We present a density functional theory calculation of the structure and C-13 chemical shifts of retinylidene molecules which constitute the chromophores of the natural pigments rhodopsin and bacteriorhodopsin. We compare our results with recent X-ray and NMR spectroscopic data on several retinylidene iminium salts characterized by different cation-anion interactions. In agreement with crystallographic data, we find that the amplitude of the bond length alternation between single and double carbon bonds is strongly reduced in the vicinity of the protonated Schiff base nitrogen. The chemical shifts along the carbon chain are in very good agreement with the experimental values for the neutral retinylidene compounds and in fairly good agreement for the charged retinylidene compounds. We find that the C-13 chemical shift is mostly affected by the cation-anion distance and to a lesser extent by the presence of hydrogen bonding interaction between the protonated Schiff base of retinal and the counterion. The correlation between C-13 chemical shift and atomic charge along the conjugated chain of retinals is found to depend strongly on the specific compound. This result suggests some caution in using atomic charges alone to establish the position of the counterion relative to the chromophore in rhodopsin.