While the majority of ferroelectrics research has been focused on inorganic ceramics, molecular ferroelectrics can also combine large spontaneous polarization with high Curie temperatures. However, the microscopic mechanism of their ferroelectric switching is not fully understood. We explore proton tautomerism in the prototypical case of croconic acid, C5O5H2. In order to determine how efficiently ferroelectricity in croconic acid is described in terms of its Γ-point phonon modes, the minimum energy path between its structural ground states is approximated by projection onto reduced basis sets formed from subsets of these modes. The potential energy curve along the minimum energy path was found to be sensitive to the order of proton transfer, which requires a large subset (≳8) of the modes to be approximated accurately. Our findings suggest rules for the construction of effective Hamiltonians to describe proton transfer ferroelectrics.