We provide the exact analytical ground state solution of one-dimensional H2+ molecule with soft Coulomb potential using our recently developed technique for solving Schrödinger equations. We show that the electronic wave function has similar structure with the ground state wave function of the 1D hydrogen, and we can still identify a power prefactor, an exponentially decaying term and a modulator function on the exponential. However, the behavior of the modulator function for 1D H2+ critically depends on the nuclear separation R. In particular, it differs qualitatively for small and large R, reflecting the different nature of the solution as a compact molecule for small R and two dissociation fragments for large R. This might inspire new strategies of density functional approximations for correctly describing molecular dissociation. The exactly solvable model obtained by our new technique could also be useful for systematically generating error-free training sets for machine-learning based quantum chemistry methods.
See the following link for more details: https://doi.org/10.1007/s10910-021-01304-9
