The calculations of thermodynamic properties from computer simulations require independent and identically distributed samples. The long correlation time of chemical processes in condensed phases plagues the simulations with slow convergence in thermodynamic properties and poses a challenge for the computational studies at ab initio levels of theory. This difficulty is more severe for PIMD, in which the representation of quantum effect in singleparticle systems is transformed into a classical problem of discrete cyclic model systems with a number of beads for each atom. The reference-potential methods can be a remedy for ameliorating the large expense by leveraging an inexpensive sampling method and a postprocessing process on the harvested samples. In this work, the proton transfer within a protonated 1,8-bis(dimethylamino)naphthalene molecule was studied, and the free energy profile at the BLYP-D3/6-31G(d)/MM level of theory was calculated using a more efficient sampling at the PM6/MM level. With a finite number of samples, the reliability of this reference-potential method heavily depends on the overlap in the phase space between the target (BLYP-D3/6-31G(d)/MM) Hamiltonian and the reference (PM6/MM) Hamiltonian.