Analytical Hartree-Fock electron densities for atoms He through Lr

The Hartree-Fock electron density has an important property that it is identical to the exact density to first order in the perturbation theory. For the neutral atoms from He (Z = 2) to Lr (Z = 103) in their ground state, we report an accurate analytical approximation F(r) to the spherically averaged electron density rho(r) obtained by the numerical Hartree-Fock method. The present density function F(r) is expressed by a linear combination of reasonable number (not more than 30) of basis functions r(ni) exp(-zeta(i)r), and has the following properties: (i) F(r) is nonnegative, (ii) F(r) is normalized, (iii) F(r) reproduces the Hartree-Fock moments (r(k)) (k = -2 to + 6), (iv) F(0) is equal to rho(0), (v) F'(0) satisfies the cusp condition, and (vi) F(r) has the correct exponential decay in the long-range asymptotic region.