Accuracy of mean field approximations for atoms and molecules

We estimate the accuracy of the mean field approximation induced by the Thomas-Fermi potential for the ground state energy of atoms and molecules. Taking the Dirac exchange correction into account, we show the error to be of the formO(Z ^5/3– )+D for any <2/231 as the total nuclear chargeZ becomes large.D is an electrostatic energy of the difference density that measures the deviation of the mean field groud state from self-consistency.