Symmetric croconate (CR) and squarylium dyes (SQ) are well-known near-infrared (NIR) dyes and, in general, are considered to be donor-acceptor-donor type molecules. It is established in the literature that CR dyes absorb in a longer wavelength region than the corresponding SQ dyes. This has been attributed to the CR ring being a better acceptor than the SQ ring. Thus increasing the donor capacity should lead to a bathochromic shift in both SQ and CR. On the other hand, some experiments reported in the literature have revealed that increasing the conjugation in the donor part of the SQ molecule leads first to red shift, which upon a further increase of the conjugation changes to a blue shift. Hence, to understand the role of the central ring and the substitutions in the absorption of these dyes, we carried out high-level symmetry-adapted cluster-configuration interaction (SAC-CI) calculations of some substituted SQ and CR dyes and compare the absorption energy with the existing experimental data. We found that there is very good agreement. We also carried out SAC-CI calculations of some smaller model molecules, which contain the main oxyallyl substructure. We varied the geometry (angle) of the oxyallyl subgroup and the substitution in these model molecules to establish a correlation with the bathochromic shift. We found that the charge transfer is very small and does not play the key role in the red shift, but on the other hand, the perturbation of the HOMO-LUMO gap (HLG) from both the geometry and substitution seems to be responsible for this shift. We suggest as a design principle that increasing the donor capacity of the groups may not help in the red shift, but introducing groups which perturb the HLG and decrease it without changing the MO character should lead to a larger bathochromic shift.