where a, b and c are parameters for the functional. The epc17-1 functional 34 was optimized to reproduce proton densities with parameters a = 2.35, b = 2.4 and c = 3.2, while the epc17-2 functional was optimized to reproduce absolute zero-point energies with parameters a = 2.35, b = 2.4 and c = 6.6. Note that the only difference between these the two functionals is the value of the parameter c. The electron-proton correlation potential for electrons and protons can be obtained by taking the functional derivative of E epc with respect to the electron density or proton densities, respectively.