Quantum-mechanical calculations are performed to investigate the interface between Au(111) surfaces and self-assembled monolayers (SAMs) of organic thiols. Dipolar pyrimidine units act as building blocks to systematically tune the molecular dipole moments via the number of repeat units. The resulting work-function modifications and the energetic alignment of the frontier electronic states in the SAM with the Fermi level are analyzed. Compared to SAMs where strong dipole moments are realized only by end-group substitutions on otherwise non-polar molecules, an entirely different evolution with backbone length is found for the present systems, where dipoles are built directly into the backbone. In particular, the achievable work-function modifications depend on peculiarities in the relative alignment of the energy levels in the SAM and in the metal. We thus introduce an additional degree of freedom for tuning surface and interface electronic properties with functional self-assembled monolayers.