The one-phonon inelastic low energy helium atom scattering theory is adapted to cases where the target monolayer is a p(1 × 1) commensurate square lattice. Experimental data for para-H2/NaCl(001) are re-analyzed and the relative intensities of energy loss peaks in the range 6 to 9 meV are determined. The case of the H2/NaCl(001) monolayer for 26 meV scattering energy is computationally challenging and difficult because it has a much more corrugated surface than those in the previous applications for triangular lattices. This requires a large number of coupled channels for convergence in the wave-packet-scattering calculation and a long series of Fourier amplitudes to represent the helium-target potential energy surface. A modified series is constructed in which a truncated Fourier expansion of the potential is constrained to give the exact value of the potential at some key points and which mimics the potential with fewer Fourier amplitudes. The shear horizontal phonon mode is again accessed by the helium scattering for small misalignment of the scattering plane relative to symmetry axes of the monolayer. For 1 misalignment, the calculated intensity of the longitudinal acoustic phonon mode frequently is higher than that of the shear horizontal phonon mode in contrast to what was found at scattering energies near 10 meV for triangular lattices of Ar, Kr, and Xe on Pt(111). © 2011 American Institute of Physics.