The essential states model (ESM) for donor–acceptor–donor (D–A–D) chromophores is used to explore absorption and photoluminescence (PL) in molecular dimers composed of centrosymmetric and non-centrosymmetric squaraine molecules. The spectral line shapes and shifts relative to the monomer spectrum are due to an interesting interplay between three-center charge distributions responsible for ground- and excited-state (permanent) dipole and quadrupole moments and two-center charge distributions responsible for transition dipole moments. The Davydov splitting is sensitive only to the interactions between the (extended) transition dipoles , whereas the permanent dipole-dipole and quadruple-quadrupole interactions impact the midpoint frequency of the two Davydov components, leading to a generally asymmetric splitting relative to the peak monomer transition frequency. The theory accurately reproduces the steady-state absorption and PL line shapes recently obtained for covalently bound squaraine dimers. The ESM also predicts an extreme type of non-Kasha behavior, where both Davydov components are blue-shifted above the monomer transition frequency.