The 2,2′-bi-1H-imidazole (H2BIM0) can change to 2,2′-bi-1H-imidazolium (H4BIM2+) by the two-step proton-transfer, then, to 2,2′-bi(2,3-dihydroimidazolylidene) (H4BIM0) by the two-step electron-transfer. From the systematic investigations of half-wave redox potentials (E 1/2) and acid dissociation constants (pKa), we estimated the repulsion energy of electrons (U1CT) and protons (U1PT) for H4BIM0 and H4BIM2+, respectively, and other systems, p-benzoquinones (BQs), diphenoquinones (DPQs), 7,7,8,8-tetracyanoquinodimethanes (TCNQs), tetrathiafulvalenes (TTFs), aromaticdiamines, hydroquinones (H2Qs), 1,4-benzenedimalononitrile (H2TCNQ), bis(4-hydroxyphenyl) sulfides (HPSs). The U1CT and U1PT values are deduced from the linear correlation between the first E1/21 (pKal) value and the second E1/22(pKa2) one. The obtained U1CT of H4BIM0 (4.68 eV) is comparable to that of TTF (4.65 eV), and U1PT of H4BIM2+ (4.26 eV) is slightly larger than that of H2TCNQ (4.22 eV). The U1CT and U1PT values are correlated to the structural parameter of φ-electron density and molecular length.