Maclaurin expansion of electron-pair densities in momentum space

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Maclaurin expansions of the spherically averaged electron-pair intracule (relative motion) h̄( ν) and extracule (center-of-mass motion) d̄( P) densities in momentum space are studied for multi-determinant wave functions. The densities h̄( ν) and d̄( P) are expanded by even powers of ν and P, respectively. Accurate Hartree–Fock values of the derivatives h̄ (2 m) (0) and d̄ (2 m) (0) ( m=0–3) are determined for the 53 atoms from He to Xe in their ground states. The signs of the second derivatives are in agreement with the modality of h̄( ν) and d̄( P) reported in the literature, and the array of the signs of the successive derivatives is found to be intimately related with the valence electron configuration.