Exchange energy for two closed shells generated by a bare Coulomb potential energy <tex>$-Ze^{2}/r$</tex> in the limit of large Z, in two dimensions
Faculty of Sciences. Physics

article

2010
Basel
, 2010

Mathematics

Chemistry

Journal of mathematical chemistry. - Basel

47(2010)
:4
, p. 1313-1322

0259-9791

000276760300010

E

English (eng)

University of Antwerp

Two-dimensional (2D) inhomogeneous electron assemblies are becoming increasingly important in Condensed Matter and associated technologies. Here, therefore, we contribute to the Density Functional Theory of such 2D electronic systems by calculating, analytically, (i) the idempotent Dirac density matrix gamma (r, r') generated by two closed shells for the bare Coulomb potential - Ze(2)/r and (ii) the exchange energy density epsilon(X) (r). Some progress is also possible concerning the exchange potential V(X) (r), one non-local approximation being the Slater potential 2(epsilon X) (r)/n(r), with n(r) the ground state electron density. However, to complete the theory of V(X) (r), the functional derivative of the single-particle kinetic energy per unit area delta t (s)/delta n(r) is still required.

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