The electron self-interaction present in local-density theory can be removed by assuming a nonlocal hole in the electron density to generate the exchange-correlation energy. The potential derived from this energy has two contributions: the electrostatic potential from the hole and terms which describe the variation of the energy as the size and shape of the hole varies with density. All previous authors have included the first contribution, but the treatment of the second ranges from neglect to including them exactly. This work examines the effect of including these terms exactly, approximating them locally or neglecting them completely. Complete neglect yields severely distorted wave functions. This work shows how these terms may be generally estimated locally, which is much simpler than treating them exactly.
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