Density Matrices and Density Functionals

Norman Henry March

Reiner M. Dreizler, Eberhard K. U. Gross

Mel Levy, Andreas Görling

Explicit formal formulas for exact density-functional correlation energies are derived and expressed in terms of correlating first-order density matrices (one-matrices) that are functionals of the density. The correlation energy for a full calculation is considered, as well as one intended as an addition to a completed calculation that excludes correlation. Several constraints for the one-matrices are shown.

Mel Levy, Andreas Görling

Explicit formal formulas for exact density-functional correlation energies are derived and expressed in terms of correlating first-order density matrices (one-matrices) that are functionals of the density. The correlation energy for a full calculation is considered, as well as one intended as an addition to a completed calculation that excludes correlation. Several constraints for the one-matrices are shown.

John E. Harriman

Density matrices for systems with a finite number of states are considered as elements in a vector space. A density matrix that is a convex combination of density matrices that are unitary transformations of some initial density matrix will be closer to, or possibly at the same distance from, the density matrix for the ensemble in which all states are equally occupied, compared with the initial density matrix. This distance is correlated, for few-state systems, with a function simply related to the entropy. This function increases (entropy decreases) with distance from the equal-occupancy density matrix. Other properties of the function are also established.

G. F. Bertsch, Kazuhiro Yabana