We make use of an aufbau principle, first suggested by Kitaigorodskii, to design a Monte Carlo cooling algorithm which can predict the local and apparent global energy minima of semiflexible molecules that are packed into translationally symmetric monolayer structures without any assumptions about the unit cell dimensions, molecular orientation, or exocyclic torsional conformation. We find the algorithm works effectively on molecules containing up to 12 exocyclic torsion bonds. Using the aufbau, the algorithm (a) packs molecules into 1-dimensional stacks generating a collection of local minima in stage 1, followed by (b) the packing of each of these minima into layers in stage 2. The only assumption is that the monolayer is made from a single molecular unit. The only additional information needed is the valence bond geometry of the molecule (viz. its atom connectivity, bond lengths, and bending angles, but not the exocyclic dihedral angles) and a suitable force field. We find, quite surprisingly, that the important features of the molecular orientation in the final monolayer packing geometry are already exhibited in stage 1 (but not the fine molecular conformational details), with the conformational details finally exhibiting themselves in stage 2. It is this expression of the orientational detail in stage 1 that makes the aufbau a practical quantitative tool for predicting the packing geometry of molecules with large numbers of single bonds. Coupled with a limited amount of experimental information, the aufbau can be used to determine which of the local minina in stage 2 are experimentally observable. The use of the aufbau for predicting full 3-dimensional crystal structures in a final stage 3 is discussed.