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.