Correlation of Electrons Within the Hydride Ion

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Abstract
The hydride ion is one of the simplest systems possessing electrons with antiparallel spins and, therefore, it is ideal for a study of electron correlation. Five wavefunctions for H− have been analysed and compared. Two functions were based on the single determinant independent‐particle model and three were correlated wavefunctions. The present article is devoted, in the main, to a discussion of radial correlation, hence, graphs are presented for the two‐particle density ρ(r 1 , r 2 ) and the radial density D(r) for each treatment. Values are determined for the coherent x‐ray scattering contribution f 00 (X), the three‐dimensional Dirac delta functions 〈δ 3 (r 1 )〉 and 〈δ 3 (r 12 )〉, and also for 〈r n 〉 when −2 ≤ n ≤ 4. In this way, the effect of electron correlation on various physical properties could be examined. In particular, by comparing the results with those obtained from a more accurate wavefunction, it was possible to assess the usefulness of a limited configuration‐interaction treatment which employed `floating' orbitals. On the whole, this treatment of H− proved to be good. Finally, it was observed that the inclusion of electron correlation effects within a wavefunction for H− causes the electron density to become more diffuse, the inner regions around the nucleus resembling, fairly closely, the density within an isolated hydrogen atom.