Analytical Hartree–Fock electron densities for atoms He through Lr
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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 ρ(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 n i exp(−ζ 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 ρ(0), (v) F′(0) satisfies the cusp condition, and (vi) F(r) has the correct exponential decay in the long-range asymptotic region.