We calculate the hopping amplitudes for an electron and for a hole added to the molecule H2. We use a linear combination of atomic orbitals approach and the Hartree approximation. The hopping amplitudes for electrons and holes are found to be different, reflecting the fundamental electron-hole asymmetry of condensed matter. The physical origin of this result is discussed. We study the dependence of hopping amplitudes on internuclear distance and on the nuclear charge Z (Z=1 for H2) and discuss the possible implication of our results to the understanding of superconductivity in solids.