We Introduce the Finite-Element Approach and Its Use to Solve Diatomic Molecular Quantum-Mechanical Problems. H2 and Hartree-Fock-Slater Measurements Findings Are Provided For Molecules Such As N2 and Co. the Precision Obtained For the Total Energies of These Structures of Less Than 5000 Grid Points Is 10-8 Au, Which Is Around 2 Orders Greater Than the Sensitivity of any Other Process Available.