Improved Theoretical Ground-State Energy of the Hydrogen Molecule

TLDR

The study employs double‑precision calculations with a 100‑term wavefunction expansion, tests diagonal nuclear‑motion corrections, and solves the vibrational equation for all hydrogen isotopes up to J = 10. The computed ground‑state potential curve (1 ≤ R ≤ 3.2 a.u.) yields an adiabatic dissociation energy 3.8 cm⁻¹ higher than experiment and vibrational quanta 0.5–0.9 cm⁻¹ larger, indicating a theoretical total energy lower by the same amount.

Abstract

The potential-energy curve for the electronic ground state of the hydrogen molecule has been calculated for 1 ≤ R ≤ 3.2 a.u. in double precision and using a 100-term expansion for the electronic wavefunction. Accuracy of the previously computed diagonal corrections for nuclear motion has been tested. The vibrational equation has been solved for all isotopes of the hydrogen molecule and for the rotational quantum number J ≤ 10. The calculated adiabatic dissociation energy of H2, corrected for relativistic and radiative effects, is by 3.8 cm−1 larger than the experimental value, hence the theoretical total energy is by the same amount lower than the experimental value. The calculated vibrational quanta for H2 are by 0.5–0.9 cm−1 larger than the experimental ones.