κ-H(Cat-EDT-TTF) (H-TTF) is a hydrogen-bonded π-electron system which was found to reveal C2/c symmetry at 50-293 K, while its isotopologue, κ-D(Cat-EDT-TTF) (D-TTF), showed the phase transition at 185 K from C2/c to P1[combining macron]. To elucidate the origin of such a difference, we calculated the potential energy curves (PECs) for the hydrogen transfer along the H-bonds in these conductors. We found that both the π-stacking and the hydrogen nuclear quantum effect drastically affected the hydrogen transfer energy. By taking account of both effects, we obtained a symmetric single-well effective PEC for H-TTF, which indicated that the hydrogen was always located at the center of the H-bond. By contrast, the effective PEC of D-TTF was a low-barrier double-well, indicating that the position of the H-bonded deuterium would change according to the temperature. We concluded that the π-stacking and the nuclear quantum effect were the key factors for the appearance of phase transition only in D-TTF.