Electron intracule densities and Coulomb holes from energy-derivative two-electron reduced density matrices

Application of the energy-derivative formalism to two-electron reduced density matrices produces a robust approach to the approximate evaluation of electron intracule densities I(R) and Coulomb holes in atoms and molecules. The versatility of this approach, which makes routine calculations of correlated I(R) feasible at any level of electronic structure theory, is demonstrated by results of selected MP2 calculations. The MP2/(20s 10p 10d) values of I(0) are within 10% of their "exact'' counterparts in systems such as H-, He, Li+, Be2+, Li, and Be. Quantitative reproduction of the exact I(R) is found to be contingent upon the inclusion of Gaussian primitives with high angular momenta in the basis sets. (C) 1898 American Institute of Physics. [S0021-9606(98)31443-9].