Phase space, density matrices, energy densities, and exchange holes

Citation
M. Springborg et al., Phase space, density matrices, energy densities, and exchange holes, Z PHYS CHEM, 215, 2001, pp. 1243-1264
Citations number
30
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physical Chemistry/Chemical Physics
Journal title
ZEITSCHRIFT FUR PHYSIKALISCHE CHEMIE-INTERNATIONAL JOURNAL OF RESEARCH IN PHYSICAL CHEMISTRY & CHEMICAL PHYSICS
ISSN journal
0942-9352 → ACNP
Volume
215
Year of publication
2001
Part
10
Pages
1243 - 1264
Database
ISI
SICI code
0942-9352(2001)215:<1243:PSDMED>2.0.ZU;2-V
Abstract
In the general case, quantum-mechanical quantities are represented by opera tors in position- or momentum-space representations, but in phase space the y are represented by functions. The correspondence between classical mechan ics and quantum mechanics is non-unique as a consequence of [(x) over cap , (p) over cap] not equal 0, and therefore the phase-space representation of quantum mechanics is also non-unique. We explain how different corresponde nce rules lead to different phase-space functions and how the latter are re lated to first-order reduced density matrices. As a special example, we dis cuss the phase-space representation of different terms of the total energy within the Hartree-Fock approximation for electronic-structure calculations . In particular we discuss how one may use the phase-space representation t o define energy densities in position space, putting special emphasis on ki netic and exchange energy densities which are not unique. While the standar d exchange energy density has an exchange hole which is normalized, the Wey l and other exchange energy densities have exchange holes which are more lo calized. We also make a numerical study of statistical correlations among v ariables commonly used in density functional theory and several energy dens ities, including the standard and Weyl exchange energy densities. Finally, we examine the spherical average of the standard exchange hole for the mole cule LiH, finding that it reflects both the ionic and the covalent characte r of the bond.