Molecular constants have been computed for the ground states ²Π of ¹⁷OH and ¹Σ of ¹⁰⁷AgH⁺. The valence-bond method and advanced computational technique were used to perform all-electron ab initio calculation of molecular electronic structures. The basic idea behind the model is to introduce the molecular wave functions in terms of Hartree-Fock many-electron atomic determinants. Full configuration interaction (CI) with nonorthogonal basis leads to the accurate calculation of molecular constants such as dissociation energy, equilibrium bond distance, vibrational and rotational constants with an agreement to the experimental data within a few percent.