Authors

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.