, 1001 (1982).CrossRefGoogle Scholar
- 11.A.J. Thakkar and A.C. Tanner, “Reduced Fermion Wigner Functions”, unpublished paper presented at the Fourth International Congress in Quantum Chemistry, Uppsala, Sweden, June 1982.Google Scholar
- 12.M. Springborg, Theor. Chim. Acta 63, 349 (1983); J. Phys. A. 16, 535 (1983); Physica A. 126, 259 (1984).Google Scholar
- 13.W. Weyrich, this volume.Google Scholar
- 14.J.P. Dahl, this volume.Google Scholar
- 15.L. Cohen, this volume.Google Scholar
- 16.J.E. Moyal, Proc. Cambridge Phil. Soc. 45, 99 (1949).CrossRefGoogle Scholar
- 17.A.J. Thakkar, A.M. Simas and V.H. Smith, Jr., Chem. Phys. 63, 175 (1981).CrossRefGoogle Scholar
- 18.R. Benesch, S.R. Singh and V.H. Smith, Jr., Chem. Phys. Lett. 10, 151 (1971).CrossRefGoogle Scholar
- 19.A.J. Thakkar, this volume.Google Scholar
- 20.E.P. Wigner in Perspectives in Quantum Theory, edited byW. Yourgrau and A. van der Merwe ( MIT Press, Cambridge, Mass., 1971 ), pp. 25–36.Google Scholar
- 21.H. Weyl, Z. Phys. 46, 1 (1927).CrossRefGoogle Scholar
- 22.J.H. Shirley and S. Stenholm, J. Phys. A 10, 613 (1977); J.H. Shirley, J. Phys. B 13, 1537 (1980); S. Stenholm, Univ. of Helsinki, Theoretical Physics Preprint No. HU-TFT-80-40 (1980).Google Scholar
- 23.E.R. Davidson, Reduced Density Matrices in Quantum Chemistry, (Academic Press, New York, 1976), pp. 18-19. Note that equations 2–68 and 2–69 are missing factors of 2 on the right hand side.Google Scholar
- 24.T. Koga and M. Morita, J. Chem. Phys. 77, 6345 (1982); T. Koga, J. Chem. Phys. 79, 1384 (1983).Google Scholar
- 25.A.J. Thakkar and T. Koga, J. Chem. Phys. 83, 747 (1985) and references cited therein.CrossRefGoogle Scholar
- 26.C. Tavard and C.D. Cappello, C.R. Acad. Sc. Paris, serie II, 295, 439 (1982).Google Scholar
Copyright information
© D. Reidel Publishing Company 1987