Bare-Nucleus Perturbation Theory: Excited States of Hydrogen Molecule

Abstract

Ground and excited Σ⁺ states of ${\text{R\hspace{0.17em}=\hspace{0.17em}1.4a}}_0$ are treated by perturbation theory. The full interelectronic repulsion is taken as the perturbation, and the energy of each of nine states is calculated through third order. The equation for the first‐order wavefunction is treated by the Hylleraas variational principle, using a linear variational function including up to 30 James–Coolidge basis functions. Comparisons with conventional linear variational calculations using the same basis functions, and with related calculations of other workers, are given. The perturbation results are in most cases superior to variation, especially when small basis sets are used, but it is noted that the inadequacy of the present basis set for excited states leads to slow convergence of the energies of both methods with addition of basis functions. The bare‐nucleus Hamiltonian also becomes a worse starting point for higher states because of electronic shielding, as evidenced by slower convergence of the perturbation energy series. For the five states of the three lowest configurations, however, accuracy to about 1 kcal is obtained.