In this work we analyze molecular complexes with two hydrogen bonds (A = H2=B) and with three hydrogen bonds (AsH3sB). In an introductory discussion of molecular complexes with a single hydrogen bond (A-Hi-B), it is argued that the presence or absence of a double-well potential depends primarily on (a) the repulsive or attractive nature of the A-Hi and Hi-B potentials, (b) on the relative position of the molecular fragments A and B, (c) on the attractive or repulsive interaction of the fragments A and B. Since the A-Hi-B complex can be stable if one of the potentials for A-Hi or H-4-B is repulsive, provided that the attraction of A and B compensates the above repulsions, it is suggested to use the designation "hydrogen bridge" as a more general designation for what is commonly referred to as "hydrogen bond." The guaninecytosine (G-C) base pair is taken as an example of three hydrogen bridges (h-b's). A number of computations were performed to assess the shape of the potential curve for the h-b in the G-C pair. It is found that, contrary to previous assumptions and computations, the potential curve obtained by moving a single H atom along the h-b has no double well, but only a single-well potential. In this computation we have explicitly taken into account with equal detail all atoms and electrons of the G-C pair, using the LCAO-MOSCF formalism with no empirical approximation. Thus this computation represents an interesting test case for computations and programming techniques of an ab initia nature in large molecules. We note, that the combination of new computers (the work was performed on the IBM 360/91 and on the IBM 360/195) and new programs (the work did use a new version of our molecular program, IBMOL) did allow to carry out the entire G-C pair computations in eight days on the IBM 360/195. Since the work required about seventy billion two electron integrals, we have computed, sorted, retrieved, and processed through the SCF phase an average of 105 integrals per second. For comparison in 1966 (with a previous version of IBMOL and on the IBM 7094) the NH4C1 reaction surface was computed about 400 times slower. On the other hand, the basis set we have adopted is too small in order to obtain definitive conclusions on the potential when two or more H atoms of h-b are simultaneously moved along the bond. The G-C pair computations for the motion of a single H atom has been tested and confirmed by a more extended computation on the dimer of formic acid. For the dimer, the simultaneous motion of two H atoms has been carried out with a number of basis sets (of different type and size). It is found that the shape of the potential is quite sensitive to the choice of basis set. For the motion of a single hydrogen atom, no double well was found. For the motion of two hydrogen atoms (symmetrical motion) a pronounced double-well potential resulted. The binding energy of the dimer was computed within 15% of the experimental value. In the concluding section of the paper, the results of this work have been tentatively extrapolated to some general conclusions relevant to the potentials for systems containing hydrogen bridges.