The Density functional theory (DFT) study was used to investigate the corrosion inhibition performance of two inhibitors namely: 2-thiophene carboxylic acid (TC) and 2-thiophene carboxylic acid hydrazide (TCH) on carbon steel using the B3LYP/6-311G(d,p) level of theory. The calculated quantum chemical parameters most relevant to their potential action as corrosion inhibitors are: EHOMO (highest occupied molecular orbital energy), ELUMO (lowest unoccupied molecular orbital energy), energy gap (ΔE), dipole moment (μ), hardness (η), softness (S), the absolute electronegativity (χ), the electrophilicity index (ω), the total energy( Etot), the fractions of electrons transferred (ΔN), back donation from the molecule (DEbackdonation).The local reactivity is analyzed through the Fukui function and condensed softness indices in order to compare the possible sites for nucleophilic and electrophilic attacks.The relationship between the inhibitory efficiency and quantum chemical parameters has been discussed in order to elucidate the inhibition mechanism.