Solving the Schrödinger equation of hydrogen molecule with the free complement-local Schrödinger equation method: Potential energy curves of the ground and singly excited singlet and triplet states, Σ, Π, Δ, and Φ.

The free-complement (FC) theory for solving the Schrödinger equation (SE) was applied to calculate the potential energy curves of the ground and excited states of the hydrogen molecule (H) with the Σ , Σ , Σ , Σ , Π, Π, Π, Π, Δ, Δ, Δ, Δ, Φ, Φ, Φ, and Φ symmetries (in total, 54 states). The initial functions of the FC theory were formulated based on the atomic states of the hydrogen atom and its positive and negative ions at the dissociation limits. The local Schrödinger equation (LSE) method, which is a simple sampling-type integral-free methodology, was employed instead of the ordinary variational method and highly accurate results were obtained stably and smoothly along the potential energy curves. Thus, with the FC-LSE method, we succeeded to perform the comprehensive studies of the H molecule from the ground to excited states belonging up to higher angular momentum symmetries and from equilibriums to dissociation limits with almost satisfying spectroscopic accuracy, i.e., 10 hartree order around 1 cm, as absolute solutions of the SE by moderately small calculations.