The generalized product function energy partitioning (GPF-EP) method has been applied to investigate the nature of the chemical bond and the origin of the inverted dipole moment of the BF molecule. The calculations were carried out with GPF wave functions treating all of the core electrons as a single Hartree-Fock group and the valence electrons at the generalized valence bond perfect-pairing (GVB-PP) or full GVB levels, with the cc-pVTZ basis set. The results show that the chemical structure of both X (1)Sigma(+) and a (3)Pi states is composed of a single bond. The lower dissociation energy of the excited state is attributed to a stabilizing intraatomic singlet coupling involving the B 2sp-like lobe orbitals after bond dissociation. An increase of electron density on the B atom caused by the reorientation of the boron 2sp-like lobe orbitals is identified as the main responsible effect for the electric dipole inversion in the ground state of BF. Finally, it is shown that pi back-bonding from fluorine to boron plays a minor role in the electron density displacement to the bonding region in both states. Moreover, this effect is associated with changes in the quasi-classical component of the electron density only and does not contribute to covalency in either of the states. Therefore, at least for the case of the BF molecule, the term back-bonding is misleading, since it does not contribute to the bond formation.