The mapping of the local contributions of Fermi and Coulomb correlation into intracule and extracule density distributions

The contributions of the correlated and uncorrelated components of the elec tron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions del(2)I(r) and del(2)E(R) are analyz ed at the Hartree-Fock (HF) and configuration interaction (CI) levels of th eory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In co ntrast, by analyzing the correlated components of I(r) and E(R), namely, I- C(r) and E-C(R), the effect of electron Fermi and Coulomb correlation can b e assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between I- C(r) and E-C(R) distributions calculated at the two levels of theory. As ap plication examples, the He, Ne, and Ar atomic series, the C-2(-2), N-2, O-2 (+2) molecular series, and the C2H4 molecule have been investigated. For th ese atoms and molecules, it is found that Fermi correlation accounts for th e main characteristics of I-C(r) and E-C(R), with Coulomb correlation incre asing slightly the locality of these functions at the CI level of theory. F urthermore, I-C(r), E-C(R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules. (C) 2000 American Institute of Physics. [S0021-9606 (00)30631-6].