The electronic structure of terpyrimidinethiols is investigated by means of density-functional theory calculations for isolated molecules and monolayers. In the transition from molecule to self-assembled monolayer (SAM), we observe that the band gap is substantially reduced, frontier states increasingly localize on opposite sides of the SAM, and this polarization in several instances is in the direction opposite to the polarization of the overall charge density. This behavior can be analyzed by analogy to inorganic semiconductor quantum-wells, which, as the SAMs studied here, can be regarded as semiperiodic systems. There, similar observations are made under the influence of a, typically external, electric field and are known as the quantum-confined Stark effect. Without any external perturbation, in oligopyrimidine SAMs one encounters an energy gradient that is generated by the dipole moments of the pyrimidine repeat units. It is particularly strong, reaching values of about 1.6 eV/nm, which corresponds to a substantial electric field of 1.6 × 10(7) V/cm. Close-lying σ- and π-states turn out to be a particular complication for a reliable description of the present systems, as their order is influenced not only by the docking groups and bonding to the metal, but also by the chosen computational approach. In the latter context we demonstrate that deliberately picking a hybrid functional allows avoiding pitfalls due to the infamous self-interaction error. Our results show that when aiming to build a monolayer with a specific electronic structure one can not only resort to the traditional technique of modifying the molecular structure of the constituents, but also try to exploit collective electronic effects.