The coupling of two trans-bent double bonds is examined theoretically through ab initio calculations on tetragermabutadiene H2Ge=HGe-GeH=GeH2. If a trans-bent arrangement is maintained for each -GeH= GeH2 fragment, there are two ways of coupling two trans-bent units, starting from an s-trans conformation around the central bond. The first one preserves an all-trans arrangement of the four pyramidalized germanium atoms. Along the rotational pathway around the central bond, this configuration has no symmetry (C-1), except for dihedral angles of 0 degrees (C-s) or 180 degrees (C-i). As in butadiene, the potential curve along this coordinate is symmetrical with respect to 0 degrees and 180 degrees, with a preferred s-trans form, t-1 and two equivalent gauche forms, g-1, lying about 3 kcal/mol above in energy (MP4/DZP//SCF/DZP). The s-cis saddle point separating the two gauche forms is higher in energy than the barrier separating the s-trans and gauche forms. In the second coupling scheme, the molecule maintains a C-2 symmetry axis for any torsional angle, but the energy curve no longer exhibits any symmetry along the entire [0-2 pi] rotational coordinate. As anticipated by simple overlap arguments within the pseudo pi orbital set, the two minima, reminiscent of a-trans and gauche arrangements, are both skewed. The gauche conformer, g-2, is now below the trans one, t-2, but still above t-1. The minima g-2 and t-2 are separated by two rotational barriers, depending on the direction of rotation. Interconversion between these coupling configurations proceeds through planar inversion at one GeH=GeH2 unit. Two pathways are possible, linking either the two a-trans forms or the two gauche forms. The barrier along both the t-1-->t-2 and g-2-->g-1 pathways is calculated at 4 kcal/mol, in line with the barrier to planarity found in isolated digermene. In both coupling schemes, adiabatic singlet-triplet separations are calculated at 13 kcal/mol. Intramolecular cyclization of g-2 into the cyclobutene form proceeds with a slight activation barrier, and a large exothermicity of 27 kcal/mol. Alternatives in which one or both double bonds of the butadiene form are replaced by a double hydrogen bridge are not favored. By contrast, the two bond-stretch isomers of the bicyclobutane form are significantly lower in energy than the butadiene forms.