In order to analyze the proton transfer events, we define the following proton transfer coordinates (δ 1,2 ) as shown in Figure lying DPT process. Therefore, in order to understand the temperature dependence of NQEs, we have plotted the effective free energy (F ef f ) corresponding to the joint probability distribution function (JPDF) between the δ 1 and δ 2 (Figure ) at 70 and 300 K for the BOMD and PIGLET simulations. The free energy (F ) corresponding to a discrete and normalized JPDF (p) between two quantities X and Y at (X i , Y j ) can be written as: