Summary
In this Chapter the concept of density matrices and especially of the reduced one-electron density matrix is reviewed with their various properties, among which phase space, chemical bonding, the relation to observables and the experimental access to density matrices are particularly emphasised. Among the observables, electron position and momentum densities play the most important part, whence the state of the art of experimental determination of those densities is sketched with the aim to give some feeling for the potential and the reliability of modern experimental data. A number of entrance points to literature are given.
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
Reduced density matrices
K. Husimi, Proc. Phys. Math. Soc. Japan 22, 264 (1940).
P.-O. Lowdin, Phys. Rev. 97, 1474, 1490, 1509 (1955).
R. McWeeny, Proc. Roy. Soc. (London) A 232, 114 (1955).
R. McWeeny, Proc. Roy. Soc. (London) A 235, 496 (1956).
R. McWeeny, Rev. Mod. Phys. 32, 335 (1960).
A.J. Coleman, Rev. Mod. Phys. 35, 668 (1963).
F. Sasaki, Phys. Rev. 138 B, 1338 (1965).
G.R. Davidson, “Reduced Density Matrices in Quantum Chemistry”, Academic Press, New York, San Francisco, London 1976.
R. Erdahl. Smith, Jr. (eds.), “Density Matrices and Density Functionals”, D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo 1987.
T. Asthalter, W. Weyrich, Ber. Bunsenges. Phys. Chem. 96, 1747 (1992).
H. Schmider, K. E. Edgecombe, V. H. Smith, Jr., W. Weyrich, J. Chem. Phys. 96, 8411 (1992).
12] T. Asthalter, W. Weyrich, submitted.
Density-functional theory
P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964).
W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965).
L. Lam, P.L. Platzman, Phys. Rev. B 9, 5122 and 5128 (1974).
G.E. W. Bauer, Phys. Rev. B 27, 5912 (1983).
R. Erdahl. Smith, Jr. (eds.), “Density Matrices and Density Functionals”, D. Reidel Publishing Company, Dordredit, Boston, Lancaster, Tokyo 1987.
R.G. Parr, W. Yang, “Density-Functional Theory of Atoms and Molecules”, International Series of Monographs in Chemistry, Vol. 16, Oxford University Press, New York, and Clarendon Press, Oxford 1989.
E.S. Kryachko, E.V. Ludena, “Energy Density Functional Theory of Many-Electron Systems”, Understanding Chemical Reactivity, Vol. 4, Kluwer Academic Publishers, Dordrecht, Boston, London 1990.
T.L. Gilbert, Phys. Rev. B 12, 2111 (1975).
J.E. Harriman, Phys. Rev. A 24, 680 (1981).
J.E. Harriman, Phys. Rev. A 34, 29 (1986).
Density matrices and observables
R. Benesch, S.R. Singh, V.H. Smith, Jr., Chem. Phys. Letters 10, 151 (1971).
V.H. Smith, Jr., Phys. Scripta 15, 147 (1977).
W. Weyrieh, Habilitationsschrift, Darmstadt 1978.
A. J. Thakkar, A. M. Simas, V. H. Smith, Jr., Chem. Phys. 63, 175 (1981).
5] A.J. Thakkar, A.C. Tanner, V.H. Smith, Jr., in [1.9], p.327.
R. A. Bonham, W. Weyrieh, J. Brazil. Chem. Soc. 1, 7 (1990).
Form factors, structure factors and position densities
P. Coppens, E.D. Stevens, Adv. Quantum Chem. 10, 1 (1977).
P. Becker (ed.), “Electron and Magnetization Densities in Molecules and Crystals”, Plenum Press, New York 1980.
P. Coppens, M. Hall (eds.), “Electron Distributions and the Chemical Bond”, Plenum Press, New York 1982.
P. Coppens, Acta Cryst. A 40, 184 (1984).
Compton profiles, reciprocal form factors and momentum densities
B. Williams (ed.), “Compton Scattering: The Investigation of Electron Momentum Distributions”, McGraw Hill, New York 1977.
W. Weyrieh, Ber. Bunsenges. Phys. Chem. 79, 1085 (1975).
R. Benesch, S.R. Singh, V.H. Smith, Jr., Chem. Phys. Letters 10, 151 (1971).
P. Pattison, B. Williams, Solid State Commun. 20, 585 (1976).
P. Pattison, W. Weyrieh, B. Williams, Solid State Commun. 21, 967 (1977).
W. Schulke, phys. stat. sol. (b) 82, 229 (1977).
W. Weyrieh, Habilitationsschrift, Darmstadt 1978.
P. Pattison, W. Weyrieh, J. Phys. Chem. Solids 40, 213 (1979).
W. Weyrieh, P. Pattison, B. Williams, Chem. Phys. 41, 271 (1979).
A.J. Thakkar, A.M. Simas, V.H. Smith, Jr., Chem. Phys. 63, 175 (1981).
E. Heuser, Dissertation, Darmstadt 1982.
M.J. Cooper, Rep. Progr. Phys. 48, 415 (1985).
E. Heuser-Hofmann, W. Weyrieh, Z. Naturforsch. 40a, 99 (1985).
M. Bräuchler, S. Lunell, I. Olovsson, W. Weyrieh, Int. J. Quantum Chem. 35, 895 (1989).
T. Asthalter, W. Weyrieh, A. H. Harker, A. B. Kunz, R. Orlando, C. Pisani, Solid State Commun. 83, 725–730 (1992).
T. Asthalter, W. Weyrieh, Ber. Bunsenges. Phys. Chem. 96, 1747–1755 (1992).
L. Dobrzynski, Z. Naturforsch. 48a, 266 (1993).
T. Asthalter, W. Weyrieh, Z. Naturforsch. 48a, 303 (1993).
M. Weisser, W. Weyrieh, Z. Naturforsch. 48a, 315 (1993).
R.O. Horenian, W. Weyrieh, Z. Naturforsch. 48a, 325 (1993).
M. Weisser, Dissertation, Konstanz 1996.
A.J. Rollason, F. Bell, J.R. Schneider, Nucl. Instr. Meth. A281, 147 (1989).
F. Bell, T. Tschentscher, J.R. Schneider, A.J. Rollason, Z. Naturforsch. 48a, 273 (1993).
T. Tschentscher, J. R. Schneider, F. Bell, Phys. Rev. B 48,16965 (1993) and references therein.
S. W. Lovesey, Rep. Progr. Phys. (UK) 56, 257 (1993).
N. Sakai, K. Ono, Phys. Rev. Lett. 37, 351 (1976).
N. Sakai, K. Ono, J. Phys. Soc. Japan 42, 770 (1977).
M. A. Coplan, J.H. Moore, J.A. Tossell, Z. Naturforsch. 48a, 358 (1993).
E. Weigold, Z. Naturforsch. 48a, 371 (1993).
Virial theorem
W. Weyrich, Ber. Bunsenges. Phys. Chem. 83, 797 (1979).
Integrals
P. Kaijser, V.H. Smith, Jr., Adv. Quantum Chem. 10, 37 (1977).
M. Barua, W. Weyrich, Acta Cryst. A 42, 257 (1986).
Experimental access to density matrices
W.L. Clinton, A. Galli, L. Massa, Phys. Rev. 177, 1 (1969).
iidem, Phys. Rev. 177, 7 (1969).
S.T. Howard, J.P. Huke, P.R. Mallinson, C.S. Frampton, Phys. Rev. B: Condens. Matter 49, 7124 (1994).
H. Schmider, Diplomarbeit, Konstanz 1986.
H. Schmider, V. H. Smith, Jr., W. Weyrich, Trans. Amer. Cryst. Assoc. 26, 125 (1990).
H. Meider, Diplomarbeit, Konstanz 1991.
H. Schmider, V.H. Smith, Jr., W. Weyrich, J. Chem. Phys. 96, 8986 (1992).
iidem, Z. Naturforsch. 48a, 211 (1993).
iidem, Z. Naturforsch. 48a, 221 (1993).
H. Schmider, Dissertation, Kingston/Ontario 1994.
J. Stahn, Diplomarbeit, Konstanz 1995.
W. Schulke, Phys. Lett. 83A, 451 (1981).
W. Schulke, U. Bonse, S. Mourikis, Phys. Rev. Lett. 47, 1209 (1982).
W. Schulke, S. Mourikis, Acta Cryst. A 42, 86 (1986).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Weyrich, W. (1996). One-Electron Density Matrices and Related Observables. In: Pisani, C. (eds) Quantum-Mechanical Ab-initio Calculation of the Properties of Crystalline Materials. Lecture Notes in Chemistry, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61478-1_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-61478-1_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61645-0
Online ISBN: 978-3-642-61478-1
eBook Packages: Springer Book Archive