The Radius of the Coulomb Hole
The radius of the Coulomb hole in an atom or molecule is discussed in general terms and illustrated in detail for the ground state of the helium isoelectronic sequence. The calculations demonstrate a general tendency for the radius of the Coulomb hole to increase as a function of the distance of the reference electron from the nucleus and the existence of a nonzero lower limit (0.800 a.u. in He and 0.111 a.u. in Mg10+) for the radius of the Coulomb hole. This limit is slightly larger than the radial distance at which the radial density distribution reaches its maximum. By expressing the correlation energy of an atom in terms of certain one and two electron expectation values, the relationship between the correlation energy and the size and shape of the Coulomb hole is discussed. Detailed comparisons for the ground and 23S states of He are used to demonstrate the relationship.