An accurate calculation of the ground state energy of the helium atom and the hydrogen negative ion using hyperspherical coordinates

Abstract

The method of hyperspherical harmonics using an adiabatic separation between the hyper-radial coordinate and the hyperspherical angles is applied to the calculation of the ground state of the helium atom and the hydrogen negative ion. For each system the simple adiabatic separation provides much of the electron correlation energy. The non-adiabatic coupling is included by means of a perturbation treatment using both the Rayleigh—Schrödinger and Brillouin—Wigner approaches. These provide rapid convergence to the exact energy of −2.90372 au.