′-((2-methoxy-naphthalene-1-yl)methylene) pyrimidine-5-carbohydrazide (H5) and

2.3.3 Atomic force microscopy (AFM) analysis.AFM is a device generates a topographic surface maps with a unique resolution, so the outer surface roughness can be measured; the surface roughness is caused due to deviations of a surface from its ideal shape due to corrosion or inhibitor adsorption. AFM device model is Pico SPM2100 operating in contact mode in air at Nanotechnology Laboratory, Faculty of Engineering Mansoura University. Five sheets of clean carbon steel were prepared, the first was taken as a free reference (not subjected to inhibitors or HCl), the second was immersed in HCl only for 24 hours and the remaining three sheets were immersed in 1 M HCl + the optimal concentration of each inhibitor (20 × 10⁻⁶ M) for 24 hours.
2.3.4 Fourier transform infrared (FT-IR) analysis.FT-IR spectrum was performed in a PerkinElmer 1600 spectrophotometer for pure solutions of (H4 & H5 & H6) and for carbon steel sheets that were immersed in 1 M HCl + the optimal concentration of each inhibitor for 24 hours.
2.3.5 X-ray photoelectron spectroscopy (XPS) examination.This test was achieved by a highly efficient device that determines the binding energies of different bonds found on the carbon steel surface that were immersed in 1 M HCl + the optimal concentration of each inhibitor for 24 hours using (XPS), hence the adsorbed atoms and functional groups on metal surface could be deduced. XPS test was done by K-ALPHA (Thermo Fisher Scientific, USA).
2.3.6 Quantum chemical calculations.Calculation method done by Material studio Dmol6 DFT software, GGA basis Set RPBE. Parameters (global and local indicators) were calculated as highest occupied molecule orbital (HOMO) and lowest occupied molecule orbital (LUMO), dipole moment (μ), energy gap (ΔE), total hardness (η), absolute electronegativity (χ), transferred electron fraction (ΔN), and softness (σ), using the DFT method.
These eqn (5)–(10) were used in the calculations:²²

ΔE = ELUMO − EHOMO	(5)

η = ΔE/2	(6)

σ(S) = 1/η	(7)

Pi = (ELUMO − EHOMO)/2	(8)

X = Pi	(9)

ΔN = (φ − χ)/2η	(10)

where φ is the work function of the metal surface (φ_Fe = 4.81 eV).