Two-Electron Homopolar Molecule: A Test for Spin-Density Waves and Charge-Density Waves

Abstract

The eigenstates of the one‐band Hamiltonian for a two‐electron homopolar molecule can be exactly determined. The exact solution for the ground state and all its properties can thus be used as a standard to assess the accuracy and validity of several commonly used approximations: the normal molecular‐orbital ground state, the Heitler–London states, the spin‐density waves and the charge‐density waves. The most general unrestricted self‐consistent field approximations are studied in both the Hartree and Hartree–Fock approximations and are compared with one another as well as with the exact results. New and simple correlated states are also proposed and tested: a symmetrized spin‐density wave and a symmetrized charge‐density wave. These new states are easily obtained from the corresponding Hartree–Fock states, and whenever they exist, they are extremely good approximations to the exact ground state. General consequences and extensions to more complicated systems can be inferred from this study.