KOHN-SHAM POTENTIALS AND EXCHANGE AND CORRELATION-ENERGY DENSITIES FROM ONE-ELECTRON AND 2-ELECTRON DENSITY-MATRICES FOR LI-2, N-2, AND F-2

A definition of key quantities of the Kohn-Sham form of density-functi onal theory such as the exchange-correlation potential upsilon(xc) and the energy density epsilon(xc) in terms of wave-function quantities ( one- and two-electron density matrices) is given. This allows the cons truction of upsilon(xc) and epsilon(xc) numerically as functions of r from ab initio wave functions. The behavior of the constructed exchang e epsilon(x) and correlation epsilon(c) energy densities and the corre sponding integrated exchange E-x and correlation E-c energies have bee n compared with those of the local-density approximation (LDA) and gen eralized gradient approximations (GGA) of Becke, of Perdew and Wang, a nd of Lee, Yang, and Parr. The comparison shows significant difference s between epsilon(c)(r) and the epsilon(c)(GGA)(r), in spite of some g ratifying similarities in shape for particularly epsilon(c)(PW). On th e other hand, the local behavior of the GGA exchange energy densities is found to be very similar to the constructed epsilon(x)(r), yielding integrated energies to about 1% accuracy. Still the remaining differe nces are a sizable fraction (similar to 25%) of the correlation energy , showing up in differences between the constructed and model exchange energy densities that are locally even larger than the typical correl ation energy density. It is argued that nondynamical correlation which is incorporated in epsilon(c)(r), is lacking from epsilon(c)(GGA)(r), while it is included in epsilon(x)(LDA)(r) and epsilon(x)(GGA)(r) but not in epsilon(x)(r) This is verified almost quantitatively for the i ntegrated energies. It also appears to hold locally in the sense that the difference epsilon(x)(GGA)(r) - epsilon(x)(r) may be taken to repr esent epsilon(c)(nondyn)(r) and can be added to epsilon(c)(GGA)(r) to bring it much closer to epsilon(c)(r).