[en] The Thomas-Fermi (TF) and Thomas-Fermi-von Weizsacker (TFW) theories of atoms and molecules with electron-electron repulsion are reviewed briefly. The main difference between the energies, E^TFW - E^TF (for large z), is a term D^TFWz². (It is also believed that E^Q - E^TF approx. D^Qz², where E^Q is the true quantum ground state energy). To calculate D^TFW, it is necessary to find the positive solution to the differential equation: ]- Δ + vertical bar psi(x) vertical bar⁴3/ - vertical bar x vertical bar^-1] psi(x) = 0 in three dimensions. While this equation arises from TFW theory with electron-electron repulsion, it also has a second interpretation - namely as the TFW equation for an atom without electron-electron repulsion. The main content of this report is the numerical solution of this equation and the evaluation of D^TFW