The elements of Flatland: Hartree-Fock atomic ground states in two dimensions for Z = 1–24

The Hartree–Fock problem in two dimensions (2D) has been solved for 1 ≤ Z ≤ 24 using a Gaussian basis and assuming r^?1 Coulomb interactions. The order of occupation of the one-electron states is like in the 3D case. The 1s shell is found to be particularly small and strongly bound, making the 2D hydrogen a “superhalogen” and the 2D He a “superinert gas.” In contrast to 3D, 4s¹3d² and 4s²3d³ configurations are preferred for the 2D “Sc” and “Cu,” respectively. The six first 2D atoms have stronger and the later ones weaker valence-bonding energies than do their 3D analogs. It is noted that the 2D Dirac energy expression for a hydrogenlike atom for m_j = l + 1/2 agrees with the 3D Klein–Gordon one.