Non-Born–Oppenheimer Electronic Structure and Relativistic Effects in the Ground States of BH and BH⁺

In this work, we report benchmark variational calculations for the boron monohydride (BH) molecule and its cation (BH⁺). The solutions to the nonrelativistic Schrödinger equations for these systems are obtained using a variational method without assuming the Born-Oppenheimer (BO) approximation, which separates electronic and nuclear motions. The ground-state wave functions for both the eight-particle (two nuclei and six electrons) BH molecule and the seven-particle (two nuclei and five electrons) BH⁺ ion are expanded in terms of all-particle explicitly correlated Gaussian with prefactors that effectively capture nucleus-nucleus correlation effects. These nonrelativistic non-BO wave functions are used to compute leading-order relativistic corrections to the total energies via perturbation theory, as well as to estimate leading-order quantum electrodynamics (QED) effects. The resulting total, dissociation, and ionization energies of BH represent the most accurate rigorously obtained theoretical values to date.