Classical and quantum formulations are used to estimate Rayleigh scattering within lidar signals. Within the classical approach, three scenarios are used to characterize atmospheric molecular composition: 2-component atmosphere (N2 and O2), 4-component atmosphere (N2, O2, Ar, and CO2), and 5-component atmosphere (N2, O2, Ar, CO2, and water vapor). First, analysis focuses on Rayleigh scattering, showing the relative difference between the three scenarios within classical approach. The relative difference in molecular scattering between 2(4)-component atmosphere and 5-component atmosphere is below ~1%. The second analysis focuses on the lidar retrieval of aerosol backscatter and extinction coefficients showing the effect of different molecular formulations. A relative difference of ±3% was found between the molecular formulation of 2-component atmosphere and the molecular formulation of 5-component atmosphere. Consideration of the Raman rotational lines blocked by the interference filter is important for the elastic channels, but of little significance in the N2 Raman channel. For lidar retrieval of aerosol profiles, the 5-component approximation is the best when the water vapor profile is known, but 2-component is still adequate and quite accurate when water vapor is only poorly known.