In this paper, we employ density functional theory (DFT) simulations to predict the energy conversion efficiency of a novel class of organic dyes based on linear carbon chain (LCC) linkers for application in dye-sensitized solar cells (DSSCs). We investigate the role of the anchoring group, which serves as a bridge connecting the linker and the surface. Specifically, we compare the performance of cyanoacrylic acid, dyes PY-4N and PY-3N, with that of phosphonate derivatives, dyes PY-4NP and PY-3NP, wherein the carboxylic group of the cyanoacrylic moiety is replaced with phosphonic acid. The observed variations in the UV/VIS absorption spectra have a slight impact on the light harvesting efficiency (LHE). Based on the empirical parameters we have taken into account, the electron injection efficiency (Φinj) and electron collection efficiency (ηcoll) values do not impact the short-circuit current density (JSC) values of all the studied dyes. The open-circuit voltage (Voc) is theoretically predicted using the improved normal model (INM) method. Among the dyes, PY-4N and PY-3N demonstrate the highest Voc values. This can be attributed to a more favorable recombination rate value, which is related to the energy gap between the HOMO level of the dyes and the conduction band minimum (CBM) of the surface. Dyes PY-4N and PY-3N are predicted to demonstrate remarkably high photoelectric conversion efficiency (PCE) values of approximately 21.79% and 16.52%, respectively, and therefore, they are expected to be potential candidates as organic dyes for applications in DSSCs. It is worth noting that PY-4NP and PY-3NP exhibit strong adsorption energy on the surface and interesting PCE values of 11.66% and 8.29%, respectively. This opens up possibilities for their application in DSSCs either as standalone sensitizers or as co-sensitizers alongside metal-free organic dyes or organic-inorganic perovskite solar cells.