The tensor character of the first-order density matrix leads to the definition of an MO multicenter bond index for closed-shell systems. Using Grassmann algebra, a straightforward meaning is attached to this multicenter bond index within the Hartree- Fock approximation. Three-center bond indices clearly distinguish between strong and normal hydrogen bonds; peptide bonds are predicted to be of the same order of magnitude than strong hydrogen bonds. In the same way that the valence of an atoms issues from the definition of bond index, we show that the three-center bond index lends itself to the definition of a bond valence. Within the charge of a bond, we show that its self-charge (i.e. the amount of electrons kept by the atoms involved in the bond) is partitioned in such a way that the more eletronegative atom tends to allocate more electronic charge than the other atom. We also show some results of four-center indices and report six-center indices for hexagonal rings