A general regularity was found based on an effective pair potential of Lennard-Jones LJ (12, 6), for both dense, nonmetallic and nonionic fluids and solids according to which (Z-1)n2 linearly varies with respect to r2 for each isotherm, and this equation of state (EoS I) is known as LIR. However, despite the fact that Ne is a simple spherical species, unexpectedly, its solid and liquid phases both show a significant deviation from EoS I. In this work, we have investigated the accuracy of the EoS I for other systems, including quantum light molecules, such as D2, H2 and He, in both fluid and solid states at different temperatures. Like Ne, we have noticed that these systems do not well obey the EoS I. Then, using a simple van der Waals equation, it is shown that significant deviations in dense systems of light molecules are because of the unbalance between repulsive and attractive interactions, due to the importance of the quantum effect. Also, we notice that at higher temperatures and for heavier species, LIR is valid due to a decrease in the quantum effect. We have shown that the hard-sphere fluid remarkably deviates from LIR. Two other EoSs have also been examined.