Peptide nucleic acid (PNA) is a synthetic analogue of deoxyribonucleic acid (DNA) capable of tightly binding to itself and DNA with high specificity. Using hybrid density functional methods, hydrogen-bond (H-bond) strengths have been evaluated for isolated Watson-Crick base pairs, PNA base pairs, and charged as well as neutral DNA base pairs. Heterogeneous base pairs of PNA with charged and neutral DNA have also been investigated. The competing effects of short-range H-bonding and long-range Coulombic repulsions in charged DNA base pairs have been analyzed. Polarizable continuum models have been employed to evaluate solvation effects on the binding energies.