The MP2(FC)/6-31G∗ energies calculation, with complete optimization geometries at RHF/6-31G∗ level, has been carried out on the neutral and protonated forms of C and N-mono-substituted pyrazoles (28 R–C(n)Pz and 12 R′–NPz with n=3, 4 and 5; R=R′=H, CH3, CHO, CN, NH2, NO, NO2, OH, F and Cl, and R′=C2H5, n-C3H7 and C6H5) and some related compounds (Pyridine, 2-Me-pyridine, 3-Me-pyridine, Pyrrole and N-Me-pyrrole). The heats of formation (using isodesmic reaction), the proton affinities (PA) and the gas basicities (GB) have been determined for pyrazole derivatives. The results are consistent with the experimental evidence and provide a better understanding of the structures and energies for mono-substituted pyrazoles. Also, the RHF/6-31G∗ geometrical parameters are compared with those obtained by AM1 method, the agreement is satisfying. Linear relationships are found between AM1 and MP2(FC)/6-31G∗//6-31G∗ for heats of formation and for PAs of R–C(n)Pz and R′–NPz. Many pyrazole derivatives fit correlation well. Furthermore, the structures and heats of formation for sizeable N-mono-substituted pyrazoles (17 compounds), which are interesting in chemical area, has been also optimized by AM1, their PAs are scaled with a reasonable precision. Substituent electronic effects (SE) has been analyzed in terms of polarizability, field, and resonance contributions using the Taft–Topsom model. The SE on nitrogen atom N(1) differs notably from those on carbon atoms C(3), C(4) and C(5). The origin of this difference has been discussed yet.