In this paper we discusses the application of a three-dimensional implementation of a geometry-based nonlocal density functional theory to the interactions between rigid polymers in solution. Deoxyribonucleic acid (DNA) provides inspiration for the three simple model polymers (cylindrical, bead chain, and periodic) we consider; however the results are more generally applicable to rigid polymers such as liquid crystals. The calculations show that fine details of polymer surface structure play a critical role in determining the solvation energy landscape. This solvation energy landscape in turn controls routes for assembly of bundles of macromolecules. This approach provides a new level of molecular insight into interactions in solvated polymer systems with wide applications to both industrial and biological polymers.