A simple quantum model for solving two-electron diatomics approximately

Analytical expressions are obtained for the total energy of two-electron heteronuclear diatomics using a minimal basis set consisting of a 1S-Gaussian orbital centered on each atom and a Heitler-London trial wavefunction. The equations are applied to the recently discovered helium hydride cation (2019, Nature 568, 357-9) to understand its stability. Special attention was given to the fulfillment of the virial theorem and the different limiting cases (homonuclear diatomics, short and long internuclear distances). The correctness of equations and numerical results was confirmed via a brute-force Metropolis Monte Carlo integration. Expressions for the moments of the electron density (including the dipole moments) were obtained. The effect of the spin state on the dipole moment is discussed and the model agrees qualitatively with results from more advanced ab initio calculations. I also applied the model to study the metastable helium dimer dication ( He 2 ++ ) and the predicted bond length (0.7359 Å) is in good agreement with the experimental value (0.75 ± 0.02 Å). The advantages and limitations of this simple quantum model are discussed.